Understanding Binary Subtraction

Direct Borrow Rules

• 1 − 0 = 1
• 1 − 1 = 0
• 0 − 0 = 0
• 0 − 1 → borrow: becomes 2₁₀ → 10₂ − 1 = 1

When subtracting a larger bit from a smaller one (0 − 1), borrow 1 from higher-order bit (worth 10₂).

Two's Complement Subtraction

Instead of borrowing, you can convert the subtrahend using two’s complement (invert bits, add 1), then add to the minuend.

Example

1100 (minuend)
- 1011 (subtrahend)
────────────
  0011 (difference)
    

• 0 − 1 → borrow → becomes 10 − 1 = 1
• Borrow reduces higher bit accordingly
• Final difference: 0011

Binary subtraction is vital for low-level computing, ALU operations, and digital logic design.