Which of the following statement(s) is (are) not correct ? i. The 2’s…

Answer: Only statement iii is not correct.

• Statement i (The 2’s complement of 0 is 0): True. Example: for n bits, 0 is 00...0. Invert bits → 11...1, add 1 → 00...0. So two's complement of 0 is 0.

• Statement ii (The leftmost bit cannot be used to express a quantity): Interpreted in the usual way this is considered correct: the leftmost bit is the sign bit in two's complement and is not a conventional positive-magnitude bit. When the leftmost bit is 1 it represents a negative weight (−2^{n-1}), so it cannot be treated like the ordinary positive-weight bits used to express magnitude.

• Statement iii (Counts of positive, negative integers and zero): Incorrect as stated. For an n-bit two's complement representation the numeric range is from −2^{n-1} to 2^{n-1}−1. Therefore:

  1. Number of negative integers = 2^{n-1} (from −2^{n-1} up to −1).

  2. Number of positive integers = 2^{n-1} − 1 (from 1 up to 2^{n-1} − 1).

  3. Zero = 1.

  These counts sum to 2^n, so any statement that gives different counts is incorrect. Example (n = 4): negatives = 8 (−8 to −1), positives = 7 (1 to 7), zero =1; total 16.

• Statement iv (Significant information in 1’s of positives and 0’s of negatives): True in the intended sense. For positive numbers the set bits (1s) directly indicate the magnitude. For negative numbers the magnitude is recovered by taking the two's complement (invert bits and add 1); thus the bits that become 1s in the magnitude after inversion were 0s in the original negative representation. Example with 4 bits: +5 = 0101; −5 = two's complement of 0101 = invert → 1010, add 1 → 1011. The magnitude bits for 5 appear as 1s after inversion/addition.