Question

Write the logic symbols and prepare the truth tables of the following gates.
(i) AND
(ii) NOR.

Answer 1

(i) AND Gate: A digital circuit in which there are two or more inputs and a single output and its output is $1$ when both the inputs are $1$.

The symbol of an AND gate is which A and B are inputs and Y is output.

By deifinition, when

$A=B=1,thenY=1$

Truth Table of AND Gate:

Input Input Output

A B Y

$0$ $0$ $0$

$1$ $0$ $0$

$0$ $1$ $0$

$1$ $1$ $1$

To obtain NOR gate by NAND and NOT gates- We can obtain NOR gate by using three NOT gates and NAND gate as shown in figure.

Boolean formula: $Y=\overline{Y^{\prime }}=\overline{\overrightarrow{A}\cdot \overrightarrow{B}}=\overline{A+B}$(By De-Morgan's law)

Truth table:

Input Input Output Output Output Output

A B $\overline{A}$ $\overline{B}$ $Y^{\prime }=A+B$ $Y=\overline{A+B}$

$0$ $0$ $1$ $1$ $0$ $1$

$1$ $0$ $0$ $1$ $1$ $0$

$0$ $1$ $1$ $0$ $1$ $0$

$1$ $1$ $0$ $0$ $1$ $0$