Question

A) You are given circuit as shown in figure, which consist of NAND gates. Identify the logic operation carried out by the circuit.

B) You are given circuit as shown in figure, which consist of NAND gates. Identify the logic operation carried out by the circuit.

Answer 1

A) Given, input for the circuit, A and B.
Output for the circuit, Y.
Output of the first NAND gate, $X=\overline{A.B}$
This output X act as input for the next NAND gate,
So, output of the combination,
$Y=\overline{\overline{A.B}.\overline{A.B}}$
$Y=\overline{\overline{A.B}}+\overline{\overline{A.B}}$
$Y=A.B$
$\begin{array}{cc}\text{INPUTS}& OUTPUT\\ AB& Y\\ 00& 0\\ 01& 0\\ 10& 0\\ 11& 1\end{array}$
This is the logic operation for AND gate.
Final answer: AND gate.

B) A is input to the upper NAND gate output of whose goes to the rightmost NAND gate. Also, B is input to the lower NAND gate whose output goes to the rightmost NAND gate.
Output of the first NAND gate,
$Y_1=\overline{A}$
Output of the second NAND gate,
$Y_2=\overline{B}$
So, output of the combination,
$Y=\overline{\overline{A}.\overline{B}}$
$Y=\overline{\overline{A}}+\overline{\overline{B}}$
$Y=A+B$
$\begin{array}{cc}\text{INPUTS}& OUTPUT\\ AB& Y\\ 00& 0\\ 01& 1\\ 10& 1\\ 11& 1\end{array}$

This is the logic operation for OR gate.
Final answer: OR gate.