Which of the following statement(s) is (are) not correct ? i. The 2’s complement of 0 is 0. ii. In 2’s complement, the left most bit cannot be used to express a quantity. iii. For an n-bit word (2’s complement) which includes the sign bit, there are \(2^{n-1}\) positive integers, \(2^{n+1}\) negative integers and one 0 for a total of \(2^{n}\) unique states. iv. In 2’s complement the significant information is contained in the 1’s of positive numbers and 0’s of the negative numbers.
iii
Statement i holds: inverting 00...0 and adding 1 gives 00...0 again after the carry is discarded.
Statements ii and iv are the usual textbook descriptions: the leftmost bit acts as the sign indicator, and the magnitude information lies in the 1s of positive numbers and the 0s of negative numbers.
Statement iii is wrong: an n-bit word has \(2^{n-1} - 1\) positive values, \(2^{n-1}\) negative values and one zero, and \(2^{n+1}\) negatives would exceed the \(2^{n}\) available patterns.
Hence, iii.
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