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Sign/Magnitude

2021-02-06 17:45:10

This is simplest method. The most significant bit is a sign bit: 1 - negative, 0 - positive. Others bits is a magnitude (absolute value). No need the inverting or something else. Range in N-bit numbers: [-2N-1+1, 2N-1-1].

Example:

8-bit
binary -> decimal
1000 0001 = -1
0000 0001 = 1

8-bit min = 1111 1111 (-127)
8-bit max = 0111 1111 (+127)

Limitations​

  • Two representation of zero: 0000 0000 (0) and 1000 0000 (-0). This needs additional verification.
  • Addition doesn't work, for example: 
  1001 = -6
+
  0110 = 6
  ----
  1111 -> Wrong!
tip

Addition and subtraction require different behavior depending on the sign bit. (Whereas ones' complement can ignore sign bit and just do the end-around carry. And two's complement can ignore sign bit and depend on the overflow behavior.)

  • Comparing two numbers also requires additional sign check.
  • Minimal negative number: -127 (instead -128 in two's complement)

Some early binary computers (IBM 7090) used this representation. Perhaps because of its naturalistic.

From: Signed Number Representation (Wikipedia)