About the Binary Calculator
Computers work in binary, and learning to calculate with it is a standard part of computing courses. This binary calculator adds, subtracts, multiplies and divides binary numbers of any length. Type the two numbers using only 0 and 1, pick the operation and read the answer in binary, grouped in fours for readability, with the same value in decimal and hexadecimal underneath. Division returns the whole-number quotient and the remainder, also in binary. Negative numbers are supported with a minus sign, so you can check homework, debug code or practise by hand and compare.
Updated October 2026
How to use the Binary Calculator
- 1Type the first binary number, using only 0 and 1.
- 2Choose add, subtract, multiply or divide.
- 3Type the second binary number.
- 4Read the result in binary, with decimal and hex versions.
- 5For division, check the remainder in the table.
Binary addition rules
- 0 + 0 = 0.
- 0 + 1 = 1.
- 1 + 0 = 1.
- 1 + 1 = 10 (write 0, carry 1).
- 1 + 1 + 1 = 11 (write 1, carry 1).
A worked example
Add 1011 (eleven) and 110 (six). Starting from the right: 1 + 0 = 1; 1 + 1 = 0 carry 1; 0 + 1 + carry 1 = 0 carry 1; 1 + carry 1 = 0 carry 1; the final carry gives 1. Reading the answer, you get 10001, which is 17 in decimal. The calculator shows the same result, with the decimal and hex forms to check your own working.
When you check homework, work out the sum by hand first, then confirm it here. Differences usually come from a dropped carry or a borrow in subtraction. For negative results, remember that computers store them in two's complement, which this calculator does not use: it writes a minus sign in front instead, as people do on paper. To see how a negative value would look in a fixed number of bits, use the Bitwise Calculator with the width you need.
Why binary matters
Every number in a computer is stored in binary. Learning how it adds and multiplies explains overflow, bit shifts and why a byte has 256 values. Addition and shifts are the building blocks of processors, and multiplication in hardware is built from shifted additions, just like the partial products you write out by hand.
Related tools
The Number Base Converter changes between binary, decimal, octal and hex, the Bitwise Calculator handles logic operations, the Binary Translator turns text into binary and back, and the Binary and Hex Calculator covers conversions between those two.
Features
- Add, subtract, multiply and divide
- Any length, using big-number arithmetic
- Negative numbers allowed
- Result in binary, decimal and hex
- Grouped in fours for easy reading
- Remainder shown for division
Frequently asked questions
How do I add binary numbers?
Add column by column from the right, as in decimal, but carry when you reach 2: 1 + 1 = 10, which is a 0 with a carry of 1. For 1011 + 110 you get 10001, which is 11 + 6 = 17.
How do I subtract binary numbers?
Subtract column by column and borrow from the next column when you need to. The calculator does it for you and shows a negative result with a minus sign, so 110 − 1011 is −101.
How do I multiply binary numbers?
Multiply like decimal long multiplication, but each partial product is either 0 or a shifted copy of the first number. 1011 × 110 is 1000010 (11 × 6 = 66).
How does binary division work?
It is long division with only 0 and 1 in the quotient. This calculator returns the whole-number quotient and the remainder, so 1011 ÷ 110 is 1 remainder 101, which is 11 ÷ 6 = 1 remainder 5.
Can I enter numbers with a 0b prefix or spaces?
Yes. A leading 0b and spaces or underscores between groups of digits are ignored, so 0b1011 and 1011 are the same, as are 1011 0110 and 10110110.
How is this different from the bitwise calculator?
Bitwise operations such as AND and XOR work on each bit separately within a fixed width. Binary arithmetic treats the digits as a number, with carrying and borrowing, and has no fixed width.