Question

You are given the two circuits as shown in Fig. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND gate.

Answer 1

(a) The left half acts as NOR gate and the right half as NOT gate.

Use the truth table :

A	B	C	D	Y
0	0	0	1	0
0	1	1	0	1
1	0	1	0	1
1	1	1	0	1

Output from left half for inputs A and B is $\overline{A+B}$

This output is fed in the right half to produce $\overline{\overline{A+B}}=A+B$

Hence the combination acts as OR gate.

(b) The two left halves act as NOT gates.

A	B	$\overline{A}$	$\overline{B}$	C	Y
0	0	1	1	1	0
0	1	1	0	1	0
1	0	0	1	1	0
1	1	0	0	0	1

Thus the outputs from the two gates are $\overline{A}$ and $\overline{B}$

They are fed into the NOR gate.

Thus $Y=\overline{\overline{A}+\overline{B}}=\overline{\overline{A}}.\overline{\overline{B}}=A.B$

Hence the combination acts as AND gate.