Logic Gates Basics

Logic Gates

Definition

• A logic gate is an electronic circuit that performs a logical operation on one or more input signals, producing an output signal based on a set of rules or logic functions.

Types of Logic Gates

• AND Gate:
  • Produces an output of 1 only if all inputs are 1.
  • Truth table:
    • 0 0 → 0
    • 0 1 → 0
    • 1 0 → 0
    • 1 1 → 1
• OR Gate:
  • Produces an output of 1 if at least one input is 1.
  • Truth table:
    • 0 0 → 0
    • 0 1 → 1
    • 1 0 → 1
    • 1 1 → 1
• NOT Gate (Inverter):
  • Produces an output that is the opposite of the input.
  • Truth table:
    • 0 → 1
    • 1 → 0
• NAND Gate:
  • Produces an output of 1 only if none of the inputs are 1.
  • Truth table:
    • 0 0 → 1
    • 0 1 → 1
    • 1 0 → 1
    • 1 1 → 0
• NOR Gate:
  • Produces an output of 1 if all inputs are 0.
  • Truth table:
    • 0 0 → 1
    • 0 1 → 0
    • 1 0 → 0
    • 1 1 → 0
• XOR Gate:
  • Produces an output of 1 if the inputs are different.
  • Truth table:
    • 0 0 → 0
    • 0 1 → 1
    • 1 0 → 1
    • 1 1 → 0
• XNOR Gate:
  • Produces an output of 1 if the inputs are the same.
  • Truth table:
    • 0 0 → 1
    • 0 1 → 0
    • 1 0 → 0
    • 1 1 → 1

Universal Gates

• NAND Gate: Can be used to implement any other logic gate.
• NOR Gate: Can also be used to implement any other logic gate.

Applications

• Digital circuits and electronics
• Computer architecture and design
• Boolean algebra and propositional logic
• Cryptography and security systems

Logic Gates

Definition

• A logic gate is an electronic circuit that performs a logical operation on one or more input signals, producing an output signal based on a set of rules or logic functions.

Types of Logic Gates

AND Gate

• Produces an output of 1 only if all inputs are 1.
• Truth table: 0 0 → 0, 0 1 → 0, 1 0 → 0, 1 1 → 1

OR Gate

• Produces an output of 1 if at least one input is 1.
• Truth table: 0 0 → 0, 0 1 → 1, 1 0 → 1, 1 1 → 1

NOT Gate (Inverter)

• Produces an output that is the opposite of the input.
• Truth table: 0 → 1, 1 → 0

NAND Gate

• Produces an output of 1 only if none of the inputs are 1.
• Truth table: 0 0 → 1, 0 1 → 1, 1 0 → 1, 1 1 → 0

NOR Gate

• Produces an output of 1 if all inputs are 0.
• Truth table: 0 0 → 1, 0 1 → 0, 1 0 → 0, 1 1 → 0

XOR Gate

• Produces an output of 1 if the inputs are different.
• Truth table: 0 0 → 0, 0 1 → 1, 1 0 → 1, 1 1 → 0

XNOR Gate

• Produces an output of 1 if the inputs are the same.
• Truth table: 0 0 → 1, 0 1 → 0, 1 0 → 0, 1 1 → 1

Universal Gates

• NAND Gate can be used to implement any other logic gate.
• NOR Gate can also be used to implement any other logic gate.

Applications

• Used in digital circuits and electronics
• Used in computer architecture and design
• Applied to Boolean algebra and propositional logic
• Used in cryptography and security systems

Logic Gates

AND Gates

• Perform logical conjunction, where output is true only if all inputs are true
• Truth table illustrates the four possible input combinations:
  • Both inputs are 0, output is 0
  • One input is 0, one input is 1, output is 0
  • One input is 1, one input is 0, output is 0
  • Both inputs are 1, output is 1
• Represented by the ∧ symbol

OR Gates

• Perform logical disjunction, where output is true if at least one input is true
• Truth table illustrates the four possible input combinations:
  • Both inputs are 0, output is 0
  • One input is 0, one input is 1, output is 1
  • One input is 1, one input is 0, output is 1
  • Both inputs are 1, output is 1
• Represented by the ∨ symbol

NOT Gates

• Perform logical negation, where output is the inverse of the input
• Truth table illustrates the two possible input combinations:
  • Input is 0, output is 1
  • Input is 1, output is 0
• Represented by the ¬ symbol

NAND Gates

• Combination of AND and NOT gates
• Output is true only if none of the inputs are true
• Truth table illustrates the four possible input combinations:
  • Both inputs are 0, output is 1
  • One input is 0, one input is 1, output is 1
  • One input is 1, one input is 0, output is 1
  • Both inputs are 1, output is 0
• Represented by the ∧ symbol with a negation bar above

De Morgan's Laws

• Two rules for simplifying digital circuits
• First law: ¬(A ∧ B) is equivalent to ¬A ∨ ¬B
• Second law: ¬(A ∨ B) is equivalent to ¬A ∧ ¬B
• Allow for the conversion of AND and OR gates to their NAND and NOR equivalents, respectively