Free One's Complement Calculator

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The one's complement of a binary number is found by flipping every single bit — every 0 becomes a 1 and every 1 becomes a 0. It's a foundational operation in digital logic and computer architecture, forming the basis of one's-complement signed number representation (an early scheme, still relevant historically and in certain checksum algorithms, for representing negative numbers in binary) and serving as the essential intermediate step in computing two's complement, the signed-number representation used by virtually all modern computer hardware.

How it works

Enter a binary number. The calculator inverts every bit position independently: each 0 becomes a 1, and each 1 becomes a 0 — equivalent to the bitwise NOT operation found in most programming languages.

Enter binary number.
Click Calculate to see your results.

Examples

10110

Flipping every bit: 1→0, 0→1, 1→0, 1→0, 0→1, giving 01001. One's complement of 10110 is 01001.

11111111 (all 1s, 8-bit)

Flipping every bit gives 00000000 — the one's complement of an all-1s byte is always all zeros, and vice versa.

Common mistakes to avoid

Confusing one's complement (flip all bits) with two's complement (flip all bits, then add 1) — they differ by that final +1 step.
Forgetting to account for leading zeros — the bit-width you flip within changes the result if the number isn't already padded to a fixed size.
Assuming one's complement of a number added to itself gives zero the same way two's complement does — one's complement arithmetic has its own quirks, including two representations of zero.

Frequently asked questions

Two's complement equals the one's complement plus 1 — this calculator's result is exactly the intermediate step used by the site's Two's Complement Converter, which takes this flipped result and adds 1 to it.

One's complement is still used today in certain checksum algorithms (like the Internet Protocol/TCP checksum), and understanding it is essential background for learning how two's complement — and therefore negative number representation in virtually all real hardware — actually works.

Yes — flipping bits only makes sense relative to a fixed bit-width. "10110" flipped is "01001", but if you first pad it to 8 bits as "00010110", flipping gives "11101001" instead — a different result because the leading zeros also get flipped to ones.

Yes — bitwise NOT and one's complement describe exactly the same operation: inverting every bit of a binary value.

One's complement has two distinct representations for zero (00000000 and 11111111 in 8 bits, i.e. positive zero and negative zero), which complicates arithmetic circuits — one reason modern computers universally use two's complement instead, which has only a single representation for zero.

Yes — flipping every bit and then flipping every bit again always restores the original value, since each bit position is toggled back to its starting state.

No — the bit-width stays exactly the same before and after; only the value of each individual bit is inverted, not the total count of bits.