📜 Lecture 2: Basic Gates

This lecture defines the fundamental and inverted logic gates, covering their symbols, Boolean expressions, and truth tables.

Key Concepts

• NOT Gate (Inverter)

  • Type: Unary (1 input).
  • Function: Inverts the input.
  • Expression: X = A' or X = A
  • Truth Table: 0 -> 1, 1 -> 0

• AND Gate

  • Type: Binary (2 or more inputs).
  • Function: Output is 1 if and only if ALL inputs are 1.
  • Expression: X = A · B
  • Truth Table (2-input): 1 only for A=1, B=1.
  • Truth Table (3-input): 1 only for A=1, B=1, C=1.

• OR Gate

  • Type: Binary (2 or more inputs).
  • Function: Output is 1 if EITHER or BOTH inputs are 1.
  • Expression: X = A + B
  • Truth Table (2-input): 0 only for A=0, B=0.
  • Truth Table (3-input): 0 only for A=0, B=0, C=0.

• XOR Gate (Exclusive-OR)

  • Type: Binary (2 or more inputs).
  • Function: Output is 1 if and only if the inputs are DIFFERENT.
  • Expression: X = A ⊕ B
  • Truth Table (2-input): 1 for A=0, B=1 and A=1, B=0.
  • Truth Table (3-input): Output is 1 if there is an odd number of 1s at the input (i.e., for 001, 010, 100, 111).

• Buffer

  • Function: Inverted NOT gate. The output is the same as the input (X = A). It is used to amplify or isolate signals.

• NAND Gate (Not-AND)

  • Function: An AND gate followed by a NOT. Output is 0 only when all inputs are 1.
  • Expression: X = (A · B)'

• NOR Gate (Not-OR)

  • Function: An OR gate followed by a NOT. Output is 1 only when all inputs are 0.
  • Expression: X = (A + B)'

• XNOR Gate (Exclusive-NOR)

  • Function: An XOR gate followed by a NOT. Output is 1 if and only if the inputs are the SAME.
  • Expression: X = (A ⊕ B)'

• Universal Gates:

  • A NAND gate with its inputs tied together (A connected to both) acts as a NOT gate.
  • This property makes NAND (and NOR) gates "universal," as they can be used to create any other gate.

• Circuit Analysis Example:

  • The lecture concludes by analyzing the circuit X = (A NAND B) AND (A OR B).
  • It shows the steps to find the final truth table by first finding the intermediate outputs (X1 = (A·B)' and X2 = A+B) and then AND-ing them together.
  • The final truth table for X is 0, 1, 1, 0, which is the same as an XOR gate.