The 1's-complement and 2's-complement binary representation methods are special cases of the (b-1)'s-complement and b's-complement representation techniques in base b number systems. For example, consider the decimal system. The sign-and- magnitude values +526, -526, +70, and -70 have 4-digit signed-number repre- sentations in each of the two complement systems, as shown in Figure P6.1. The 9's-complement is formed by taking the complement of each digit position with re- spect to 9. The 10's-complement is formed by adding 1 to the 9's-complement. In each of the latter two representations, the leftmost digit is zero for a positive number and 9 for a negative number.

Representation Examples Sign and magnitude +526 -526 +70 -70 9's complement 0526 9473 0070 9929 10's complement 0526 9474 0070 9930 Figure P6:1 Signed numbers in base 10 used in Problem 6.3.