Last Updated on March 2, 2026 | 1 : 40 pm by Anas Brittany
Use this binary subtraction calculator to subtract one binary (base-2) number from another. Enter two binary values and the calculator will return the difference in binary and decimal. You can also view step-by-step borrowing to learn how binary subtraction works.
Binary Subtraction Calculator
What Is Binary Subtraction?
Binary subtraction is subtracting numbers written in base-2, where only the digits 0 and 1 are used. The process is similar to decimal subtraction but uses base-2 borrowing instead of base-10.
Binary subtraction is widely used in computer systems, digital electronics, and low-level programming.
Binary Subtraction Rules
There are four basic subtraction cases:
- 0 − 0 = 0
- 1 − 0 = 1
- 1 − 1 = 0
- 0 − 1 = borrow → result becomes 1 (because 10₂ − 1 = 1)
When borrowing in binary, you borrow 2 (10 in binary) instead of 10 as in decimal.
How Binary Borrowing Works
If the top bit is smaller than the bottom bit:
- Borrow from the next left position
- The borrowed value equals 2 in decimal (10 in binary)
- Add it to the current bit
- Continue subtracting
This is the same concept as decimal borrowing but uses base-2 place values.
Example: Binary Subtraction
A = 10110
B = 00101
Subtract from right to left, borrowing when needed:
10110
−00101
=10001
So the result is 10001 (binary).
Binary Subtraction vs Two’s Complement
Computers often perform subtraction using two’s complement addition instead of manual borrowing. However, the borrowing method shown here is easier for learning and manual calculations.
Frequently Asked Questions
Can the result be negative?
This calculator assumes A ≥ B. If the result would be negative, a two’s complement method is typically used in computing.
Why does borrowing add 2?
Binary is base-2, so each position represents a power of 2. Borrowing from the next position adds 2 to the current bit.
Where is binary subtraction used?
It is used in processors, digital circuits, computer arithmetic, and low-level programming.
Brittany Anas is a freelance lifestyle journalist and editorial writer with experience covering culture, food, lifestyle, entertainment, and evergreen guides for digital publications. Her writing focuses on clear research, approachable storytelling, and practical ideas designed for everyday readers.
On Fiestasline, Brittany contributes editorial content across lifestyle, ideas, food & drink, culture, and curated guides, helping readers discover inspiration that’s timely, accessible, and easy to enjoy.
