GATE | GATE CS 2018 | Question 53
Consider the unsigned 8-bit fixed point binary number representation, below,
b7b6b5b4b3 ⋅ b2b1b0
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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?
(A) None of (i), (ii), (iii), (iv) can be exactly represented
(B) Only (ii) cannot be exactly represented
(C) Only (iii) and (iv) cannot be exactly represented
(D) Only (i) and (ii) cannot be exactly represented
Explanation:(i) 31.500 can be represented as :
(31.5)10 = (11111.100)2
24 + 23 22 + 21 + 20 + 2-1 = 16 + 8 + 4 + 2 + 1 + 0.5 = (31.05)10
(ii) 0.875 can be represented as :
(0.875)10 = (00000.111)2
2-1 + 2-2 2-3 = 0.50 + 0.25 + 0.125 = (0.875)10
(iii) and (iv) can not be be represented.
Therefore, option (C) is Correct.