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The binary number 0.111111…. (where the digit 1 is recurring) is equivalent in decimal system to which one of the following?
A. `(1)/(10)`
B. `(11)/(10)`
C. 1
D. `(10)/(11)`

1 Answer

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Best answer
Correct Answer - C
Let binary number 0.1111111….=x
`impliesx=2^(-1)+2^(-2)+2^(-3)+....oo=(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+....oo`
This is an infinite G.P. series with first term = `(1)/(2)` and common ration = `(1)/(2)`
`impliesx=(1//2)/(1-(1)/(2))=(1//2)/(1//2)=1`

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