How does one's complement represent negatives?

A negative number is the bitwise inversion of the positive magnitude at the chosen width. Equivalently the unsigned pattern equals 2^W minus 1 minus the magnitude. Positive values are stored as plain binary.

Why does one's complement have two zeros?

All-zero bits represent positive zero, and all-one bits represent negative zero. This dual representation is the main reason one's complement was largely replaced by two's complement.

What is the range of an 8-bit one's complement number?

It is symmetric: -127 to +127. In general W bits cover -(2^(W-1)-1) to 2^(W-1)-1, one value narrower than two's complement because of the extra zero.

Where was one's complement used?

Early machines like the CDC 6600 and PDP-1 used one's complement. It needs an end-around carry during addition, which adds hardware complexity that two's complement avoids.

Is the conversion private?

Yes. It runs locally with exact BigInt arithmetic up to 64 bits, and nothing is sent over the network.

One's Complement Converter

One’s complement represents a negative number simply by inverting every bit of its positive counterpart. It is conceptually simpler than two’s complement but has a notable quirk: two distinct encodings of zero. This converter shows the exact bit pattern at common widths.

How it works

For a width of W bits:

A non-negative value is written in plain binary, zero-padded to W bits.
A negative value -v is the bitwise NOT of v’s binary — equivalently the unsigned pattern is (2^W - 1) - v.

Because flipping all the bits of 0 (all zeros) gives all ones, you end up with both positive zero (000…0) and negative zero (111…1). The representable range is therefore symmetric: -(2^(W-1) - 1) to 2^(W-1) - 1.

Example

Encode -42 in 8 bits. The magnitude 42 is 00101010. Invert every bit to get 11010101, which is 0xD5 and reads as 213 unsigned (equal to 255 - 42). Compare this with two’s complement, where -42 is 11010110 — they differ by exactly one because two’s complement adds a final +1.

Notes

One’s complement requires an end-around carry when adding, where a carry out of the most significant bit is added back into the least significant bit. This extra step, together with the dual-zero ambiguity, is why modern processors standardized on two’s complement instead.