Reprentation of Signed Integers

binary digits (bits) of memory can store different numbers. They can be positive integers between and . For example, using bits, we can represent any integer between and .

If we want to represent signed integers (i.e. both positive and negative numbers) using bits, we can use one of the following methods:

• Sign/Magnitude representation. Reserve the first bit for the signum (for example, let 0 denote positive numbers, and 1 negative numbers); the other bits will store the magnitude (the absolute value) of the number. In this case the range of numbers represented is to . With there are bits for the magnitude, different possible magnitudes, between and ; each of these can have a positive and negative sign. Note that with this representation we have both positive and negative zero. If we make the convention that the sign bit is 1 for negative numbers we have

  Number	([S]M)
  -3	[1]11
  -2	[1]10
  -1	[1]01
  -0	[1]00
  +0	[0]00
  +1	[0]01
  +2	[0]10
  +3	[0]11

• Two's complement representation. All numbers from to are represented by the smallest positive integer with which they are congruent modulo . With , for example, we have

  Number	(2C)	(2C)
  -4	4	100
  -3	5	101
  -2	6	110
  -1	7	111
  0	0	000
  1	1	001
  2	2	010
  3	3	011

  Note that the first bit is 1 for negative numbers, and 0 for nonnegative numbers.

• Biased representation. A number is represented by the positive value . Adding the bias gives positive results.

  Number	(biased)	(biased)
  -4	0	000
  -3	1	001
  -2	2	010
  -1	3	011
  0	4	100
  1	5	101
  2	6	110
  3	7	111

The first bit is 0 for negative numbers, and 1 for nonnegative numbers.