Question

If A = 1, B = 0, then in terms of Boolean algebra, $A + \overline B$ equals to:
A) $A$
B) $B$
C) $\overline A$
D) $\overline {A + B}$

Answer 1

From the given equation, it can be seen that two gates have been used in the Boolean equation: NOT gate and OR gate. The most appropriate way to solve such a question is to make a truth table for the given equation. Also note that since particular values of $A$ and $B$ are given, there is no need to make the entire truth table. Just the one corresponding to these particular values.

Complete step by step solution:
Before we solve the Boolean equation, we should make ourselves familiar with the two gates present in the equation: NOT and OR gate.
1. NOT gate
NOT gate is a gate that inverts the input and returns the value as output. Therefore, if the input is high, output is low and when input is low, output is high.
The logic equation of NOT gate is as follows:
$Y = \overline A$
Where, $Y$ is the output and $A$ is the input.
Truth table of NOT Gate IS:

INPUT (A)	OUTPUT (Y)
1	0
0	1

2. OR gate
OR gate is a gate that gives positive output (high) when both the outputs are positive (high) or either of the outputs are positive (high). When both inputs are negative, then only it gives a negative (low) output.
The logic equation of OR gate is as follows:
$Y = A + B$
Where, $Y$ is the output and $A$ and $B$ are the input.
Truth table of OR gate IS:

INPUT 1 ( $A$ )	INPUT 2 ( $B$ )	OUTPUT ( $Y = A + B$ )
$0$	$0$	$0$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

The Boolean equation is $Y = A + \overline B$ . Therefore, the truth table will be

INPUT 1 ( $A$ )	INPUT 2 ( $B$ )	$\overline B$	$Y = A + \overline B$
$1$	$0$	$1$	$1$

In the given options;
A) $A = 1$
B) $B = 0$
C) $\overline A = 0$
D) $\overline {A + B} = \overline {1 + 0} = \overline 1 = 0$

Therefore, the correct option is (A), $A = 1$.

Note: In these types of questions, it is easier to draw the table to avoid any silly mistakes. Boolean algebra can be quite simple if done in a concise and schematic manner.