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Previous Year Question (PYQs)

Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in: 
(i) 1's complement, 
(ii) 2's complement




Solution

For an n-bit system:

  • 1’s complement range: $-(2^{n-1}-1)$ to $+(2^{n-1}-1)$ ⇒ smallest $=-(2^{8}-1)={-255}$.
  • 2’s complement range: $-2^{n-1}$ to $+(2^{n-1}-1)$ ⇒ smallest $=-2^{8}={-256}$.

(9-bit means sign + 8 magnitude bits.)


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