Question 3685 – Computer-Organization
May 30, 2024Question 3745 – Computer-Organization
May 30, 2024Question 7878 – Digital-Logic-Design
Consider the unsigned 8-bit fixed point binary number representation below,
b7 b6 b5 b4 b3 b2 b1 b0
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?
Correct Answer: C
Question 10 Explanation:
(i) (31.5)10 = (11111.100)2 = 24 + 23 + 22 + 21 + 20 + 2-1
= 16 + 8 + 4 + 2 + 1 + 0.5
= (31.5)10
(ii) (0.875)10 = (00000.111)2
= 2-1 + 2-2 + 2-3
= 0.5 + 0.25 + 0.125
= (0.875)10
(iii) (12.100)10
It is not possible to represent (12.100)10
(iv) (3.001)10
It is not possible to represent (3.001)10
= 16 + 8 + 4 + 2 + 1 + 0.5
= (31.5)10
(ii) (0.875)10 = (00000.111)2
= 2-1 + 2-2 + 2-3
= 0.5 + 0.25 + 0.125
= (0.875)10
(iii) (12.100)10
It is not possible to represent (12.100)10
(iv) (3.001)10
It is not possible to represent (3.001)10
None of (i), (ii), (iii), (iv) can be exactly represented
Only (ii) cannot be exactly represented
Only (iii) and (iv) cannot be exactly represented
Only (i) and (ii) cannot be exactly represented
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