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Definition of "One’s Complement Representation" |
In the 1’s complement representation, a nonnegative number is represented in the same manner as an unsigned number. A negative number (−N) is represented by the 1’s complement of the positive number N. The 1’s complement of an n-bit number N is obtained by complementing each bit of N (or equivalently,by subtracting it from 2n − 1). For example, the 4-bit words 01102 = 610, 01012 = 510, and 10102 = −510.Now consider 6−5. Direct subtraction yields 0110−0101 = 0001. However, if we express it as 6 + (−5) and carry out the addition, we have 0110 + 1010 = 10000 and so the 4-bit sum word is 0000 (due to the 4-bit word length). Since 0000 = 0001, the Requirement A is not satisfied. |
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