Binary maths without mistakes
Enter two binary numbers and choose an operation: +, −, ×, ÷ (with remainder), bitwise AND, OR, XOR, or shift left/right. The result is shown in binary, grouped in fours for readability, along with its decimal, hexadecimal and octal equivalents.
You can also enter the inputs in octal, decimal or hex. All maths uses arbitrary-precision integers, so even very long numbers are exact.
How to calculate with binary numbers
- 1
Choose the input base
Binary by default; octal, decimal or hex also work.
- 2
Enter two numbers
Digits only (a leading minus is allowed).
- 3
Pick an operation
Arithmetic, bitwise or shift.
- 4
Read the result
In binary, decimal, hex and octal.
Key features
Arithmetic and bitwise
Nine operations.
All bases
Binary, octal, decimal and hex.
Exact big numbers
No overflow or rounding.
Readable output
Binary grouped in nibbles.
Common uses
- Computer science students: Check binary arithmetic homework.
- Programmers: Work out bit masks and flags.
- Electronics: Verify digital logic results.
Tips and good to know
- Shifting left by one place doubles a number; shifting right halves it (rounding down).
- To convert text to binary, use Text to Binary.
Frequently asked questions
How do you add binary numbers?
Add column by column from the right: 0+0=0, 1+0=1, 1+1=10 (write 0, carry 1). 101101 + 1011 = 111000.
What does XOR do?
It sets a bit to 1 when the two input bits differ and to 0 when they match.
Can I divide binary numbers?
Yes. The tool gives the whole-number quotient and the remainder.