Editing Signed number representations (section)

== Sign–magnitude ==

{|class="wikitable" style="float:right; width: 20em; margin-left: 1em; text-align:center"
|+ Eight-bit sign–magnitude
|-
! Binary value
! Sign–magnitude interpretation
! Unsigned interpretation
|-
| 00000000 || 0 || 0
|-
| 00000001 || 1 || 1
|-
| ⋮ || ⋮ || ⋮
|-
| 01111101 || 125 || 125
|-
| 01111110 || 126 || 126
|-
| 01111111 || 127 || 127
|-
| 10000000 || −0 || 128
|-
| 10000001 || −1 || 129
|-
| 10000010 || −2 || 130
|-
| ⋮ || ⋮ || ⋮
|-
| 11111101 || −125 || 253
|-
| 11111110 || −126 || 254
|-
| 11111111 || −127 || 255
|}

In the '''sign–magnitude''' representation, also called '''sign-and-magnitude''' or '''signed magnitude''', a signed number is represented by the bit pattern corresponding to the sign of the number for the [[sign bit]] (often the [[most significant bit]], set to 0 for a positive number and to 1 for a negative number), and the magnitude of the number (or [[absolute value]]) for the remaining bits. For example, in an eight-bit [[byte]], only seven bits represent the magnitude, which can range from 0000000 (0) to 1111111 (127). Thus numbers ranging from −127<sub>10</sub> to +127<sub>10</sub> can be represented once the sign bit (the eighth bit) is added. For example, −43<sub>10</sub> encoded in an eight-bit byte is '''1'''0101011 while 43<sub>10</sub> is '''0'''0101011. Using sign–magnitude representation has multiple consequences which makes them more intricate to implement:<ref name="cs315">{{cite web |last1=Bacon |first1=Jason W. |url=http://www.cs.uwm.edu/classes/cs315/Bacon/Lecture/HTML/ch04s11.html |title=Computer Science 315 Lecture Notes |access-date=21 February 2020 |date=2010–2011 |archive-date=14 February 2020 |archive-url=https://web.archive.org/web/20200214050150/http://www.cs.uwm.edu/classes/cs315/Bacon/Lecture/HTML/ch04s11.html |url-status=dead }}</ref>

# There are two ways to represent zero, 00000000 (0) and 10000000 ([[−0]]).
# Addition and subtraction require different behavior depending on the sign bit, whereas ones' complement can ignore the sign bit and just do an end-around carry, and two's complement can ignore the sign bit and depend on the overflow behavior.
# Comparison also requires inspecting the sign bit, whereas in two's complement, one can simply subtract the two numbers, and check if the outcome is positive or negative.
# The minimum negative number is −127, instead of −128 as in the case of two's complement.

This approach is directly comparable to the common way of showing a sign (placing a "+" or "−" next to the number's magnitude). Some early binary computers (e.g., [[IBM 7090]]) use this representation, perhaps because of its natural relation to common usage. Sign–magnitude is the most common way of representing the [[significand]] in [[Floating-point arithmetic|floating-point]] values.