Binary arithmetic and base conversion — add, subtract, multiply and divide in binary, or convert between binary, decimal, hex and octal.
Digits 0 and 1 only.
Result
—How to use this tool
Arithmetic works on two binary numbers; conversion translates one number between bases.
Binary uses only 0 and 1 — anything else is refused with an explanation.
Every result is shown in binary, decimal, hexadecimal and octal at once.
Division shows the whole-number quotient plus the remainder in both bases.
Formula & worked example
1010₂ + 1100₂ = 10110₂ (10 + 12 = 22 in decimal). Converting 255 gives 11111111₂, FF₁₆ and 377₈.
Limitations — read this before you rely on it
Very large binary numbers lose precision in JavaScript beyond 53 bits — the calculator refuses numbers too large to convert exactly. Negative results are shown with a minus sign, not in two's complement, unless the note is switched on.
Frequently asked questions
The base-2 number system computers use: every digit is 0 or 1, and each place is worth twice the previous one.
Add the place values of the 1s: 1010 = 8 + 2 = 10.
Hex is a compact way to write binary — one hex digit stands for exactly four binary digits, which is why colours and memory addresses use it.
Binary division, like decimal division, does not always come out even: 13 ÷ 5 = 2 remainder 3.
Results can be negative (shown with a minus sign). For two's complement form, switch on the Advanced note.