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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.

  1. $i$ & $iv$ 
  2. $i$ & $ii$ 
  3. $iii$ 
  4. $iv$ 
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1 Answer

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iii) statement is incorrect.

b2b1b0 2's complement representation
011 +3
010 +2
001 +1
000 0
100 -4
101 -3
110 -2
111 -1

i) correct

ii) Correct. Because it is a sign bit. REMEMBER: In any number representation(sign magnitude/ 1's complement/ 2's complement) left most bit is sign bit.

iii)Incorrect. As in the table above, 3 bits --  ∙ one zero  ∙ total 23 unique states  ∙ 2n-1 positive numbers=23-1=4 positive numbers. But how come 2n+1 negative numbers? hence incorrect.

iv) Correct. I'm not able to find example illustrating this point.

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