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# GATE | GATE CS 2018 | Question 53

• Last Updated : 27 Sep, 2021

Consider 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?

(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.

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