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Question 1.1.5: 4-bit 2’s complement representation of a decimal number is 1...

4-bit 2’s complement representation of a decimal number is 1000. The number is

(a) +8                                             (b) 0

(c) −7                                             (d) −8

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2’s complement = 1000——, MSB = 1 ⇒ – ve number.
Take inverse of 2’s comp:
Subt 1: 1000

\frac{-1}{\underline{0111}}

Take 1’s comp = 1000 = 8 (mag) and sign = –ve
⇒ number of (–8)
Hence, the correct option is (d).

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