Signed numbers can be represented with the two's-complement form. In this form the most significant bit is the sign bit. With one bit used as a sign then the magnitude of the number is reduced by one bit. for a data word with 8-bits, the normal capacity would be 256 numbers. With the sign bit there are 128 positive numbers (0 to +127) and 128 negative numbers (–1 to –128). This is still 256 numerical combinations.
Care must be taken, however, when working with signed numbers not to exceed the range of positive or negative numbers. For example: if the number +2 (0000 0010) is added to +126 (0111 1110) the results will be 1000 0000.
This is not +128 but a negative number –127. Two positive numbers added together resulted in a negative answer. This is a condition called overflow. Most computers have special circuits to detect an overflow condition.
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Date last modified: August 16, 2012.
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