Boolean Logic

Boolean logic is the foundation of digital circuits. It deals with logical operations that can have only two possible outcomes: true (1) or false (0). These outcomes are represented by Boolean values.

Basic Boolean Operators

There are three basic Boolean operators:

• AND (≈): The output is true only if both inputs are true.
• OR (+): The output is true if at least one input is true.
• NOT (~): The output is the opposite of the input (true becomes false, and false becomes true).

Truth Tables

A truth table shows all possible input combinations and their corresponding output for a Boolean expression.

AND Truth Table

Input A	Input B	Output (A AND B)
0	0	0
0	1	0
1	0	0
1	1	1

OR Truth Table

Input A	Input B	Output (A OR B)
0	0	0
0	1	1
1	0	1
1	1	1

NOT Truth Table

Input	Output (NOT Input)
0	1
1	0

Logic Gates

Logic gates are electronic circuits that implement Boolean logic operations.

AND Gate

An AND gate has two or more inputs and one output. The output is high (1) only if all inputs are high (1).

OR Gate

An OR gate has two or more inputs and one output. The output is high (1) if at least one input is high (1).

NOT Gate

A NOT gate has one input and one output. The output is the inverse of the input. If the input is high (1), the output is low (0), and vice versa.

Creating Logic Circuits

Logic circuits are constructed by combining logic gates. A problem statement, logic expression, or truth table can be used to design a logic circuit.

Example: Implementing a simple logic expression

Consider the Boolean expression: $Y = (A \text{ AND } B) \text{ OR } C$

This expression can be implemented using logic gates as follows:

1. An AND gate with inputs A and B.
2. An OR gate with inputs from the AND gate (output) and C.

Practice

You should practice designing logic circuits from problem statements, logic expressions, and truth tables to master the concept of Boolean logic.