Math
Binary Calculator
Enter two binary numbers and choose an operation.
The calculator lines the digits up in columns exactly as you would on paper, marks every carry or borrow, lists each partial product for multiplication, and draws the long-division tableau for division. Every answer comes with its decimal, hexadecimal, and octal equivalent so you can check the work.
Digits 0 and 1 only. A leading minus sign is allowed; spaces or underscores can group bits (1011 0110).
Digits 0 and 1 only.
Try an example
Result
Binary result
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- Decimal check
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- Hexadecimal
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- Octal
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Student quick launch
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Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the binary calculator solves
Binary numbers use only the digits 0 and 1, and each place is worth twice the place to its right. Arithmetic works the same way as in decimal, except that you carry or borrow whenever a column reaches 2 instead of 10. This calculator performs the four operations on whole binary numbers of any length (negatives allowed with a minus sign) and shows the column-by-column work.
Binary arithmetic rules
| Operation | Rule | Example |
|---|---|---|
| Addition | 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1) | 1011 + 110 = 10001 |
| Subtraction | 0−0=0, 1−0=1, 1−1=0, 0−1 needs a borrow: 10−1=1 | 110010 − 1011 = 100111 |
| Multiplication | Copy the top number for each 1 in the multiplier, shifted left by its position; add the rows | 1011 × 101 = 110111 |
| Division | Bring bits down one at a time; write 1 when the divisor fits, subtract, and continue | 100010 ÷ 11 = 1011 R 1 |
How to use it
- Choose add, subtract, multiply, or divide.
- Type the two binary numbers using only 0 and 1. A leading 0b prefix, spaces, or underscores are fine.
- Put a minus sign in front of a number to make it negative; the work is done on the magnitudes and the sign is applied afterward.
- For division, set the number of fraction bits if you want the quotient continued past the binary point.
- Read the column grid: amber digits are carries or borrows, blue digits are the answer.
How to read the answer
The binary answer is shown first, then the same value in decimal, hexadecimal, and octal. The decimal check line converts both inputs to decimal and does the arithmetic there, so you can confirm that the binary result is right. Division shows the integer quotient with the remainder (R) and, when fraction bits are requested, the quotient continued as a binary fraction.
Common mistakes and edge cases
- Writing 1 + 1 = 2. In binary that column is 10: write 0 and carry the 1.
- Forgetting a chained carry: 1 + 1 + 1 = 11, so you write 1 and still carry 1.
- Borrowing from a 0: skip left to the nearest 1, turn it into 0, and every 0 you passed becomes 1.
- Subtracting a larger number from a smaller one gives a negative answer here; hardware would wrap around in two's complement instead.
- Dividing by zero is undefined, and the calculator says so rather than guessing.
- Fraction bits in division are truncated, not rounded, and repeating fractions never terminate (1 ÷ 11 = 0.010101…).
Worked examples
Addition with carries
1011 + 110
Binary result
10001
Subtraction with borrows
110010 − 1011
Binary result
100111
Negative difference
101 − 1101
Binary result
-1000
Multiplication
1011 × 101
Binary result
110111
Division with remainder
100010 ÷ 11
Binary result
1011 R 1
Division with fraction bits
1 ÷ 100 with 4 fraction bits
Binary result
0 R 1
Adding zero
0 + 0
Binary result
0
Invalid digit
102 + 1
Binary result
—
Division by zero
1010 ÷ 0
Binary result
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Frequently asked questions
How do you add binary numbers?+
Line the numbers up on the right and add each column from right to left. 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), and 1+1+1=11 (write 1, carry 1). The carry row in the grid shows where each carry lands.
How does borrowing work in binary subtraction?+
When a column has 0 on top and 1 below, borrow from the nearest 1 to the left. That 1 becomes 0, every 0 you skipped becomes 1, and the current column becomes 10 (two), so 10 − 1 = 1.
Why does binary multiplication only need copying and shifting?+
Each multiplier bit is either 0 or 1, so each partial product is either 0 or the top number shifted left by that bit's position. Adding the shifted copies gives the product, just like long multiplication in decimal.
What does R mean in the division result?+
R is the remainder. 100010 ÷ 11 = 1011 R 1 means 3 × 11 + 1 = 34 in decimal. Set fraction bits above 0 to continue the division past the binary point instead.
Can I enter negative binary numbers?+
Yes, put a minus sign in front (for example -1011). The calculator does the column work on the magnitudes and applies the sign rules afterward. For hardware-style negatives, use the two's complement calculator.
How big can the numbers be?+
Up to 200 bits each. The math is exact integer arithmetic, so long inputs never lose precision the way floating-point converters do.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026