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.