Editing Signed number representations (section)

== Other systems ==

Google's [[Protocol Buffers]] "zig-zag encoding" is a system similar to sign–magnitude, but uses the [[least significant bit]] to represent the sign and has a single representation of zero. This allows a [[variable-length quantity]] encoding intended for nonnegative (unsigned) integers to be used efficiently for signed integers.<ref>[http://developers.google.com/protocol-buffers/docs/encoding#types Protocol Buffers: Signed Integers]</ref>

A similar method is used in the [[Advanced Video Coding|Advanced Video Coding/H.264]] and [[High Efficiency Video Coding|High Efficiency Video Coding/H.265]] video compression standards to [[Exponential-Golomb coding#Extension to negative numbers|extend exponential-Golomb coding]] to negative numbers. In that extension, the [[least significant bit]] is almost a sign bit; zero has the same least significant bit (0) as all the negative numbers. This choice results in the largest magnitude representable positive number being one higher than the largest magnitude negative number, unlike in two's complement or the Protocol Buffers zig-zag encoding.

Another approach is to give each [[numerical digit|digit]] a sign, yielding the [[signed-digit representation]]. For instance, in 1726, [[John Colson]] advocated reducing expressions to "small numbers", numerals 1, 2, 3, 4, and 5. In 1840, [[Augustin Cauchy]] also expressed preference for such modified decimal numbers to reduce errors in computation.