Mathematics
July 22, 2026 · 10 min read
Binary Subtraction: Borrow Propagation and Two's Complement
Master binary subtraction with borrow propagation, two's complement method, and step-by-step worked examples.
Try the free calculator
Put these formulas into practice with our instant, step-by-step Binary Subtraction Calculator.
Binary subtraction subtracts two binary numbers with borrow propagation. The rules are: 0-0=0, 1-0=1, 1-1=0, 0-1=1 (borrow 1). In hardware, subtraction is performed using two\'s complement addition.
Key Takeaway
Binary subtraction uses borrow propagation. Hardware implements it as A + (two\'s complement of B) using only an adder circuit.
1. Direct Subtraction
- 0 - 0 = 0
- 1 - 0 = 1
- 1 - 1 = 0
- 0 - 1 = 1 (borrow from next column)
2. Two\'s Complement Method
A - B = A + (complement of B) + 1. Find two\'s complement by inverting all bits and adding 1. This allows subtraction using the same adder circuit as addition.
© 2026 Calculator Archive.