gate 2018

Question

there was a question

b7 b6 b5 b4 b3 . b2 b1 b0

and some numbers were given like 0.825 0.001 etc

and it asked which of these numbers cannot be exactly represented by it ???

can anyone explain????

Answer 1

last two value cannot store properly

Comments

means???

please elaborate

Answer 2

IN the question we are asked which  numbers cant be represented "EXACTLY"...

now as per given system we have 3 bits in decimal points like  b7 b6 b5 b4 b3 . b2 b1 b0

now from options we have (only focus on decimal points)

a) number.50  we can represent it as number.100 

b) we have number.825 we can represent it as number.111

c) here we have number.100 ..NOW we cant represent .100 exactly by just 3 bits of decimal (that is all possible combination of 3 bits =000.001,010,100,101,110,111 cant represent 100)

d) same as per above answer c we cant represent number.001 

so 1st and 2nd number can be represented but not 3rd and 4th as per given Specifications.

(I DON'T REMEMBER THE OPTIONS EXACTLY BUT ALL VALUES BEFORE DECIMAL WERE EASILY REPRESENTED BY SYSTEM..SO I ONLY FOCUSED ON DECIMAL VALUES ...AND WROTE "NUMBER" INSTEAD OF ACTUAL VALUES.) 

Comments

i think it was .5 and not .05

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It was 0.875 not 0.825

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Option C