Binary is the native language of computers, and while converting between binary and decimal is a solved problem — the base converter on this site does it — actually doing arithmetic in binary is a different skill, and a useful one for students, engineers and anyone learning how computers add. This calculator performs addition, subtraction, multiplication and division on binary numbers, showing both the binary result and its decimal equivalent, so you can check your hand-working against a trusted answer. It validates input strictly: only 0 and 1 are accepted, and anything else is flagged rather than silently interpreted. Whether you are studying two complement, checking a subnet calculation, or just curious how 1010 plus 0101 becomes 1111, this tool gives you the answer and the decimal cross-check in one step.
Quick Answer: Enter two binary numbers, choose add, subtract, multiply or divide, and get the binary result with its decimal equivalent.
Free Online Tool
Binary Calculator
How to Use the Binary Calculator
- Enter the first binary number using only 0 and 1.
- Enter the second binary number the same way.
- Choose the operation: add, subtract, multiply or divide.
- Press Calculate and read the binary result and decimal equivalent.
- Copy the result for your homework, notes or calculation.
Key Features
- All four operations on binary numbers
- Strict validation: only 0 and 1 accepted
- Decimal equivalent shown alongside every result
- Clear errors for invalid input and division by zero
- Free, instant and entirely in your browser
Best Practices and Tips
- Double-check results by converting to decimal: binary arithmetic errors are easy to make by hand.
- Remember that binary subtraction can go negative: this tool shows negative results in decimal and with a minus sign.
- Division in binary, as in decimal, can produce fractions: this tool shows the decimal result for clarity.
- For very long binary numbers, split them into groups of four digits while typing to avoid transcription slips.
- Use the calculator to verify hand-working when learning binary addition with carries.
Common Mistakes to Avoid
- Typing digits other than 0 and 1, which are not binary digits at all.
- Forgetting that leading zeros do not change a value: 0101 and 101 are the same number.
- Assuming binary division always gives a whole number: it does not, any more than decimal division does.
- Mixing up binary and decimal results when copying an answer into homework.
Frequently Asked Questions
How does binary addition work?
Like decimal addition, but with only two digits: 0 + 0 is 0, 0 + 1 and 1 + 0 are 1, and 1 + 1 is 0 with a carry of 1 to the next column. The carry rule is the whole trick, and it works exactly like carrying tens in decimal.
What is 1010 + 0101 in binary?
1111, which is 15 in decimal: 10 plus 5 equals 15. This calculator confirms it instantly, along with the decimal equivalents of both inputs.
Can binary numbers be negative?
In pure binary arithmetic, subtraction can produce a negative result, which this tool shows with a minus sign and its decimal value. In computer storage, negatives use two complement representation, which is a separate topic.
Why is the decimal equivalent shown?
Because most people verify binary work in decimal. Showing both lets you cross-check a binary result against familiar decimal arithmetic in one glance.
Is the binary calculator free?
Yes — free, unlimited and no sign-up required.