Chapter 4, Problem 37E

Explanation of Solution

Three ways to represent a AND gate:

• A gate is a device which is used to perform the basic logical operation.
• It accepts one or more input signals and produces the single output signal.
• It contains the following three types of methods to represent the processing of gates:
  • Boolean expressions
  • Logic diagrams
  • Truth tables
• It contains several types of gates. The most common types are:
  • NOT gate
  • AND gate
  • OR gate
  • XOR gate
  • NAND gate
  • NOR gate
• AND gate:
  • An AND gate is represented in three ways:
  • The “Boolean expression” for AND gate:
    • The AND operation is expressed using the “.” dot operator or “*” asterisk operator.

      $\text{X = A }\cdot \text{ B}$     or      $\text{X = A * B}$

  Where, A and B are the inputs and X is the output.

• The “logic diagram” for AND gate:
  • It takes two inputs and generates a single output:

Where, A and B are the inputs and X is the output