Understanding 2-Bit Multiplier Circuits

Sep 8, 2024

2-Bit Multiplier Circuit Lecture Notes

Introduction

  • Explanation of a 2-bit multiplier circuit.
  • Used for multiplying two 2-bit numbers.

Components of the Multiplier

  • Inputs:
    • A (2 bits): A1 (MSB), A0 (LSB)
    • B (2 bits): B1 (MSB), B0 (LSB)
  • Output:
    • P (Product, a 4-bit number): P3, P2, P1, P0

Multiplication Process

  1. Understanding the Inputs:

    • Multiply A (A1A0) by B (B1B0).
    • Process mirrors decimal multiplication but in binary.
  2. Steps to Calculate P0, P1, P2, P3:

    • Step 1: Multiply A0 by B0 → Result = A0B0 (P0).
    • Step 2: Multiply A1 by B0 → Result = A1B0.
    • Step 3: Multiply B1 by A0 → Result = A0B1.
    • Step 4: Multiply A1 by B1 → Result = A1B1.
  3. Weighting System:

    • Each result has a corresponding weight:
      • P0 = A0B0 (weight 2^0)
      • P1 = A1B0 + A0B1 (weight 2^1)
      • P2 = A1B1 + C1 (weight 2^2)
      • P3 = C2 (weight 2^3)
  4. Adding Results:

    • Sum results column-wise:
      • P0 = A0B0
      • P1 = A1B0 + A0B1 + carry C1
      • P2 = A1B1 + C1 + carry C2
      • P3 = C2

Half Adder Concept

  • Utilize half adders for addition of products:
    • Sum: x XOR y
    • Carry: x AND y

Circuit Implementation

  • Components Needed:
    • 4 AND gates for calculations
    • 2 XOR gates for sum calculations

Example Implementation:

  • Given Example
    • A = 11 (3 in decimal)
    • B = 10 (2 in decimal)
  • Calculating Product:
    • 0 (A0B0)
    • 0 (A1B0)
    • 1 (A0B1)
    • 1 (A1B1)
  • Final Binary Result:
    • 0110 = 6 in decimal (Correct result)

Conclusion

  • The circuit functions correctly for 2-bit numbers.
  • The same technique can be extended to create a 4-bit multiplier.