Notes on Subtraction Circuits in Digital Electronics

Introduction to Subtraction Circuits

• Focus on digital circuits for subtraction following previous lessons on adder circuits.

Half Subtractor

• Definition: Combinational circuit that subtracts two bits.
• Outputs: Provides both difference and borrow outputs.
• Truth Table:
  • Inputs: A, B (2 inputs, 4 combinations)
  • Outputs when both A and B are zero: Difference = 0, Borrow = 0
  • Outputs when A = 0, B = 1: Difference = 1, Borrow = 1
  • Outputs when A = 1, B = 0: Difference = 1, Borrow = 0
  • Outputs when A = 1, B = 1: Difference = 0, Borrow = 0
• Boolean Expressions:
  • Difference (D) = A ⊕ B = A'B + AB'
  • Borrow (B_out) = A'B
• Logic Circuit:
  • Implemented using XOR gate for difference.
  • NOT gate to invert A, combined with AND gate for borrow.
• Use Case:
  • Suitable for subtraction of Least Significant Bits (LSBs) due to no incoming borrow.

Full Subtractor

• Definition: Combinational circuit for subtracting one bit including borrow input.
• Truth Table:
  • Inputs: A, B, Borrow (3 inputs, 8 combinations)
  • Outputs vary based on combinations providing difference and borrow values.
• Boolean Expressions:
  • Difference = A ⊕ B ⊕ Bin
  • Borrow (B_out) = A'B + Bin(A ⊕ B)'
• Logic Circuit:
  • Uses XOR gates for difference output.
  • AND, NOT, and OR gates used to construct the borrow expression.
• Design Concept:
  • Can be built using two half subtractors and an OR gate.

Practical Application

• Building a Full Subtractor:
  • Use half subtractor for initial subtraction.
  • Chain another half subtractor for additional inputs.
  • Logic OR gate combines outputs for the final borrow.
• Scaling:
  • To perform subtraction for N-bit numbers, N full subtractor blocks are needed.
• Upcoming lessons will cover designing N-bit subtractors and using adder circuits for subtraction.

Conclusion

• Overview of half and full subtractors provided.
• Encouragement to engage with tutorial content through comments and interaction.

Additional Notes

• The video emphasizes understanding through Boolean algebra and logic circuit design.