Boolean Logic

Boolean logic is the foundation of digital circuits and computer science. It deals with logical operations on binary values (0 and 1, representing 'false' and 'true' respectively). This section will cover the standard logic gates and their symbols.

Basic Boolean Operations

The fundamental Boolean operations are:

• AND: The output is 1 only if both inputs are 1.
• OR: The output is 1 if at least one input is 1.
• NOT: The output is the inverse of the input (1 becomes 0, and 0 becomes 1).

Logic Gate Symbols and Truth Tables

1. AND Gate

Symbol:

Truth Table:

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

Boolean Expression: $A \cdot B$ or $A \land B$

2. OR Gate

Symbol:

Truth Table:

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

Boolean Expression: $A + B$ or $A \lor B$

3. NOT Gate

Symbol:

Truth Table:

Input	Output (NOT Input)
0	1
1	0

Boolean Expression: $\overline{A}$ or $\neg A$

4. NAND Gate

Symbol:

Truth Table:

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

Boolean Expression: $\overline{A \cdot B}$ or $\neg (A \land B)$

5. NOR Gate

Symbol:

Truth Table:

Input A	Input B	Output (A NOR B)
0	0	1
0	1	0
1	0	0
1	1	0

Boolean Expression: $\overline{A + B}$ or $\neg (A \lor B)$

6. XOR Gate

Symbol:

Truth Table:

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

Boolean Expression: $A \oplus B$ or $A \land \neg B$ or $\neg A \land B$

Applications of Boolean Logic

Boolean logic is used extensively in:

• Digital circuit design (e.g., logic gates, flip-flops)
• Computer programming (e.g., conditional statements, loops)
• Database queries (e.g., using WHERE clauses with AND, OR, NOT)