## Chapter 3: NUMBER SYSTEM AND THEIR CONVERSION

1. Convert 333₁0 Denary numbers into Hexadecimal and back to base two number system.

 16 333 Remainder 13=D 16 20 4 16 1 1 0

Hence, (333)10 = (14D)16

Now, converting back to base two number system (i.e. binary number system)

Arranging in 4-bits,

 Hexadecimal 1 4 D Binary 0001 0100 1101

Hence, (14D) 16 = (000101001101)2

2. Convert the following numbers according to the given instruction

• 24010 into Octal number

Hence, (240)10 = (360)8

• ABC16 in to Binary number.

Arranging in 4-bits,

 Hexadecimal A B C Binary 1010 1011 1100

Hence, (ABC) 16 = (101010111100)2

3. What is octal number system? Convert 35610 int base 8.

Octal number is a base 8 number system. It uses 8 digits (0, 1, 2, 3, 4, 5 6 and 7). Base of this number system is 8 or 0.

Example: (405)s or (405)o.

For second part of the question,

Hence, (356)10 =  (544)8

4. What is binary number system? Convert 52010 into base 16.

Binary number system is a base 2 number system. It uses 2 digits, 0 and 1. It is the only number system, which is directly understood by the computer. Example: (10101)2 or (10101) B

For second part of the question,

Hence, (520)10 =(208)16

5. What is hexadecimal number system? Convert 11 10 112 into base 16.

Hexadecimal number system is a base 16 number system. It uses 16 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Example: (A05)16 or (A05)H. For second part of the question,

Grouping into 4 bits, 0011 1011

 Binary 0011 1011 Hexadecimal 3 B

Hence, (111011) 2= (3B)16

42.2074 Set A Q.No. 14 OR Subtract (10011), from (11110), by using 1’s and 2’s complement method.

Subtracting (11110)2 – (10011)₂

[Using 1’s complement method]

1’s complement of  10011                      = 01100

Adding it with minuend (i.e. 11110)      = 11110

+ 01100

101010

Since, there exists’ one additional bit,

Difference=                                                 01010

+1

01011

Hence, 11110 – 10011 = (01011)2.

[Using 2’s complement method]

2’s complement of 10011

= 01100

+1

01101

Adding it with 11110                              = 11110

+01101

101011

Since, there exists’ one additional bit, Difference = 01011 (Neglect additional bit i.e. 1)

Hence, 11101 – 10011 = (01011)2.