**Short Answer Questions**

**1. Define Boolean functions. Construct truth table for AND operation of Boolean algebra.**

A Boolean function is an expression formed by binary variables, binary operators OR, AND, unary operator NOT.

Example: F=A’.B.C+A.B.C, where A, B, C are the Boolean variables, represents AND operation, + represents OR operation, represents NOT operation.

**AND operation:**

AND operation produces true output (1) only when all the inputs true and produces false output (0) when at least one input is false. AND gate is used for AND operation. are

Algebraic expression: X-A.B, where A and B are inputs, X is output and . represents AND operation.

**Truth table:**

Inputs | Output | |

A | B | X = A.B |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

**2. Construct the truth table of the AND & OR operations of Boolean algebra.**

**AND operation:**

AND operation produces true output (1) only when all the inputs are true and produces false output (0) when at least one input is false. AND gate is used for AND operation.

Algebraic expression: X=A.B, where A and B are inputs, X is output and . represents AND operation.

**Truth table:**

Inputs | Output | |

A | B | X = A.B |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

**OR operation:**

OR operation produces true output (1) when at least one input is true and produces false output (0) only when all the inputs are false. OR gate is used for OR operation

Algebraic expression: X=A+B, where A and B are inputs, X is output and + represents OR operation.

**Truth table:**

Inputs | Output | |

A | B | X= A+ B |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

**3. Write truth table for NAND operation of Boolean algebra.**

**NAND operation:**

NAND operation produces true output (1) when at least one input if false and produces false (0) output when all the inputs are true. It is the combination of NOT operation and AND operation. NAND gate is used for NAND operation.

Algebraic expression: X=(A.B)’, where A and B are inputs, X is output.

**Truth table:**

Inputs | Output | |

A | B | X = (A.B)¹ |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

**4. Write truth table for NOR operation of Boolean algebra. [5]**

**NOR operation:**

NOR operation produces true output (1) only when all the inputs are false and produces false (0) output when any one input is true. It is the combination of NOT operation and OR operation. NOR gate is used for NOR operation.

Algebraic expression: X=(A+B)’, where A and B are inputs, X is output.

**Truth table:**

Inputs | Output | |

A | B | X = (A + B)’ |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

**1. What is Boolean algebra? Describe AND gate, OR gate and NOT gate and NAND gate with gate symbol and Truth Table. **

**Boolean Algebra**

Boolean algebra is the algebra of logic. It is a two valued system that represents Boolean variables and Boolean operations. It is introduced by George Boole. It is used for designing digital electronic circuits.

**AND Gate**

AND gate is an electronic circuit, which produces true output (1) only when all the inputs are true and produces false output (0) when at least one input is false.

Algebraic expression: X=A.B, where A and B are inputs, X is output and represents AND operation.

**OR Gate**

OR gate is an electronic circuit, which produces true output (1) when at least one input is true and produces false output (0) only when all the inputs are false.

Algebraic expression: X=A+B, where A and B are inputs; X is output and + represents OR operation.

**NOT Gate**

NOT gate is an electronic circuit, which produces true output (1) when the input is false (0) and vice-versa. It inverts the input. Algebraic expression: X=A’, where A is input, X is output.

**NAND Gate**

NAND gate is an electronic circuit, which produces true output (1) when at least one input is false and produces false (0) output when all the inputs are true. It is the combination of NOT gate and AND gate. Algebraic expression: X=(A.B)’, where A and B are inputs, X is output.

**2. Describe any five with a truth table and gate symbol.**

Different logic gates are as follows:

**AND Gate**

AND gate is an electronic circuit, which produces true output (1) only when all the inputs are true and produces false output (0) when at least one input is false.

Algebraic expression: X=A.B, where A and B are inputs, X is output and represents AND operation.

**OR Gate**

OR gate is an electronic circuit, which produces true output (1) when at least one input is true and produces false output (0) only when all the inputs are false.

Algebraic expression: X=A+B, where A and B are inputs; X is output and + represents OR operation.

**NOT Gate**

NOT gate is an electronic circuit, which produces true output (1) when the input is false (0) and vice-versa. It inverts the input. Algebraic expression: X=A’, where A is input, X is output.

**NAND Gate**

NAND gate is an electronic circuit, which produces true output (1) when at least one input is false and produces false (0) output when all the inputs are true. It is the combination of NOT gate and AND gate. Algebraic expression: X=(A.B)’, where A and B are inputs, X is output.

**NOR gate:**

NOR gate is an electronic circuit, which produces true output (1) only when all the inputs are false and produces false (0) output when any one input is true. It is the combination of NOT gate and OR gate.

Algebraic expression: X= (A+B)’, where A and B are inputs, X is output.

**3. What is logic gate? Describe any four logic gates with a truth table and gate symbol.**

**Logic Gate**

Logic gate is an electronic circuit that operates on one or more input signals to produce an output signal. It is used for designing digital electronic circuits. Each gate has its specific function and symbol. Different logic gates used are: AND gate, OR gate, NOT gate, NAND gate, NOR gate, XOR gate and XNOR gate.

Different logic gates are as follows:

**AND Gate**

AND gate is an electronic circuit, which produces true output (1) only when all the inputs are true and produces false output (0) when at least one input is false.

Algebraic expression: X=A.B, where A and B are inputs, X is output and represents AND operation.

**OR Gate**

OR gate is an electronic circuit, which produces true output (1) when at least one input is true and produces false output (0) only when all the inputs are false.

Algebraic expression: X=A+B, where A and B are inputs; X is output and + represents OR operation.

**NOT Gate**

NOT gate is an electronic circuit, which produces true output (1) when the input is false (0) and vice-versa. It inverts the input. Algebraic expression: X=A’, where A is input, X is output.

NAND Gate

NAND gate is an electronic circuit, which produces true output (1) when at least one input is false and produces false (0) output when all the inputs are true. It is the combination of NOT gate and AND gate. Algebraic expression: X=(A.B)’, where A and B are inputs, X is output.