# GATE | GATE CS 2018 | Question 53

Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3 â‹… 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 represented.   Therefore, option (C) is Correct

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