Skip to content
Related Articles

Related Articles

GATE | GATE CS 2018 | Question 53

Improve Article
Save Article
  • Last Updated : 27 Sep, 2021
Improve Article
Save Article

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


Answer: (C)

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.



Quiz of this Question

My Personal Notes arrow_drop_up
Related Articles

Start Your Coding Journey Now!