Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed “radix t”, that is, in the form a = a0 + a1t + ··· + antn where ai are of like sign and have magnitudes less than t. t is a positive integer determined by the word length of the computer. Consider the expression c = a ± b = (a0 ± b0) + (a1 ± b1)t + ··· + (an ± bn)tn. Here ai ± bi may exceed the storage capacity of one word or may have a sign different from c.
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