Lecture on Logic Gate Diagrams and Truth Tables

Overview

• Discussion on logic gate diagrams and truth tables.
• Importance for exams involving Boolean operators.

Logic Gates

NOT Gate

• Symbol: Triangle with a circle at the point.
• Function: Reverses the input.
  • Input 0 (false) results in output 1 (true).
  • Input 1 (true) results in output 0 (false).
• Truth Table:
  • 0 → 1
  • 1 → 0

AND Gate

• Symbol: D-shape.
• Function: Outputs true if both inputs are true.
  • Inputs both 0 → Output 0
  • Inputs one 0, one 1 → Output 0
  • Inputs both 1 → Output 1
• Truth Table:
  • 00 → 0
  • 01 → 0
  • 10 → 0
  • 11 → 1

OR Gate

• Symbol: Curved shape fitting around 'O'.
• Function: Outputs true if at least one input is true.
  • Inputs both 0 → Output 0
  • Any other case → Output 1
• Truth Table:
  • 00 → 0
  • 01 → 1
  • 10 → 1
  • 11 → 1

XOR Gate (Exclusive OR)

• Symbol: OR with an additional line.
• Function: Outputs true if exactly one input is true.
  • Both inputs same → Output 0
  • One input different → Output 1
• Truth Table:
  • 00 → 0
  • 01 → 1
  • 10 → 1
  • 11 → 0

Constructing Truth Tables and Boolean Expressions

• Boolean Expressions: Represent logic in algebraic form.
• Truth Tables: List all possible input combinations and their outputs.
• Circuit Diagrams: Visual representation of logic operations.
• Conversion Skills: Important for exams to convert between expressions, tables, and diagrams.

Example: Logic Diagram to Truth Table

• Inputs: A, B, C
• Steps:
  1. List all combinations of inputs (000 to 111).
  2. Determine interim outputs and final outputs using logic gates.
  3. Complete truth table for OR and AND gates.

Example: Constructing Boolean Expressions

• Start with final output (e.g., D = A and B or not C).
• Use symbols for operations (AND: ∧, OR: ∨, NOT: ¬).

Advanced Logic Gates

NAND Gate

• Symbol: AND with a circle.
• Function: Reverses output of an AND gate.

NOR Gate

• Symbol: OR with a circle.

• Function: Reverses output of an OR gate.

• Universal Gates: NAND and NOR can construct any other logic gate.

Conclusion

• Essential understanding of logic gates, truth tables, and Boolean expressions for exams and further studies in logic and computing.