Binary Subtraction

Binary subtraction: a reliable method

Binary subtraction works like decimal subtraction, but each digit can only be 0 or 1. The main challenge is borrowing, because sometimes you need to subtract 1 from 0.

1) Subtract from right to left

Start with the least significant bit (the rightmost digit). For each column:

• 1 − 0 = 1
• 1 − 1 = 0
• 0 − 0 = 0
• 0 − 1 requires a borrow

2) Borrow in binary

When you borrow in base 2, a 1 from the next column becomes 10 in the current column. So if a column is 0 − 1, borrow from the next available 1 to the left, turning that 1 into 0 and adding 2 to the current column.

If the next column is also 0, keep borrowing until you find a 1.

3) Simplify the final answer

After all columns are processed, remove any unnecessary leading zeros so the result is in simplest binary form.

4) Check your work

A good check is to add your answer to the number you subtracted. If the sum matches the original number, your subtraction is correct.

Example idea: if a column is impossible directly, borrow first, then subtract column by column until the full binary difference is complete.