Logic Gates

Logic Gates

Overview

Logic gates are the fundamental building blocks of digital circuits. They perform basic logical functions such as AND, OR, NOT, NAND, NOR, XOR, and XNOR. These gates implement Boolean functions and form the basis for complex digital systems.

Detailed Explanation

Basic Logic Gates

1. AND Gate:
   - Function: Output is HIGH only when all inputs are HIGH.
   - Truth Table:
     A B | Y
     0 0 | 0
     0 1 | 0
     1 0 | 0
     1 1 | 1

2. OR Gate:
   - Function: Output is HIGH if any input is HIGH.
   - Truth Table:
     A B | Y
     0 0 | 0
     0 1 | 1
     1 0 | 1
     1 1 | 1

3. NOT Gate (Inverter):
   - Function: Outputs the complement of the input.
   - Truth Table:
     A | Y
     0 | 1
     1 | 0

4. NAND Gate:
   - Function: Inverted AND.
   - Truth Table: Complement of AND.

5. NOR Gate:
   - Function: Inverted OR.
   - Truth Table: Complement of OR.

6. XOR Gate:
   - Function: Output is HIGH when inputs differ.
   - Truth Table:
     A B | Y
     0 0 | 0
     0 1 | 1
     1 0 | 1
     1 1 | 0

7. XNOR Gate:
   - Function: Output is HIGH when inputs are the same.
   - Truth Table: Complement of XOR.

Applications

- Forming arithmetic circuits (e.g., adders, subtractors)
- Designing comparators and decision circuits
- Constructing complex logic functions

Practice Problems

  1. Draw the symbol and truth table for each basic gate.
  2. Implement a NOT gate using only NAND gates.
  3. Design an XOR gate circuit using only NAND gates.

References

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