Two's complement - Revision history

Jnc: /* External links */ +Minus Zero

2025-06-02T12:42:15Z

‎External links: +Minus Zero

Jnc: +cat

2018-12-15T23:22:17Z

+cat

Jnc: A pretty good start

2018-12-03T13:38:11Z

A pretty good start

New page

'''Two's complement''' is the now-universal system for representing integers (both positive and negative) in [[binary]]; if the high [[bit]] is '1', the number is negative; if '0', the remaining bits encode either 0 (if all '0'), or a positive number.

Negative numbers are formed by taking the positive number, complementing it (bit-by-bit inversion), and adding one to the result. So. for example, using a 4-bit [[word]], 1 is '0001'; to get -1, invert, which gives '1110', and add one, giving '1111'.

Note that when considering the possible values available with an N-bit word, since 0 is 'taken' from the 'space' allocated to positive numbers, there is always one more possible negative number than positive. I.e. with a N-bit number, there are 2N-1 negative values, 0, and 2N-1-1 positive values. This means that there is a negative number whose positive counterpart cannot be expressed.

==Predecessor==

The predecessor to two's complement was [[one's complement]], in which the negative is simply the complement, without the 'add one' step.

Two's complement is preferred because i) the same [[hardware]] can be used for unsigned (considering the N bits of a word as representing a number in the range 0 to 2N-1) and two's complement arithmetic, and ii) one's complement has a 'negative zero' (all 1's) as well the other zero, which makes [[program]]s more complex.

← Older revision		Revision as of 12:42, 2 June 2025
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	Two's complement is preferred because i) the same [[hardware]] can be used for unsigned (considering the N bits of a word as representing a number in the range 0 to 2<sup>N</sup>-1) and two's complement arithmetic, and ii) one's complement has a 'negative zero' (all 1's) as well the other zero, which makes [[program]]s more complex.		Two's complement is preferred because i) the same [[hardware]] can be used for unsigned (considering the N bits of a word as representing a number in the range 0 to 2<sup>N</sup>-1) and two's complement arithmetic, and ii) one's complement has a 'negative zero' (all 1's) as well the other zero, which makes [[program]]s more complex.
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		+	==External links==
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		+	* [https://www.fourmilab.ch/documents/univac/minuszero.html Minus Zero] - amusing detailed description of the difference between the two systems

	[[Category: Theory]]		[[Category: Theory]]

← Older revision		Revision as of 23:22, 15 December 2018
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	Two's complement is preferred because i) the same [[hardware]] can be used for unsigned (considering the N bits of a word as representing a number in the range 0 to 2<sup>N</sup>-1) and two's complement arithmetic, and ii) one's complement has a 'negative zero' (all 1's) as well the other zero, which makes [[program]]s more complex.		Two's complement is preferred because i) the same [[hardware]] can be used for unsigned (considering the N bits of a word as representing a number in the range 0 to 2<sup>N</sup>-1) and two's complement arithmetic, and ii) one's complement has a 'negative zero' (all 1's) as well the other zero, which makes [[program]]s more complex.
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		+	[[Category: Theory]]