Gate2018 cs Q58

58Consider the unsigned 8-bit fixed point binary number representation, below,
b₇b₆b₅b₄b₃ ⋅ b₂b₁b₀
Where the position of the binary point is between b₃ and b₂ Assume b₇ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
i. 31.500 ii. 0.875
iii. 12.100 iv. 3.001
Which one of the following statements is true?

Option : C
Explanation :
Binary code: (b₇b₆b₅b₄b₃ ⋅ b₂b₁b₀)₂
(31.5)₁₀ = (11111.1)₂
(0.875)₁₀ = (0.111)₂
(12.100)₁₀ = (01100.000110.....)₂
↓
Only 3 bits of fraction
space available
So can't be stored.
(3.001)₁₀ = (00011.000000..........)₂
It is also not accurate storage.

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