Chapter 4, Problem 73E

Explanation of Solution

Boolean expression for XOR gate using the other operators:

XOR gate:

• An XOR gate accepts two inputs and produces a single output.
• When both the inputs are same, then the output is 0. Otherwise, the output is 1.
• The “Boolean expression” for XOR gate:
  • The XOR operation is expressed by using the “$\oplus$” symbol.

  $\text{X = A }\oplus \text{ B}$

  Where “A” and “B” are the inputs and “X” is the output.

• Truth table for the above expression for XOR gate:

A	B	X = A$\oplus$B
0	0	0
0	1	1
1	0	1
1	1	0

Boolean expression for XOR gate using “AND” and “OR” gate:

• The Boolean expression for XOR gate is expressed using the “AND” gate and “OR” gate operators:

  $\text{X = A}\cdot \overline{\text{B}}\text{ + }\overline{\text{A}}\cdot \text{B}$

Where “A” and “B” are the inputs and “X” is the output.

• Truth table for the above expression for XOR gate:

A

B

$\overline{A}$

$\overline{B}$

$A\cdot \overline{B}$

$\overline{A}\cdot B$

$X=A\cdot \overline{B}+\overline{A}\cdot B$