Binary Calculator · Practical guide
Binary Subtraction Calculator with Steps
Borrowing in binary works like decimal, except you borrow 2 instead of 10.
At a glance
The Subtraction Rules
Binary subtraction has four facts: 0 − 0 = 0, 1 − 0 = 1, 1 − 1 = 0, and 0 − 1 = 1 after borrowing. When you borrow, the 1 you take from the next column is worth 2 in the current column — the binary version of borrowing 10 in decimal.
Interactive tool
Binary Calculator
Enter your own values, then compare the result with the examples below.
Result
Worked Example: 1101 − 0110
- Column 1 (rightmost): 1 − 0 = 1
- Column 2: 0 − 1 needs a borrow. Column 3 holds 0, so the borrow cascades from column 4: its 1 becomes 0, column 3 receives 2 and relends 1, leaving column 2 with 2 − 1 = 1
- Column 3: after lending, it holds 1, so 1 − 1 = 0
- Column 4: after lending, it holds 0, so 0 − 0 = 0
Result: 1101 − 0110 = 0111, written as 111.
Verify in Decimal
1101 is 13 and 0110 is 6, and 13 − 6 = 7. Binary 111 = 4 + 2 + 1 = 7, confirming the answer. The calculator reports the result in binary, decimal, and hexadecimal (0x7) with the decimal step shown, so hand work is easy to audit.
Subtracting a Larger Number
If the second number is larger, the result is negative: 0110 − 1101 = -111 (6 − 13 = −7). The tool shows the minus sign in both binary and decimal output, so order matters — enter the larger number first if you want a positive result.
Frequently Asked Questions
How is binary borrowing different from decimal?
The mechanics are identical except the borrowed unit is worth 2 instead of 10, because each column is a power of 2.
What is two's complement subtraction?
It is how computers actually subtract: flip the bits of the subtrahend, add 1, then add. 13 − 6 becomes 13 + (−6 in two's complement), turning subtraction into addition.
Why does the calculator show a steps line?
The steps line restates the operation in decimal (for example, 13 − 6 = 7) and then the binary conversion, so you can confirm the result against hand work.
Can I subtract more than two binary numbers at once?
The tool handles two operands at a time. For longer chains, subtract pairwise and feed each result into the next step.