Write the truth table for the circuits given in following figure consisting of NOR gates only. Identify the logic operations (OR, AND, NOT) performed by the two circuits.

**(a)**

**(b)**

#### Solution

**(a) **A acts as the two inputs of the NOR gate and Y is the output, as shown in the following figure. Hence, the output of the circuit is `bar(A+A)`.

The truth table for the same is given as:

A |
Y`(=bar"A")` |

0 | 1 |

1 | 0 |

This is the truth table of a NOT gate. Hence, this circuit functions as a NOT gate.

**(b) **A and B are the inputs and Y is the output of the given circuit. By using the result obtained in solution **(a)**, we can infer that the outputs of the first two NOR gates are `barA` and `barB` as shown in the following figure.

`bar"A" and bar "B"` are the inputs for the last NOR gate. Hence, the output for the circuit can be written as:

`"Y" = bar(bar"A" + bar"B") = bar(bar"A") . bar(bar"B") = "A.B"`

The truth table for the same can be written as:

A |
B |
Y (=A⋅B) |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

This is the truth table of an AND gate. Hence, this circuit functions as an AND gate.