In-depth Notes on Logic Gates

Logic Gates Overview

  • Logic gates are the fundamental building blocks of digital electronics, performing basic logical functions.
  • Events in digital logic are represented as binary states: '0' (off) and '1' (on).

Positive and Negative Logic Systems

Positive Logic
  • In a positive logic system:
    • Logical True (1): High voltage (typically +5V).
    • Logical False (0): Low voltage (typically 0V).
    • Example:
    • Switch ON: Bulb lights up (5V)
    • Switch OFF: Bulb unlit (0V)
Negative Logic
  • In a negative logic system:
    • Logical True (1): Low voltage (0 to 0.4V)
    • Logical False (0): High voltage (2.4V or higher, commonly up to 5V).

Basic Logic Gates

  • The seven basic logic gates include:
    1. Inverter (NOT)
    2. AND
    3. NAND
    4. OR
    5. NOR
    6. Exclusive-OR (XOR)
    7. Exclusive-NOR (XNOR)
  • Each gate has multiple inputs but produces a single output.

Truth Tables

  • A truth table outlines every possible input combination and corresponding output.
  • The number of input combinations is $2^N$, where $N$ is the number of inputs.
Example Truth Table (AND Gate)
AB*Y = A * B*
000
010
100
111

AND Gate

  • The output is Logic 1 when all inputs are Logic 1.
  • The Boolean equation:
    • For 2-input: Y = A ullet B
    • For 3-input: Y = A ullet B ullet C
AND Gate Truth Table
AB*Y = A * B*
000
010
100
111

OR Gate

  • The output is Logic 1 when at least one input is Logic 1.
  • The Boolean equation:
    • For 2-input: Y=A+BY = A + B
    • For 3-input: Y=A+B+CY = A + B + C
OR Gate Truth Table
ABY = A + B
000
011
101
111

Inverter (NOT) Gate

  • The output is the inverse of the input.
  • The Boolean equation: Y=<br/>egAY = <br /> eg A.

NAND Gate

  • The output is Logic 0 when all inputs are Logic 1.
  • The Boolean equation:
    • For 2-input: Y =
      eg (A ullet B)
NAND Gate Truth Table
AB*Y = A * B*
001
011
101
110

NOR Gate

  • The output is Logic 1 when all inputs are Logic 0.
  • The Boolean equation:
    • For 2-input: Y=<br/>eg(A+B)Y = <br /> eg (A + B).
NOR Gate Truth Table
ABY = A + B
001
010
100
110

Exclusive-OR (XOR) Gate

  • The output is Logic 1 when the inputs are different.
  • The Boolean equation:
    • For 2-input: Y = A igoplus B.
XOR Gate Truth Table
ABY = A \oplus B
000
011
101
110

Exclusive-NOR (XNOR) Gate

  • The output is Logic 1 when the inputs are the same.
  • The Boolean equation:
    • For 2-input: Y =
      eg (A igoplus B).

Universality of NAND and NOR Gates

  • Both NAND and NOR gates can be used to construct any other logic gate in circuits.
  • This flexibility makes them essential in digital circuit design.

Alternate Gate Symbols

  • Alternate symbols are used in schematics for gates, incorporating "bubbles" to represent negation, as per DeMorgan's Theorem.
  • These alternate symbols facilitate circuit analysis.