How does sign-magnitude work?

The most significant bit is the sign: 0 for positive, 1 for negative. The remaining bits hold the absolute value (magnitude) in plain binary. So -5 in 8 bits is 10000101.

Why does sign-magnitude have two zeros?

Positive zero is all zeros and negative zero sets only the sign bit (for example 10000000 in 8 bits). This dual zero, plus harder arithmetic, is why integers rarely use sign-magnitude today.

What is the range of an 8-bit sign-magnitude number?

It is symmetric: -127 to +127. One bit is spent on the sign, leaving seven magnitude bits, so the maximum magnitude is 2^7 - 1 = 127.

Is sign-magnitude used anywhere today?

Yes — IEEE-754 floating-point numbers use a sign bit separate from the magnitude (exponent and mantissa). For integers, two's complement is preferred because addition and subtraction are uniform.

Is this tool private?

Yes. The conversion runs locally in your browser with exact BigInt arithmetic, so nothing is uploaded and it works offline once loaded.

Sign-Magnitude Converter

Sign-magnitude is the most human-intuitive way to store a signed integer: dedicate one bit to the sign and use the rest for the plain magnitude, exactly like writing a minus sign in front of a number. This converter shows the precise bit layout for any signed integer at common widths.

How it works

For a width of W bits:

The most significant bit is the sign — 0 means positive, 1 means negative.
The remaining W - 1 bits hold the magnitude (absolute value) in ordinary unsigned binary.

Because the sign and magnitude are independent, the representable range is symmetric: -(2^(W-1) - 1) to 2^(W-1) - 1. Like one’s complement, zero can be written two ways — positive zero (0 000…0) and negative zero (1 000…0).

Example

Encode -42 in 8 bits. The magnitude 42 is 0101010 in 7 bits. Prepend a sign bit of 1 (negative) to get 10101010, which is 0xAA. Positive 42 would be 00101010 — the only difference is that leading sign bit.

Notes

Sign-magnitude makes negation trivial (just flip the top bit) but complicates addition, since the hardware must compare signs and decide whether to add or subtract magnitudes. That overhead is why integer ALUs use two’s complement instead. The format still appears prominently in floating-point: an IEEE-754 number stores its sign as a separate bit, exactly the sign-magnitude idea applied to the significand.