Binary addition
10101010 + 11001100 = 101110110 in binary, or 170 + 204 = 374 in decimal.
Binary calculator
Result
Fill in the fields to see your result.
How it works
Every operation is computed exactly using arbitrary-precision integers internally, then converted to binary for display, and the decimal equivalent is shown alongside as a cross-check — if you worked the same problem by hand, the decimal figure confirms whether your binary answer is right.
Division uses whole-number (integer) division: the result is truncated, with the leftover shown separately as a remainder, the same convention used for long division.
Formulas used
Reading a binary number
Each digit represents a power of 2, read right to left: 1, 2, 4, 8, 16, …
Worked examples
Converting to decimal
11111111 in binary is 255 in decimal — eight 1s is the largest value an 8-bit byte can hold.
Assumptions and limits
- All numbers are treated as non-negative (unsigned) binary integers.
- Division is integer (whole-number) division, with any remainder shown separately.
Frequently asked questions
Why does computing use only 0s and 1s?
Binary matches how digital circuits work directly: a bit is either off (0) or on (1), a natural fit for switches and transistors — every other data type a computer handles is ultimately built from binary underneath.
How do I convert decimal back to binary?
Repeatedly divide by 2 and record the remainders, or find the largest powers of 2 that sum to the number — either method produces the same binary digits, read in reverse order for the division method.
What happens if I subtract a larger number from a smaller one?
This calculator flags it as an error, since it only represents non-negative binary numbers directly — for a genuinely negative result, note which number is larger and subtract in that order instead.
Is there a limit to how large the numbers can be?
No practical limit for typical use — the calculator uses arbitrary-precision arithmetic internally, so it stays exact even for very long binary strings.
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