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Binary Calculator

Do arithmetic and bitwise operations on binary numbers and see the result in binary, octal, decimal and hexadecimal at the same time.

Formulas last reviewed: September 2026

Disclaimer: Results are calculated with standard formulas and are meant for learning and quick checks. Please double-check important work, especially anything used for exams, engineering, finance or safety.

Numbers in base 2

Binary is the number system computers use. It has only two digits, 0 and 1, and each place is worth twice the one to its right: 1, 2, 4, 8, 16 and so on.

This calculator adds, subtracts, multiplies and divides binary numbers and applies the bitwise operations AND, OR and XOR. The answer is shown in binary and also in octal, decimal and hexadecimal so you can check your understanding.

How it is calculated

1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11
Binary addition: 0+0=0, 0+1=1, 1+1=10 (carry 1)

Worked example

1011 + 110

In decimal
11 + 6 = 17
Result in binary
10001
Result in hex
11

Bitwise operations

OperationRule1100 and 1010
AND1 only if both bits are 11000
OR1 if either bit is 11110
XOR1 if the bits differ110

Frequently asked questions

How do I convert binary to decimal?

Multiply each digit by its place value (1, 2, 4, 8 …) counting from the right, then add. For 1011 that is 8 + 0 + 2 + 1 = 11.

How do I convert decimal to binary?

Divide the number by 2 repeatedly and write down the remainders from bottom to top. The calculator also shows every result in binary automatically.

Can it handle negative binary numbers?

Yes. Type a minus sign in front of the number. Results are shown with a minus sign rather than in two's complement form.

Why is binary used in computers?

Electronic circuits are easiest to build with two states, on and off, which map directly to the digits 1 and 0.