Digital logic SAQ
Unit 1: Number Systems, Operations and Codes
- Define Digital Systems.
A system which processing discrete or digital signal is called as Digital System.
- Define Radix.
It specifies the number of symbols used for corresponding number system. .
- Define binarylogic?
Binary logic consists of binary variables and logical operations. The variables aredesignated by the alphabets such as A, B, C, x, y, z, etc., with each variable having onlytwo distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
- What is a Logic gate?
Logic gates are electronic circuits that operate on one or more input signals to produce an output signal. Electrical signals such as voltages or currents exist throughout a digital system in either of two recognizable values. Voltage- operated circuits respond to two separate voltage levels that represent a binary variable equal to logic 1 or logic 0.
- Which gates are called as the universal gates? What are itsadvantages?
Circuits using NAND and NOR are popular as they are easier to design and therefore cheaper. Functions of other gates can easily be implemented using NAND and NOR gates. For this reason they are called universal gates.
6… What are the applications of octal number system?
The applications of octal number system are:
- It is used for entering the binary data and displaying certain information’s.
ii.It is very important for the efficient use of microprocessors and other digital circuits.
- Why is a hexadecimal number system called as an alpha numeric number system?
Hexadecimal number system has the base as 16 and therefore it requires 16distinct symbols to represent the numbers. These are numerals 0 to 9 and alphabets A toF. Since both numeric digitals and alphabets are used to represent the digits in hexadecimal number system, it is also called as an alphanumeric number system.
- Define Boolean algebra & Boolean Expression.
i). A system of algebra that operates on Boolean variables. The binary nature of Boolean algebra makes it useful for analysis, simplification and design of logic circuits.
- What are basic properties of Boolean algebra?
The basic properties of Boolean algebra are commutative property, associative property and distributive property.
- State the associative property of Boolean algebra.
The associative property of Boolean algebra states that the OR in of several variables results in the same regardless of the grouping of the variables. The associative property is stated as follows: i). A+ (B+C) = (A+B) +C ii). A (B C) = (A B) C
- State the commutative property of Boolean algebra.
The commutative property states that the order in which the variables are OR makes no difference. The commutative property is: i). A+B=B+A ii). AB = BA
- State the distributive property of Boolean algebra.
The distributive property states that AND in several variables and OR inthe result with a single variable is equivalent to OR in the single variable with each of the several variables and then AND in the sums. The distributive property is: i). A+BC = (A+B) (A+C) ii). A (B+C) = AB + AC
- State De Morgan’s theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They are,
1) The complement of a product is equal to the sum of the complements. (A. B)’ = A’ + B’
2) The complement of a sum term is equal to the product of the complements. (A + B)’ = A’B’
- What are the 2 forms of Boolean expression?
The two forms of Boolean expressions are:
i).Sum of Products Form
ii).Product of Sum Form
- Define Minterm & Maxterm.
The products of Boolean expression where all possible variables appear once in complement or complement variables are calledMinterm.
A sum terms in a Boolean expression where all possible variables appear once, in complement or uncomplement form are called
Maxterm.
- What is meant by karnaugh map or K-Map method?
A karnaugh map or k map is a pictorial form of truth table, in which the map diagram is made up of cells, with each cell representing one minterm or maxterm of the function. This method provides a simple straight forward procedure for minimizing Boolean function.
- Define Cell.
The smallest unit of a karnaugh map, corresponding to one rows of a truth table.The input variables are the cells coordinates and the output variable is the cells contents.
- What are called don’t care conditions?
In some logic circuits certain input conditions never occur, therefore the corresponding output never appears. In such cases the output level is not defined, it can be either high or low. These output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or incompletely specified functions.
- What is tabulation method?
A method involving an exhaustive tabular search method for the minimum expression to solve a Boolean equation for more variables is called as a tabulation method.
- State the limitations of karnaugh map.
- i) Generally it is limited to six variable map (i.e.) more than six variable involving expressions are not reduced.
- ii) The map method is restricted in its capability since they are useful for simplifying only Boolean expression represented in standard form.
- Explain or list out the advantages and disadvantages of K-map method?
The advantages of the K-map method are:
i). It is a fast method for simplifying expression up to four variables.
ii). It gives a visual method of logic simplification.
iii). Prime implicants and essential prime implicants are identified fast.
iv). Suitable for both SOP and POS forms of reduction.
v). It is more suitable for class room teachings on logic simplification.
The disadvantages of the K-map method are:
i). It is not suitable for computer reduction.
ii). K-maps are not suitable when the number of variables involved exceed four.
iii). Care must be taken to fill in every cell with the relevant entry, such as a 0, 1 (or)don’t care terms
- Define Duality Theorem.
The Duality theorem states that starting with a Boolean relation we can derive another Boolean relation by:
i). Changing OR (operation) i.e., + (Plus) sign to an AND (operation) i.e., (dot) and Vice-versa.
ii). Complement any 0 or 1 appearing in the expression i.e., replacing contains 0 and 1by 1 and 0 respectively.
Principle of duality is use in Boolean algebra to complement the Boolean expression.
- List the characteristics of digital ICs
- i) Propagation delayii) Power dissipationiii) Fan-iniv) Fan-outv) Noise margin
- What is propagation delay?
It is defined as the time taken for the output of a gate to change after the inputs havechanged.Propagation delay times are defined as follows:-
t_{PLH} It is the propagation delay time in going from low level (0) to high level (1).-
t_{PHL} It is the propagation delay time in going from High level (1) to high level (0)
25.What is power dissipation?
The electrical energy used by logic circuits in specified period of time. (Expresses inmill watts or Nano watts).
Power dissipation = Supply voltage * meant current taken from that supply.
- Define Fan-in & Fan-out.
Fan-in:
The fan-in of a gate is the number of inputs connected to the gate without any degradation in the voltage levels.
Fan-out
: It is defined as the maximum number of inputs of the same IC family that a gate can drive maintaining its output levels within the specified limits.
- What is Noise margin?
Noise margin is the maximum external noise voltage added to an input signal that does not cause an undesirable change in the circuit output.
- Define Figure of Merit (SPP).
Figure of merit is defined as the product of speed and power. The speed is specified in terms of propagation delay time expressed in nano seconds.
Figure of merit = Propagation delay time (ns) * Power (mW).
- Mention the characteristics of MOS transistor?
- The n- channel MOS conducts when its gate- to- source voltage is positive.2. The p- channel MOS conducts when its gate- to- source voltage is negative3. Either type of device is turned off if its gate- to- source voltage is
Zero.
- Why totem pole outputs cannot be connected together.
Totem pole outputs cannot be connected together because such a connection might produce excessive current and may result in damage to the devices.
- State advantages and disadvantages of TTL
Advantage:
- Easily compatible with other ICs2. Low output impedance
Disadvantage:
- Wired output capability is possible only with tristate and open collector types2. Special circuits in Circuit layout and system design are required.
- What is Operating temperature?
All the gates or semiconductor devices are temperature sensitive in nature. The temperature in which the performance of the IC is effective is called as operating temperature. Operating temperature of the IC vary from 0’C to 70’C.
- How is gray code different from normal binary code?
Gray code does not follow binary progression, instead in gray code each successive number differs only in one place.
- 35. When does an XOR gate produce a high output? When does an XNOR gate produce a high output?
An XOR gate produces a high output when the input combination has odd number of 1’s and an XNOR gate produces
a high output when the input combination has even number of 1’s.
38.State the distributive laws of Boolean algebra. How do they differ from the distributive laws of ordinary algebra?
Distributive laws of Boolean algebra state that
- X(Y + Z) = XY +XZ
- X + YZ = (X + Y)(X +Z)
1^{st} law X(Y + Z) = XY + XZ holds good for all values of X, Y and Z in ordinary algebra whereas X + YZ = (X + Y)(X + Z) holds good only for two values (0, 1) of X, Y and Z.
- 37. What do you understand by ‘logical function’? What is its alternative name? Give examples for logical functions. Logic statements or truth functions are combined with the help of Logical Operators like AND, OR and NOT to form a Logical function. Its alternative name is Compound statement.
Examples for logical functions are as Following :
- He prefers tea notcoffee.
- He plays guitar and she playssitar.
I watch TV on Sundays or I go forswimming.
38.What are the basic postulates of Booleanalgebra?
Following are the basic postulates of Boolean algebra:
- If X not equal to 0 then X equal to 1; and If X not equal to 1 then X equal to0
- OR Relations (LogicalAddition)
(i) 0 + 0=0 (ii) 0 + 1=1 (iii) 1 + 0=1 (iv) 1 + 1 =1
- AND Relations (LogicalMultiplication)
(i)0 . 0=0 (ii) 0 . 1=0 (iii) 1 . 0=0 (iv) 1 . 1 =0
4) Complement Rules (i)0’=1 (ii) 1’=0
39.what is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s either even or odd. Consider the following two characters and their even and odd parity: With even parity with odd parity ASCII A = 1000001 01000001 11000001, ASCII T = 1010100 11010100 01010100. In each case we add an extra bit in the left most position of the code to produce an even
number of1’s in the character for even parity or an odd number of 1’s in the character for odd parity. The parity bit is helpful in detecting errors during the transmission of information from one location to another.
Unit –II Combinational Circuits
- What are combinational circuits?
A combinational circuit consists of logic gates whose outputs at any time are determined from the present combination of inputs. A combinational circuit performs an operation that can be specified logically by a set of Boolean functions. It consists of input variables, logic gates, and output variables.
- Explain the design procedure for combinational circuits.
- The problem definition 2. Determine the number of available input variables & required O/P variables.
- Truth Table Construction 4. Obtain simplified Boolean expression for each O/P (using K-Map).5. Obtain the logic diagram.
- Define half adder and full adder
Half Adder:
The logic circuit that performs the addition of two bits is a half adder.A half adder needs two binary inputs and two binary outputs. The input variables designate the augend and addend bits; the output variables produce the sum and carry.
Full Adder:
A combinational circuit that performs the addition of three bits is a full adder.It consists of three inputs and two outputs.
- Define Decoder?
A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines. If the n bit coded information has unused combinations, the decoder may have fewer than 2n outputs.
- What is binary decoder?
A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2^{n} outputs lines.
- What are encoders?
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n and n output lines. The output lines generate the binary code corresponding to the input value.
- What is priority Encoder?
A priority encoder is an encoder circuit that includes the priority function. In priority encoder, if 2 or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence.
- Define multiplexer?
A multiplexer is combinational circuit that selects binary information from one of many input lines and directs it to a single output line. The selection of a particular input line is controlled by a set of selection lines. Normally there are 2n input lines and n selection lines whose bit combinations determine which input is selected.
- What is DE multiplexer?
A Demultiplexer is a circuit that receives information on a single line and transmits this information on one of 2^{n}possible output lines
- What is code conversion?
If two systems working with different binary codes are to be synchronized in operation, then we need digital circuit which converts one system of codes to the other. The process of conversion is referred to as code conversion
- What is code converter?
It is a circuit that makes the two systems compatible even though each uses different binary code. It is a device that converts binary signals from a source code to its output code. One example is a BCD to Ex-3 converter.
- What do you mean by analyzing a combinational circuit?
The reverse process for implementing a Boolean expression is called as analyzing combinational circuit. (i.e.) the available logic diagram is analyzed step by step and finding the Boolean function.
- Give the applications of Demultiplexer.
- i) It finds its application in Data transmission system with error detection.
- ii) One simple application is binary to Decimal decoder.
- Mention the uses of Demultiplexer.
Demultiplexer is used in computers when a same message has to be sent to different receivers. Not only in computers, but any time information from one source can be fed to several places.
- Give other name for Multiplexer and Demultiplexer.
Multiplexeris otherwise called as Data selector.
Demultiplexeris otherwise called as Data distributor.
- What is the function of the enable input in a Multiplexer?
The function of the enable input in a MUX is to control the operation of the unit.
- List out the applications of decoder?
- Decoders are used in counter system.
- They are used in analog to digital converter.
- Decoder outputs can be used to drive a display system.
- Application of Mux.
- They are used as a data selector to select one output of many data inputs.
- They can be used to implement combinational logic circuits
- They are used in time multiplexing systems.
- They are used in frequency multiplexing systems.
- They are used in A/D & D/A Converter.
- They are used in data acquisition system.
- List out the applications of comparators?
- Comparators are used as a part of the address decoding circuitry in computers to select a specific input/output device for the storage of data.
- They are used to actuate circuitry to drive the physical variable towards the reference value.
- They are used in control applications
- What is carry look-ahead addition?
The speed with which an addition is performed limited by the time required forth carries to propagate or ripple through all of the stage of the adder. One method of speeding up the process is by eliminating the ripple carry delay.
- Difference between Decoder & Demux
Decoder is a many inputs to many outputs device. There are no selection lines.
Demux is a single input to many outputs the selection of specific output line is controlled by the value of selection lines
- What are the classifications of sequential circuits?
The sequential circuits are classified on the basis of timing of their signals into two types. They are: 1) Synchronous sequential circuit.2) Asynchronous sequential circuit.
Unit-3 Sequential circuit
- Difference between Combinational & Sequential Circuits.
- What are the classifications of sequential circuits?
The sequential circuits are classified on the basis of timing of their signals into two types. They are:
1) Synchronous sequential circuit. 2) Asynchronous sequential circuit.
- Define Flip flop.
The basic unit for storage is flip flop. A flip-flop maintains its output state either at 1or 0 until directed by an input signal to change its state.
- What are the different types of flip-flop?
There are various types of flip flops. Some of them are mentioned below they are:
- SR flip-flop 2. D flip-flop 3. JK flip-flop 4. T flip-flop
- What is the operation of D flip-flop?
In D flip-flop during the occurrence of clock pulse if D=1, the output Q is set and if D=0, the output is reset.
Set – 1, Reset – 0.
- What is the operation of JK flip-flop?
When K input is low and J input is high the Q output of flip-flop is set.2. When K input is high and J input is low the Q output of flip-flop is reset.3. When both the inputs K and J are low the output does not change4. When both the inputs K and J are high it is possible to set or reset the flip-flop(i.e.) the output toggle on the next positive clock edge.
- What is the operation of T flip-flop?
T flip-flop is also known as Toggle flip-flop.1. When T=0 there is no change in the output.2. When T=1 the output switch to the complement state (i.e.) the output toggles.
- Define race around condition.
In JK flip-flop output is fed back to the input. Therefore change in the output results change in the input. Due to this in the positive half of the clock pulse if both J and K are high then output toggles continuously. This condition is called ‘race around condition’.
- What is edge-triggered flip-flop?
The problem of race around condition can solved by edge triggering flip flop. The term edge triggering means that the flip-flop changes state either at the positive edge or negative edge of the clock pulse and it is sensitive to its inputs only at this transition of the clock.
- What is a master-slave flip-flop?
A master-slave flip-flop consists of two flip-flops where one circuit serves as a master and the other as a slave.
- Define rise time.
The time required to change the voltage level from 10% to 90% is known as risetime(tr).
- Define fall time.
The time required to change the voltage level from 90% to 10% is known as falltime(tf).
- Define skew and clock skew.
The phase shift between the rectangular clock waveforms is referred to as skew and the time delay between the two clock pulses is called clock skew.
- Define setup time.
The setup time is the minimum time required to maintain a constant voltage levels at the excitation inputs of the flip-flop device prior to the triggering edge of the clock pulse in order for the levels to be reliably clocked into the flip flop. It is denoted astsetup.
- Define hold time.
The hold time is the minimum time for which the voltage levels at the excitation inputs must remain constant after the triggering edge of the clock pulse in order for the levels to be reliably clocked into the flip flop. It is denoted as
thold
.
- Define propagation delay.
A propagation delay is the time required to change the output after the application of the input
- Define registers.
A register is a group of flip-flops; flip-flop can store one bit information. So an-bit register has a group of n flip-flops and is capable of storing any binary information/number containing n-bits.
Register is a group of binary cells. A register with n cells can store any discrete quantity of information that contains n bits. The state of a register is an n-tuple number of 1’s and 0’s, with each bit designating the state of one cell in the register.
- Define shift registers.
The binary information in a register can be moved from stage to stage within the register or into or out of the register upon application of clock pulses. This type of bit movement or shifting is essential for certain arithmetic and logic operations used in microprocessors. This gives rise to group of registers called
Shift registers
.
- What are the different types of shift type?
There are five types. They are:
- Serial in Serial out Shift Register
- Serial in Parallel out Shift Register
- Parallel in Serial out Shift Register
- Parallel in Parallel out Shift Register
- Bidirectional Shift Register
- Define sequential circuit?
In sequential circuits the output variables dependent not only on the present input variables but they also depend up on the past output of these input variables.
- What do you mean by present state?
The information stored in the memory elements at any given time defines the present state of the sequential circuit.
- What do you mean by next state?
The present state and the external inputs determine the outputs and the next state of the sequential circuit.
- Define synchronous sequential circuit
In synchronous sequential circuits, signals can affect the memory elements only at discrete instant of time.
- Applications of Flip-Flop.
- Used as a memory Element.
- Used as a Delay Element.
- Used as a basic building block in sequential circuits such as counters and registers.
- Data Transfer.
- Frequency Division & Counting.
- Steps or Design procedure for Synchronous Counter.
- State Diagram. 2. State Table. 3. State Assignment. 4. Excitation Table (Consider which Memory Unit Using) 5. K-Map 6.Circuit Diagram.
- Give some applications of clocked RS Flip-flop.
- Clocked RS flip flops are used in Calculators & Computers.
- It is widely used in modern electronic products.
- Define Shift Register Counter.
A shift register can also be used as a counter. A shift register with the serial output connection back to the serial input is calledShift register counter.
- What are the two types of shift register counters?
There are 2 types of shift Register counters are:
i). Ring counter:
A ring counter is a circular shift register with only one flip flop being set, at any particular time, all others are cleared.
ii).Johnson counters:
The Johnson counter is a K-bit switch-tail ring counter with2^{k }decoding gates to provides outputs for
2^{k}timing signals
- Define state diagram.
A graphical representation of a state table is called a state diagram.
- What is the use of state diagram?
- i) Behavior of a state machine can be analyzed rapidly.
- ii) It can be used to design a machine from a set of specification.
- What is state table?
A table, which consists time sequence of inputs, outputs and flip-flop states, is called state table. Generally it consists of three section present state, next state and output.
- What is a state equation?
A state equation also called, as an application equation is an algebraic expression that specifies the condition for a flip-flop state transition. The left side of the equation denotes the next state of the flip-flop and the right side; a Boolean function specifies the present state.
- What is bi-directional shift register and unidirectional shift register?
A register capable of shifting both right and left is called bi-directional shift register. A register capable of shifting only one direction is called unidirectional shift register
Unit – IV Memory Devices
- Explain PROM.
PROM (Programmable Read Only Memory)
It allows user to store data or program. PROMs use the fuses with material like in chrome and polycrystalline. The user can blow these fuses by passing around 20 to 50mA of c urgent for the period 5 to 20µs.The blowing of fuses is called programming of ROM. The PROMs are one time programmable. Once programmed, the information is stored permanent.
- Explain EPROM.
EPROM (Erasable Programmable Read Only Memory)
EPROM use MOS circuitry. They store 1’s and 0’s as a packet of charge in a buried layer of the IC chip. We can erase the stored data in the EPROMs by exposing the chip to ultraviolet light via its quartz window for 15 to 20 minutes. It is not possible to erase selective information. The chip can be reprogrammed.
- Explain EEPROM.
EEPROM (Electrically Erasable Programmable Read Only Memory)
EEPROM also use MOS circuitry. Data is stored as charge or no charge on an insulated layer or an insulated floating gate in the device. EEPROM allows selective erasing at the register level rather than erasing all the information since the information can be changed by using electrical signals.
- List the types of ROM.
- i) Programmable ROM (PROM) ii) Erasable ROM (EPROM) iii) Electrically Erasable ROM (EEROM
- Differentiate ROM & PLD’s.
- What are the different types of RAM?
a). NMOS RAM (Nitride Metal Oxide Semiconductor RAM)
b). CMOS RAM (Complementary Metal Oxide Semiconductor RAM)
c). Schottky TTL RAM
- What is RAM?
RAM is Random Access Memory. It is a random access read/write memory. Thedata can be read or written into from any selected address in any sequence.
- Define ROM
ROM is a type of memory in which data are stored permanently or semi permanently. Data can be read from a ROM, but there is no write operation
- Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit combination that comes out of the output lines is called a word.
- What are the types of ROM.?
- Masked ROM. 2. Programmable Read only Memory 3. Erasable Programmable Read only memory.
- Electrically Erasable Programmable Read only Memory.
- What is programmable logic array? How it differs from ROM?
In some cases the number of don’t care conditions is excessive, it is more economical to use a second type of LSI component called a PLA. A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables and does not generates all the minterms as in the ROM.
- What is mask – programmable ROM?
A type of memory where the stored data are permanently stored into the memory device during the manufacturing process.
- What is field programmable logic array?
The second type of PLA is called a field programmable logic array. The user by means of certain recommended procedures can program the FPLA.
- Define PLD.
Programmable Logic Devices consist of a large array of AND gates and OR gates that can be programmed to achieve specific logic functions.
- Give the classification of PLDs.
PLDs are classified as PROM (Programmable Read Only Memory), Programmable Logic Array (PLA), Programmable Array Logic (PAL), and Generic Array Logic (GAL)
- Define PROM.
PROM is Programmable Read Only Memory. It consists of a set of fixed AND gates connected to a decoder and a programmable OR array.
- Define PLA
PLA is Programmable Logic Array (PLA). The PLA is a PLD that consists of a programmable AND array and a programmable OR array.
- Define PAL
PAL is Programmable Array Logic. PAL consists of a programmable AND array and a fixed OR array with output logic.
- Why was PAL developed?
It is a PLD that was developed to overcome certain disadvantages of PLA, such as longer delays due to additional fusible links that result from using two programmable arrays and more circuit complexity.
- What is CPLD?
CPLDs are Complex Programmable Logic Devices. They are larger versions of PLD with a centralized internal interconnect matrix used to connect the device macro cells together.
22 .Define bit, byte and word.
The smallest unit of binary data is bit. Data are handled in a 8 bit unit called byte. Complete unit of information is called a word which consists of one or more bytes.
- How many words can a 16×8 memory can store?
A 16×8 memory can store 16,384 words of eight bits each
- Define address of a memory.
The location of a unit of data in a memory is called address.
- Define Capacity of a memory.
It is the total number of data units that can be stored.
- What is Read and Write operation?
The Write operation stores data into a specified address into the memory and the Read operation takes data out of a specified address in the memory.
- Why RAMs are called as Volatile?
RAMs are called as Volatile memories because RAMs lose stored data when the power is turned OFF.
- List the two categories of RAMs.
- Static RAM (SRAM) 2. Dynamic RAM (DRAM).
- Define Static RAM and dynamic RAM
- Static RAM
Use flip flops as storage elements and therefore store data indefinitely as long as dc power is applied.2.
- Dynamic RAMs
Use capacitors as storage elements and cannot retain data very long without capacitors being recharged by a process called refreshing
- Define Cache memory
It is a relatively small, high-speed memory that can store the most recently used instructions or data from larger but slower main memory.
- What is the technique adopted by DRAMs.
DRAMs use a technique called address multiplexing to reduce the number of address lines.
- Give the feature of UV EPROM
UV EPROM is electrically programmable by the user, but the store data must be erased by exposure to ultra violet light over a period of several minutes.
- Give the feature of flash memory.
The ideal memory has high storage capacity, non-volatility; in-system read and write capability, comparatively fast operation. The traditional memory technologies such as ROM, PROM, EEPROM individually exhibits one of these characteristics, but no single technology has all of them except the flash memory.
- What are Flash memories?
They are high density read/write memories that are non-volatile, which means data can be stored indefinitely without power.
- Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit combination that comes out of the output lines is called a word.
- What is programmable logic array? How it differs from ROM?
In some cases the number of don’t care conditions is excessive, it is more economical to use a second type of LSI component called a PLA. A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables and does not generates all the minterms as in the ROM.
- What are the types of arrays in RAM?
RAM has two type of array namely, a. Linear array b. Coincident array
- What are the terms that determine the size of a PAL?
The size of a PLA is specified by the a. Number of inputs b. Number of products terms c. Number of outputs
- What are the advantages of RAM?
The advantages of RAM area. Non-destructive read out b. Fast operating speed c. Low power dissipation
- Compatibility e. Economy
- Define FPGA.
Afield-programmable gate array is an integrated circuit designed tobe configured by the customer or designer after manufacturing “field-programmable”. The FPGA configuration is generally specified using a hardware description language (HDL). FPGAs contain programmable logic components called “logic blocks”, and a hierarchy of reconfigurable interconnects that allow the blocks to be “wired together “somewhat like a one-chip programmable breadboard
Unit – V
Synchronous & Asynchronous Sequential Circuits
- What is mealy and Moore circuit?
Mealy circuit is a network where the output is a function of both present state and input.
Moore circuitis a network where the output is function of only present state.
- Define hazards.
Hazards are unwanted switching transients that may appear at the output of a circuit because different paths exhibit different propagation delays.
- What is static 1 hazard?
Output goes momentarily 0 when it should remain at 1.
- What is static 0 hazard?
Output goes momentarily 1 when it should remain at 0.
- What is dynamic hazard?
Output changes 3 or more times when it changes from 1 to 0 or 0 to 1.
- How can the hazards in combinational circuit be removed?
Hazards in the combinational circuits can be removed by covering any two min terms that may produce a hazard with a product term common to both. The removal of hazards requires the addition of redundant gates to the circuit.
- How does an essential hazard occur?
An essential hazard occurs due to unequal delays along two or more paths that originate from the same input. An excessive delay through an inverter circuit in comparison to the delay associated with the feedback path causes essential hazard.
- What are the types of asynchronous circuits?
- Fundamental mode circuits 2. Pulse mode circuits
- What is fundamental mode sequential circuit?
A). Input variables changes if the circuit is stable.
b). Inputs are levels, not pulses.
c). only one input can change at a given time.
- What are pulse mode circuits?
A). Inputs are pulses. b). width of pulses are long for circuit to respond to the input.
c). pulse width must not be so long that it is still present after the new state is reached.
- What are the steps for the design of asynchronous sequential circuit?
A). Draw the State Diagram. b). Construction of primitive flow table.
c). Merger Graph. d). Reduction of flow table. e). State assignment or Transition Table is made.
f). K-Map. g). Circuit Diagram.
- Define primitive flow table:
It is defined as a flow table which has exactly one stable state for each row in the table. The design process begins with the construction of primitive flow table.
- Give the comparison between state Assignment Synchronous circuit and state assignment asynchronous circuit.
In synchronous circuit, the state assignments are made with the objective of circuit reduction. In asynchronous circuits, the objective of state assignment is to avoid critical races.
- What are races?
When 2 or more binary state variables change their value in response to a change in an input variable, race condition occurs in an asynchronous sequential circuit. In case of unequal delays, a race condition may cause the state variables to change in an unpredictable manner.
- Define non critical race.
If the final stable state that the circuit reaches does not depend on the order in which the state variable changes, the race condition is not harmful and it is called a noncritical race.
- Define critical race?
If the final stable state depends on the order in which the state variable changes, the race condition is harmful and it is called a critical race
- What is a cycle?
A cycle occurs when an asynchronous circuit makes a transition through a series of unstable states. If a cycle does not contain a stable state, the circuit will go from one unstable to stable to another, until the inputs are changed.
- List the different techniques used for state assignment.
- Shared row state assignment2. One hot state assignment.
- Define secondary variables.
The delay elements provide a short term memory for the sequential circuit. The present state and next state variables in asynchronous sequential circuits are called secondary variables.
- Write short note on shared row state assignment.
Races can be avoided by making a proper binary assignment to the state variables. Here, the state variables are assigned with binary numbers in such a way that only one state variable can change at any one state variable can change at any one time when a state transition occurs. To accomplish this, it is necessary that states between which transitions occur be given adjacent assignments. Two binary are said to be adjacent if they differ in only one variable.
- Write short note on one hot state assignment.
The one hot state assignment is another method for finding a race free state assignment. In this method, only one variable is active or hot for each row in the original Flow table, i.e., it requires one state variable for each row of the flow table. Additional row are introduced to provide single variable changes between internal state transitions.
- What are the problems involved in asynchronous circuits?
The asynchronous sequential circuits have three problems namely,
- Races
.c. Hazards
Digital Logic Circuits
1) Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a) X -Y and (b) Y – X using 2’s complements.
- a) X = 1010100
2’s complement of Y = + 0111101 ————–
Sum = 10010001
Discard end carry
Answer: X – Y = 0010001
- b) Y = 1000011
2’s complement of X = + 0101100 —————
Sum = 1101111
There is no end carry,
Therefore the answer is Y-X = -(2’s complement of 1101111) = -0010001
2). Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a) X -Y and (b) Y – X using 1’s complements.
a). X – Y = 1010100 – 1000011
X = 1010100
1’s complement of Y = + 0111100 ————–
Sum = 10010000
End -around carry = + 1 ————–
Answer: X – Y = 0010001
b). Y – X = 1000011 – 1010100
Y = 1000011
1’s complement of X = + 0101011 ———–
Sum = + 1101110
There is no end carry.
Therefore the answer is Y – X = -(1’s complement of 1101110) = -0010001
3). what is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s either even or odd. Consider the following two characters and their even and odd parity: With even parity with odd parity ASCII A = 1000001 01000001 11000001, ASCII T = 1010100 11010100 01010100. In each case we add an extra bit in the left most position of the code to produce an even number of1’s in the character for even parity or an odd number of 1’s in the character for odd parity. The parity bit is helpful in detecting errors during the transmission of information from one location to another.
4).What are registers?
Register is a group of binary cells. A register with n cells can store any discrete quantity of information that contains n bits. The state of a register is an n-tuple number of 1’s and 0’s, with each bit designating the state of one cell in the register.
5). What is meant by register transfer?
A register transfer operation is a basic operation in digital systems. It consists of transfer of binary information from one set of registers into another set of registers. The transfer may be direct from one register to another, or may pass through data processing circuits to perform an operation.
6). Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only two distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
7). Define logic gates?
Logic gates are electronic circuits that operate on one or more input signals to produce an output signal. Electrical signals such as voltages or currents exist throughout a digital system in either of two recognizable values. Voltage- operated circuits respond to two separate voltage levels that represent a binary variable equal to logic 1 or logic 0.
8).Define duality property.
Duality property states that every algebraic expression deducible from the postulates of Boolean algebra remains valid if the operators and identity elements are interchanged. If the dual of an algebraic expression is desired, we simply interchange OR and AND operators and replace 1’s by 0’s and 0’s by 1’s.
9).Find the complement of the functions F_{1}= x’yz’ + x’y’z and F_{2}= x(y’z’ + yz) by applying De Morgan’s theorem as many times as necessary.
F_{1}’ = (x’yz’ + x’y’z)’ = (x’yz’)’(x’y’z)’ = (x + y’ + z)(x + y +z’)
F_{2}’ = [x(y’z’ + yz)]’ = x’ + (y’z’ + yz)’ = x’ + (y’z’)’(yz)’
= x’ + (y + z)(y’ + z’)
10).Find the complements of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz) by taking their duals and complementing each literal.
F1= x’yz’ + x’y’z. The dual of F1 is (x’ + y + z’)(x’ + y’ + z).
Complementing each literal: (x + y’ + z)(x + y + z’)
F2= x(y’z’ + yz). The dual of F2 is x + (y’ + z’)(y + z).
Complement of each literal: x’ + (y + z)(y’ + z’)
11).State De Morgan’s theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They are, 1) The complement of a product is equal to the sum of the complements. (AB)’ = A’ + B’ 2) The complement of a sum term is equal to the product of the complements. (A + B)’ = A’B’
12).Reduce A.A’C
A.A’C = 0.c [A.A’ = 1] = 0
13). Reduce A(A + B)
A(A + B) = AA + AB = A(1 + B) [1 + B = 1] = A.
- Reduce A’B’C’ + A’BC’ + A’BC
A’B’C’ + A’BC’ + A’BC = A’C’(B’ + B) + A’B’C = A’C’ + A’BC [A + A’ = 1]
= A’(C’ + BC) = A’(C’ + B) [A + A’B = A + B]
15.) Reduce AB + (AC)’ + AB’C(AB + C)
AB + (AC)’ + AB’C(AB + C) = AB + (AC)’ + AAB’BC + AB’CC
= AB + (AC)’ + AB’CC [A.A’ = 0]
= AB + (AC)’ + AB’C [A.A = 1]
= AB + A’ + C’ =AB’C [(AB)’ = A’ + B’]
= A’ + B + C’ + AB’C [A + AB’ = A + B]
= A’ + B’C + B + C’ [A + A’B = A + B]
= A’ + B + C’ + B’C
=A’ + B + C’ + B’
=A’ + C’ + 1
= 1 [A + 1 =1]
- Simplify the following expression Y = (A + B)(A + C’ )(B’ + C’ )
Y = (A + B)(A + C’ )(B’ + C’ )
= (AA’ + AC +A’B +BC )(B’ + C’) [A.A’ = 0]
= (AC + A’B + BC)(B’ + C’ )
= AB’C + ACC’ + A’BB’ + A’BC’ + BB’C + BCC’
= AB’C + A’BC’
17).Simplify the following using De Morgan’s theorem [((AB)’C)’’ D]’
[((AB)’C)’’ D]’ = ((AB)’C)’’ + D’ [(AB)’ = A’ + B’]
= (AB)’ C + D’
= (A’ + B’ )C + D’
18.Show that (X + Y’ + XY)( X + Y’)(X’Y) = 0
(X + Y’ + XY)( X + Y’)(X’Y) = (X + Y’ + X)(X + Y’ )(X’ + Y) [A + A’B = A + B]
= (X + Y’ )(X + Y’ )(X’Y) [A + A = 1]
= (X + Y’ )(X’Y) [A.A = 1]
= X.X’ + Y’.X’.Y
= 0 [A.A’ = 0]
19).Prove that ABC + ABC’ + AB’C + A’BC = AB + AC + BC
ABC + ABC’ + AB’C + A’BC =AB(C + C’) + AB’C + A’BC
=AB + AB’C + A’BC
=A(B + B’C) + A’BC
=A(B + C) + A’BC
=AB + AC + A’BC
=B(A + C) + AC
=AB + BC + AC
=AB + AC +BC …Proved
20).Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC(B + B’ ) + AB(C + C’ ) + (A + A’)BC
=ABC + ABC’ + AB’C + AB’C’ + ABC + ABC’ + ABC
=ABC + ABC’ +AB’C + AB’C’ [A + A =1]
21).Convert the given expression in canonical POS form Y = ( A + B)(B + C)(A + C)
Y = ( A + B)(B + C)(A + C)
= (A + B + C.C’ )(B + C + A.A’ )(A + B.B’ + C)
= (A + B + C)(A + B + C’ )(A + B +C)(A’ + B +C)(A + B + C)(A + B’ + C) [A + BC = (A + B)(A + C) Distributive law]
= (A + B + C)(A + B + C’)(A’ + B + C)(A’ + B + C)(A + B’ + C)
22). Find the minterms of the logical expression Y = A’B’C’ + A’B’C + A’BC + ABC’
Y = A’B’C’ + A’B’C + A’BC + ABC’ =m0 + m1 +m3 +m6 =ôP____________
23).Write the maxterms corresponding to the logical expression Y = (A + B + C’ )(A + B’ + C’)(A’ + B’ + C)
Y = (A + B + C’ )(A + B’ + C’)(A’ + B’ + C) =M1.M3.M6 =ö0_______
24).Convert (4021.2)_{5}to its equivalent decimal.
(4021.2)_{5}= 4 x 5^{3}+ 0 x 5^{2}+ 2 x 5^{1}+ 1 x 5^{0}+ 2 x 5^{-1}
= (511.4)_{10}
25) Using 10’s complement subtract 72532 – 3250
M = 72532 10’s complement of N = + 96750 ———–
Sum = 169282
Discard end carry
Answer = 69282
26) What are called don’t care conditions?
In some logic circuits certain input conditions never occur, therefore the corresponding output never appears. In such cases the output level is not defined, it can be either high or low. These output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or incompletely specified functions.
27) Write down the steps in implementing a Boolean function with levels of NAND Gates?
Simplify the function and express it in sum of products. Draw a NAND gate for each product term of the expression that has at least two literals. The inputs to each NAND gate are the literals of the term. This constitutes a group of first level gates. Draw a single gate using the AND-invert or the invert-OR graphic symbol in the second level, with inputs coming from outputs of first level gates. A term with a single literal requires an inverter in the first level. How ever if the single literal is complemented, it can be connected directly to an input of the second level NAND gate.
28) Give the general procedure for converting a Boolean expression in to multilevel NAND diagram?
Draw the AND-OR diagram of the Boolean expression. Convert all AND gates to NAND gates with AND-invert graphic symbols. Convert all OR gates to NAND gates with invert-OR graphic symbols. Check all the bubbles in the same diagram. For every bubble that is not compensated by another circle along the same line, insert an inverter or complement the input literal.
29) What are combinational circuits?
A combinational circuit consists of logic gates whose outputs at any time are determined from the present combination of inputs. A combinational circuit performs an operation that can be specified logically by a set of Boolean functions. It consists of input variables, logic gates, and output variables.
30) Give the design procedures for the designing of a combinational circuit.
The procedure involves the following steps, From the specification of the circuit, determine the required number of inputs and outputs and assign a symbol to each. Derive the truth table that defines the required relationships between inputs and outputs. Obtain the simplified Boolean functions for each output as a function of the input variables. Draw the logic diagram and verify the correctness of the design.
31) Define half adder.
A combinational circuit that performs the addition of two bits is called a half adder. A half adder needs two binary inputs and two binary outputs. The input variables designate the augend and addend bits; the output variables produce the sum and carry
32) Define full adder?
A combinational circuit that performs the adtion of three bits is a full adder.It consists of three inputs and two outputs.
33) Define binary adder.
A binary adder is a digital circuit that produces the arithmetic sum of two binary numbers. It can be constructed with full adders constructed in cascade, with the output carry from each full adder connected to the input carry of the next full adder in the chain.
34) What is overflow?
Over flow is a problem in digital computers because the number of bits that hold the number is finite and a result that contains n + 1 bits cannot be accommodated. For this reason many computers detect the occurrence of an overflow, and when it occurs a corresponding flip flop is set that can be checked by the user. An overflow condition can be detected by observing the carry into sign bit position and the carry out of the sign bit position. If these two carries are not equal, an overflow has occurred.
35) Define magnitude comparator?
A magnitude comparator is a combinational circuit that compares two numbers, A and B, and determines their relative magnitudes. The outcome of the comparison is specified by three binary variables that indicate whether a>b, A = b, or A < B.
36) What are decoders?
A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines. If the n bit coded information has unused combinations, he decoder may have fewer than 2n outputs.
37) What are encoders?
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n and n output lines. The output lines generate the binary code corresponding to the input value.
38) Define priority encoder?
A priority encoder is an encoder circuit that includes the priority function. The operation of priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence.
39) Define multiplexer?
A multiplexer is combinational circuit that selects binary information from one of many input lines and directs it to a single output line. The selection of a particular input line is controlled by a set of selection lines. Normally there are 2n input lines and n selection lines whose bit combinations determine which input is selected.
40) Define binary decoder?
A decoder which has an n- bit binary input code and a one activated output out-of -2n output code is called binary decoder. A binary decoder is used when it is necessary to activate exactly one of 2n outputs based on an n-bit input value.
- Represent binary number 1101 – 101 in power of 2 and find its decimal equivalent
N = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3 = 13.625 10
- Convert (634) 8 to binary
6 3 4
110 011 100
Ans = 110 011 100
- Convert (9 B 2 – 1A) H to its decimal equivalent.
N = 9 x 16 2 + B x 16 1 + 2 x 16 0 + 1 x 16 -1 + A (10) x 16 -2
= 2304 + 176 + 2 + 0.0625 + 0.039
= 2482.1 10
- What are the different classifications of binary codes?
- Weighted codes 2. Non – weighted codes 3. Reflective codes 4. Sequential codes 5. Alphanumeric codes 6. Error Detecting and correcting codes
- Convert 0.640625 decimal number to its octal equivalent.
0.640625 x 8 = 5.125
0.125 x 8 = 1.0
Ans. = 0.640 625 10 = 0.51
- Convert 0.1289062 decimal number to its hex equivalent
0.1289062 x 16 = 2.0625 0.0625 x 16
= 1.0
Ans. = 0.21 16
- Convert decimal number 22.64 to hexadecimal number.
16 22 -6
16 1 -1
0
0.64 x 16 = 10.24
0.24 x 16 = 3.84
0.84 x 16 = 13.44
.44 x 16 = 7.04
Ans. = (16 . A 3 D 7) 16.3
- What are the two steps in Gray to binary conversion?
The MSB of the binary number is the same as the MSB of the gray code number. So write it down.Toobtain the next binary digit, perform an exclusive OR operation b/n the bit just written down and the next gray code bit. Write down the result.
- Convert gray code 101011 into its binary equivalent.
Gray Code : 1 0 1 0 1 1 Binary Code 1 1 0 0 1 0
- Convert 10111011 is binary into its equivalent gray code.
Binary Code: 1 0 1 1 1 0 1 0 1 1
Gray code : 1 1 1 0 0 1 1 0
1 0 1 0
0 0 1 1
1 1 0 1
- Substract (0 1 0 1) 2 from (1 0 1 1) 2
1 0 1 0 0 1 0 1 0 1 1 0
- Find 2’S complement of (1 0 1 0 0 0 1 1) 2
0 1 0 1 1 1 0 0 1 1’s Complement
+ 0 0 0 0 0 0 0 1
0 1 0 1 1 1 0 1 0 2’s complement.
- Substract 1 1 1 0 0 1 2 from 1 0 1 0 1 1 2 using 2’s complement method
1 0 1 0 1 1
+ 0 0 0 1 1 1 2’s comp. of 1 1 1 0 0 1
1 1 0 0 1 0 Ans. in 2’s complement form
– 0 0 1 1 1 0 Answer in true form.
- What are the advantages of 1’s complement subtraction?
1) The 1’s complement subtraction can be accomplished with an binary adder. Therefore, this method is useful in arithmetic logic circuits. 2) The is complement of a number is easily obtained by inverting each bit in the number
- Find the excess -3 code and 9’s complement of the number 403_{10}
4 0 3
0 1 0 0 0 0 0 0 0 0 1 1
0 0 1 1 0 0 1 1 0 0 1 1 +
0 1 1 1 0 0 1 1 0 1 1 0 excess 3 code
9’s complement 1 0 0 0 1 1 0 0 1 0 0 1
- Write the names of basic logical operators.
- NOT / INVERT 2. AND 3. OR
- Simplify the following expression
y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C = A B C
- Show that the NAND connection is not associative
The NAND connection is not associative says that
A . B . C A . B. C
A . B + C A + B C
AB + C A + BC
- What is a Logic gate?
Logic gates are the basic elements that make up a digital system. The electronic gate is a circuit that is able to operate on a number of binary inputs in order to perform a particular logical function.
- Write the names of Universal gates.
- NAND gate 2. NOR gate
- Why are NAND and NOR gates known as universal gates?
The NAND and NOR gates are known as universal gates, since any logic function can be implemented using NAND or NOR gates.
- Define combinational logic
When logic gates are connected together to produce a specified output for certain specified combinations of input variables, with no storage involved, the resulting circuit is called combinational logic.
- Explain the design procedure for combinational circuits
¢ The problem definition ¢ The determination of number of available input variables & required O/P variables. ¢ Assigning letter symbols to I/O variables ¢ Obtain simplified boolean expression for each O/P. ¢ Obtain the logic diagram.
- Define half adder and full adder
The logic circuit which performs the addition of two bits is a half adder. The circuit which performs the addition of three bits is a full adder.
- Define Decoder?
A decoder is a multiple – input multiple output logic circuit which converts coded inputs into coded outputs where the input and output codes are different.
- What is binary decoder?
A decoder which has an n-bit binary i/p code and a one activated output out of 2l. output code is called binary decoder. It is used when it is necessary to activate exactly one of 2 n out puts based on an n – bit input value.
- Define Encoder?
An encoder has 2n input lines and n output lines. In encoder the output lines gener- ate the binary code corresponding to the input value.
- What is priority Encoder?
A priority encoder is an encoder circuit that includes the priority function. In priority encoder, if 2 or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence.
- Define multiplexer?
Multiplexer is a digital switch. If allows digital information from several sources to be routed onto a single output line.
- What do you mean by comparator
A comparator is a special combinational circuit designed primarily to compare the relative magnitude of two binary numbers.
- List basic types of programmable logic devices.
- Programmable Read only memory (PROM)
- Programmable logic Arrays (PLA)
- Programmable Array Logic (PAL)
- Field Programmable Gate Array (FPGA)
- Complex Programmable Logic Devices (CPLD)
- Define ROM
A read only memory is a device that includes both the decoder and the OR gates within a single IC package.
- Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit combination that comes out of the output lines is called a word.
- What are the types of ROM
- Masked ROM.
- Programmable Read only Memory 3. Erasable Programmable Read only memory.
- Electrically Erasable Programmable Read only Memory.
- What is programmable logic array?
How it differs from ROM? In some cases the number of don™t care conditions is excessive, it is more economical to use a second type of LSI component called a PLA A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables and does not generates all the minterms as in the ROM..
- What is mask – programmable?
With a mask programmable PLA, the user must submit a PLA program table to the manufacturer.
- What is field programmable logic array?
The second type of PLA is called a field programmable logic array. The EPLA can be programmed by the user by means of certain recommended procedures.
- Give the comparison between prom and PLA.
PROM 1. AND array is fixed and OR array is programmable 2. Cheaper and simple to use.
PLA 1. Both AND and OR arrays are Programmable 2. Costliest and complex than PROMS.
- Define even parity
In even parity the added parity bit will make the total number of 1s an even amount.
- Define sequential circuit?
In sequential circuits the output variables dependent not only on the present input variables but they also depend up on the past history of these input variables.
- Give the comparison between combinational circuits and sequential circuits.
Memory unit is not required Memory unity is required Parallel adder is a combinational circuit Serial adder is a sequential circuit
- What do you mean by present state?
The information stored in the memory elements at any given time define™s the present state of the sequential circuit.
- What do you mean by next state?
The present state and the external inputs determine the outputs and the next state of the sequential circuit.
- What are the types of sequential circuits?
- Synchronous sequential circuits 2. Asynchronous sequential circuits
- Define synchronous sequential circuit
In synchronous sequential circuits, signals can affect the memory elements only at discrete instant of time.
- Define Asynchronous sequential circuit?
In asynchronous sequential circuits change in input signals can affect memory element at any instant of time
- Define flip-flop
Flip – flop is a sequential device that normally. samples its inputs and changes its outputs only at times determined by clocking signal.
- List various types of flip-flop
1] S.R. latch 2] D latch 3] Clocked J.K. flip-flop 4] T flip-flop
- What is race around condition?
In the JK latch, the output is feedback to the input, and therefore change in the output results change in the input. Due to this in the positive half of the clock pulse if J and K are both high then output toggles continuously. This condition is known as race around condition.
- Define rise time and fall time?
The time required to change the voltage level from 10% to 90% is known as rise time, and the time required to change the voltage level from 90% to 10% is known as fall time.
- Define propagation Delay?
A propagation delay is the time required to change the output after application of the input.
- Define shift Registers
The binary information in a register can be moved from stage to stage within the register or into or out of the register upon application of clock pulses. This type of bit movement or shifting is essential for certain arithmetic and logic operations used in microprocessors. This gives rise to a group of registers called shift registers.
- What are the types of shift register?
- Serial in serial out shift register? 2. Serial in parallel out shift register 3. Parallel in serial out shift register 4. Parallel in parallel out shift register 5. Bidirectional shift register shift register.
- What are the types of counter?
- Synchronous counter 2. Asynchronous Counter
- What are the two models in synchronous sequential circuits.
- Moore circuit 2. Mealy circuit
- What is moore circuit?
When the output of the sequential circuit depends only on the present state of the flip-flop, the sequential circuit is referred to as moore circuit.
- What is Mealy circuit?
When the output of the sequential circuit depends on both the present state of flip- flop and on the input, the sequential circuit is referred to as mealy circuit.
- Define successor
In a state diagram, if an input sequence, x takes a machine from state si to state sj, then sj is said to be the x – successor of si.
- Define strongly connected machine?
In a sequential machine many times certain subsets of states may not be reachable from other subsets of states, even if the machine does not contain any terminal state. However, if for every pair of states si, sj of a sequential machine, there eights an input sequence which takes M from Si to Sj then sequential machine M is said to be strongly connected.
- State and prove consensus theorem in Boolean algebra?
In simplification of Boolean expression, the redundant term in an expression can be eliminated to form the equivalent expression. The theorem used for this simplification is called consensus theorem. For ex in expression of the AB+A’C+BC, the term BC is redundant and can be eliminated using Consensus theorem.
- What do you mean by Literal?
In Boolean function, the total numbers of variables in complemented or uncomplemented form are called literals.
- Give Applications of MUX?
Applications:
- MUX can be used to realize a Boolean function
- It can be used in communication systems e.g. time division multiplexing
- Define Latch?
It is a sequential device that checks all of its inputs continuously and changes its outputs accordingly at any time, independent of a clocking signal.
- What is Lock out?
In a counter, if the next state of some unused state is again some unused state, it may happen that the counter remains in unused state never to arrive at a used state. Such a condition is called Lock out condition.
- How to avoid Lock out Condition?
- The counter should be provided with an additional circuit. This will force the counter from an unused state to the next state as initial state.
- It is not always necessary to force all unused states into an initial state. Because from unused states which are not forced, the circuit may eventually arrive at a forced unused state. This frees the circuit from the Lock out condition.
- State the advantages and disadvantages of Totem pole output?
Advantages:
- External pull up resistor is not required
- Operating speed is high
Disadvantages:
Output of two gates cannot be tied together.
- Explain the wired And connection?
When the open collector outputs of two or more gates can be connected together, the connection is called a wired AND.
It is represented as:
- In wired AND connection, the output is high only when all the switches are open
- Hence, the output is equivalent to the logical AND operation of the logic function performed by the gates.
- State the advantages and disadvantages of wired AND connection.
Advantage is, Outputs of two gates can be tied together using wired-AND technique.
Disadvantage is, Operating Speed is Low.
- What is open collector output.
When the collector terminal of the transistor is kept open without any pull up transistor the arrangement is called open collector output.
BIM TU Question Bank Solution
Digital logic Short Answer
Year 2017
- Express FOM in ASCII code.
=100 0110 100 1111 100 1101
- Why gray codes are used in k-map instead of binary codes? (2012)
Gray codes actually follow Adjacency property i.e. between two successive gray codes there is only one-bit change and in the binary code, there will be multiple value changes. Because of Adjacency property when one plots a K-MAP, literals can be grouped keeping other literal constant.
- What is the maximum number of half adder that we can use in n bit parallel adder & why?
A FA has both a carry in and a carry out. A HA doesn’t have a carry in. A half adder can be used to add the least significant digit of a binary number or two binary digits alone. FAs can be chained together to add a multi-bit number:
// an N- bit parallel adder, there must be N number of full adder circuits.
- Identify & state the similarity between latch & flip-flop.
- Latch is level sensitive whereas flip flop is edge sensitive.
- Latch has no clock signal but flip flop has.
- Latch is asynchronous sequential circuit but flip flop is synchronous.
- FLIP flop IS SYNCHRONOUS VERSION OF latch. Latch is made from gates but Flip flop is made up of Latches.
- Latch is a temporary buffer but Flip flop is a 1 bit storage element.
- What is the use of cascaded counters?
used to divide a high-frequency clock signal to obtain the highly accurate pulse frequencies.
//The cascade is the larger counters that can be built by combining of
smaller counters together
- Which shift register constructed using n flip flops can count 2n states & why?
An n-stage Johnson counter yields a count sequence of length 2n, so it may be considered to be a mod 2n counter. They can be implemented easily using D- or JK-type flip-flops.
- Difference between grained & coarse grained FPGA.
- In terms of architecture, FPGAs are considered as ‘fine-grain’ devices while CPLDs are ‘coarse-grain’.
- FPGAs are great for more complex applications while CPLDs are better for simpler ones.
- FPGAs are made up of tiny logic blocks while CPLDs are made of larger blocks.
- FPGA is a RAM-based digital logic chip while CPLD is EEPROM-based.
// FPGA is short for Field-Programmable Gate Array, is a type of a programmable logic chip
- Define Noise immunity.
Noise immunity is the ability of a device or component to operate in the presence of noise disturbance or . Noise Immunity. the ability of an apparatus or system to perform its functions when interference (noise) is present. Noise immunity is rated according to the noise intensity at which the disruption of the equipment’s functions is still within permissible limits.
- Difference between truth table & characteristics table & excitation table.(2015,2014)
An excitation table shows the minimum inputs that are necessary to generate a particular next state when the current state is known.
Truth table lists possible inputs and the corresponding output. Or Truth Table is a table which represents all the possible values of logical variables/statements along with all the possible results of the given combinations of values.
A state table is a truth table in which at least one of the inputs is the current state, and at least one of the outputs is the next state. It is also known as a state transition table
Year 2016
- Mention advantage of parity method of error detection
- Errors on a noisy line can be caught quickly
- only the errant word has to be re-transmitted
- Is it possible to design a combinational circuit that adds two 3-bit numbers using only half adder?
- It is not possible to design a combination circuit that add two 3 bit number using only half adder .For addition of two bit binary number there is a need of two full adder & 1 half adder because there exist carry while adding the bits.
- What is the advantage of flip flop over latch?
- flip-flops are controllable latch.
- flip plop is an edge-triggered sensitive device but latch is a level sensitive device.
- flip-flop outputs are free from the state transitions that occur with transparent latches as data inputs change.
- Why BCD counter is defined as truncated counter?
BCD counter is defined as truncated counter because it doesn’t count the full sequence i.e. BCD counter counts a 4-bit counter from 0000 state to 1001 state.
- What is the strength of Johnson counter over Ring counter?(2011)
The main advantage of the Johnson counter is that it only needs half the number of flip-flops compared to the standard ring counter for the same MOD.
- What is the importance of refreshing circuit in DRAM?
In a DRAM chip, each bit of memory data is stored as the presence or absence of an electric charge on a small capacitor on the chip. As time passes, the charges in the memory cells leak away, so without being refreshed the stored data would eventually be lost.
- Difference between CPLD & SPLD.
//SPLD – simple programmable logic device
//CPLD – complex programmable logic device
//FPGA- field programmable gate array
- In terms of architecture, FPGAs are considered as ‘fine-grain’ devices while CPLDs are ‘coarse-grain’.
- FPGAs are great for more complex applications while CPLDs are better for simpler ones.
- FPGA is a RAM-based digital logic chip while CPLD is EEPROM-based.
- FPGAs are more expensive while CPLDs are much cheaper.
Year 2015
- Is gray code weight or un-weighted code?
It is the non-weighted code and it is not arithmetic codes. That means there are no specific weights assigned to the bit position. It has a very special feature that, only one bit will change each time the decimal number is incremented
- Suppose you are adding 1101 & 1001 using binary adder. What is final carry out bit?
=10110 so carry out bit is 1
- Define power dissipation (consumption) of flip flop.
It is the total power required to operate the device & functioning properly.
- If the initial state of 4–bit ring counter is 1001, what is its state after 7^{th}clock pulse?
= 0001
- List the advantage of PLDs over fixed function ICs.
- Reduction in board space requirement.
- Reduction in power requirement.
- Design security.
- Compact circuitry.
- Higher switching speed.
- Compare between TTl & ECL. (2012)
TTL- Transistor Transistor Logic
ECL- Emitter Coupled Logic
CMOS – Complementary Metal Oxide Semiconductor
Following are the typical feature of CMOS
- lowest power dissipation
- excellent noise immunting
- high parking density
- wide range of power supply
- highest fan-out among all logic families
Following are characteristics of ECL logic family
- Propagation rate is about 1 to 2ns
- Noise immunity and power dissipation is worst of all the logic families.
- High Level is 0.8V and Low Level 1.8V
- it has differential input amplifier, internal temperature and voltage compensated bias network; either follower output
Year 2014
- Difference periodic & non periodic wave.
A wave which repeats pattern over a period is called periodic wave. It can be represented by a mathematical equation. They are deterministic signals.
Random signals, can’t represented by any mathematical equation.
- Decimal numbers are weighted numbers. Justify
Yes, because each digit position is being assigned with a specific weight.
- What is the number of selection line if multiplexer have 1234 input lines?
- 11
- How many flip flops are required to divide a frequency by 16?
=2^{4} = 16 ,so 4 flip flops are required
// freq divide by 2^{N } N=3 => divide by 8 (8 counters required 3 flip flop)
- Is it possible to implement counting function using data flip flop? support your answer
Yes, synchronous & Asynchronous counteris used for counting
- If state of 4-bit Johnson counter is 1100, what is its state after 4^{th}clock pulse?
1^{st} clock pulse=0000
2^{nd} clock pulse =0000
3^{rd} clock pulse=1000
4^{th} clock pulse=1100
- How sizes of data register & address register are calculated in computer system?
Capacity(c) =2^{M}*N
Where ,
2^{M}=Distnict location
M=size of address
N=Size of data
- Write advantage of PLA over ROM.
- In PLA both AND and OR arrays are configurable unlike in ROM, whereas only the OR gates array is configurable.
- PLA has the capability to take ‘don’t care terms’ (Boolean overlaps) into account in which ROMs are incapable.
- . ROM has all the combinations of product terms, and therefore, considered as the most general purpose combinational logic device in contrast to PLA, which doesn’t have all the combinations.
- Explain any two operational characteristics of an IC.
Fan-out:
Fan out specifies the number of standard loads that the output of the gate can drive without impairment of its normal operation
power dissipation:
Power dissipation is measure of power consumed by the gate when fully driven by all its inputs.
propagation delay:
Propagation delay is the average transition delay time for the signal to propagate from input to output when the signals change in value. It is expressed in ns.
Noise margin:
It is the maximum noise voltage added to an input signal of a digital circuit that does not cause an undesirable change in the circuit output. It is expressed in
volts.
Fan in:
Fan in is the number of inputs connected to the gate without any degradation in the voltage level.
Year 2013
- On what basis flip flop is categorized?
- On the basis of data movement
- Right shift register
- Left shift register
- Universal shift register
- On the basis of input and output
- SISO (serial in serial out) , SIPO (serial in parallel out) ,PIPO (parallel in parallel out), PISO (parallel in serial out)
- Why the output of last flip flop is connected to the input of first flip flop in case of Ring counter?
A ring counter is literally a ring of flip-flops with the output of one flip-flop connected to the input of the next. By connecting the output of the last flip-flop to the input of the first, you’ve created a ring. This allows data to circulate around the ring with each clock pulse.
- Difference between PAL & PLA.
Drawbacks of PLA
- PLA were hard to be implemented
- †PLA reduced the speed performance of circuits.
„
Advantage of PAL
- †Simple to manufacturers
- †Less expensive
- †Better performance
Disadvantage of PAL
- Not flexible as compared PLA, because OR plane is fixed.
- In case of memory read operation what is the function of data register?
Data register holds the data that has been retrieved from memory (in case of read) or to be stored into memory (in case of write).
- Compare between LCD & LED on the basis of power consumption, viewing angle & picture quality. (2012,2010)
LED | LCD | |
Viewing Angles | Very good. Wider viewing angle than LCD TVs. | Good to very good: Image fades slightly from extreme angles at sides, above, or below. |
Power consumption | consume less power around 70% | Requires less power to operate |
picture Quality | Excellent. | Very good |
Year 2012
- Which logic gates have output same when two units are same?
AND logic gate
- How many flip flops are required to construct a mod-90 counter
2^7 = 128 so 7 flip flop required
- List two advantage of analog signal. (2011,2009)
Analog – No quantization errors, requires less bandwidth, low cost and can be easily constructed because of less pre-processing requirements.
Digital – Fast processing, easier for storage, strong immunity to noise, parallel processing possibility, error correction possibilities, easy portability
- Show the necessary steps to convert analog to digital signal.
a.sampling
b.Quantization
c.code word generation
Year 2011
- Write advantage of BCD code.
it is a fast and efficient system to convert the decimal numbers into binary numbers as compared to the pure binary system.
- What is the output of frequency to the Mod-8 counter is 800 Hz?
Output frequency = 800 HZ/2^4 = 50 HZ
- What is the weight of 1 in binary number 0.0000100?
=0.03125 (5^{th} position)
// 0.5 0.25 ,0.125,0.0625
- List the level of integration.
From list complexity to most complex
1.Small scale Integration (SSI)
- Medium Scale Integration (MSI)
3.Large Scale Integration (LSI)
4.Very Large Scale Integration(VLSI)
5.Ultra large Scale Integration (ULSI)
Year 2009
- Write one advantage of alphanumeric code from other codes.
Using these codes, we can interface input-output devices such as keyboards, monitors, printers. with computer.
// alphanumeric codes are the codes that represent numbers and alphabetic characters.
- Draw a circuit diagram to count 6 different numbers using Johnson Counter.
= 6 ( D- flip flop)
- Write one application area of ECL & CMOS each.
- TTL circuits utilize BJTs while CMOS circuits utilize FETs.
- CMOS allows a much higher density of logic functions in a single chip compared to TTL.
- TTL circuits consumes more power compared to CMOS circuits at rest.
- CMOS chips are a lot more susceptible to static discharge compared to TTL chips.
- There are CMOS chips that have TTL logic and are meant as replacements for TTL chips
- Why PLA is better than PAL?
Programmable Logic Array | Programmable Array Logic |
PLA has both programmable AND and OR planes | PAL has only programmable AND planes and OR plane is fixed |
PLA has more flexibility in the logic circuit function implementation | PAL has less flexibility in the logic circuit function implementation |
PAL is quite difficult to manufacture | PAL is simpler to manufacture |
PLA has reduced speed performance | PLA has good speed performance |
PLA devices are manufactured in a larger size. | PAL devices are manufactured in a smaller size. |
- How many flip flops are required to generate a 7Hz pulse from 56 Hz pulse?
= 2^3 required for 7Hz ,so 3 flip flop & additional 2^3 so total flip flop 2^6 .so we need now only 3 flip flop.
Year 2010
- Define a Clock Pulse?
clock pulse is a signal used to synchronize the operations of an electronic system. Clock pulses are continuous, precisely spaced changes in voltage. See clock speed.
- What are error detection codes? Give an example.
Error detection is the process of detecting the errors that are present in the data transmitted from transmitter to receiver, in a communication system. We use some redundancy codes to detect these errors, by adding to the data while it is transmitted from source (transmitter). These codes are called “Error detecting codes”.
- What is the weight of 0 in binary number 10111?
= 8
- How many Full Adders and Half Adders are required if you want to add two 4 bit words?
= 3 full hader & 1 half adder
- Differentiate Combinational circuit from Sequential Circuit.
Combinational Logic Circuits | Sequential Logic Circuits |
Output is a function of the present inputs (Time Independent Logic). | Output is a function of clock, present inputs and the previous states of the system. |
Do not have the ability to store data (state). | Have memory to store the present states that is sent as control input (enable) for the next operation. |
Used mainly for Arithmetic and Boolean operations. | Used for storing data (and hence used in RAM). |
Logic gates are the elementary building blocks. | Flip flops (binary storage device) are the elementary building unit. |
Independent of clock and hence does not require triggering to operate. | Clocked (Triggered for operation with electronic pulses). |
Example: Adder [1+0=1; Dependency only on present inputs i.e., 1 and 0]. | Example: Counter [Previous O/P +1=Current O/P; Dependency on present input as well as previous state]. |
- List the properties of TTL.
- Higher power Consumption
- Large Propagation delay
- Less packing density
Year 2006
- A De-multiplexor is having 5 select lines. How many input lines does it have?
= 32
- How many flip flops are required to construct a mod-65 counter?
=7
- How many clock pulses are required to take all the output bits from a 5-bit serial-in parallel-out shift register if the shift register is already loaded?
= 1
- What are the two most important advantages of LCD displays compared to the conventional types of displays?
- no radiation emission from screen
- lighter in weight with respect to the screen size
- less power and generate less heat
Year 2005
- Why NAND & NOR gates are called universal gates?’
The NAND and NOR gates are known as universal gates, since any logic function can be implemented using NAND or NOR gates.
Circuits using NAND and NOR are popular as they are easier to design and therefore cheaper. Functions of other gates can easily be implemented using NAND and NOR gates. For this reason they are called universal gates
- State De-Morgan’s theorem mathematically.
De Morgan suggested two theorems that form important part of Boolean algebra. They are, 1) The complement of a product is equal to the sum of the complements. (AB)’ = A’ + B’ 2) The complement of a sum term is equal to the product of the complements. (A + B)’ = A’B’
- What are the number of 2-input NAND gates to construct 3-input AND gate?
=2
- If n are the input select lines of a MUX, how many data input lines are there in the MUX?
=2^{n inout }input lines are required
- . How many JK flip-flops are needed to construct a mod-80 counter?
=7 flip flops are needed.