Question

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

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

Answer 1

A) Step 1: Find output for the given circuit.
Given, input for the circuit, = A and A
Output of the circuit, = Y
The given gate is NOR gate.
So, output of the circuit,
$Y=\overline{A+A}$
$Y=\overline{A}.\overline{A}$
$Y=\overline{A}$
This is the logic operation for NOT gate.

Step 2: Write truth table for the given circuit.
$\begin{array}{cc}\text{INPUTS (A)}& \text{OUTPUT}(Y=\overline{A})\\ 0& 1\\ 1& 0\end{array}$

Final answer : NOT gate.

B) Step 1: Find output for the given circuit.
Given, input for the circuit, =A and B
Output of the circuit, = Y
In the given circuit first two gates are NOR gates.
Output of the first two gate are $\overline{A}$ and $\overline{B}$ and this will be input for the right most gate. So, the output of the circuit,
$Y=\overline{\overline{A}+\overline{B}}$
$Y=\overline{\overline{A}}.\overline{\overline{B}}$
$Y=A.B$
This is the logic operation for AND gate.

Step 2: Write truth table for the given circuit.

$\begin{array}{ccc}\text{Input (A)}& \text{Input (B)}& \text{Output}(Y=A.B)\\ 0& 0& 0\\ 0& 1& 0\\ 1& 0& 0\\ 1& 1& 1\end{array}$
Final answer: AND gate.