C Programming

Question

If variable can take any integral values from $0$ to $n$, where $n$ is a constant integer, then the variable can be represented as a bits field whose width is the integral parts of

(a) $\log_{2}(n)+1$

(b) $\log_{2}(n+1)+2$

(c) $\log_{2}(n-1)+1$

(d) None of these

Comments

It should be d) none of these:-

Explanation:-

They are indirectly asking about the number of bits in the unsigned number.

n is the max number represented using m bits.

n = 2^m - 1

n + 1 = 2^m

Taking log on both side

log(n+1) = m.

which does not match to any option.

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I too agree with your answer and explanation....but the given answer is (a) with this explanation below

Variable with integral values from 0 to n.

Then it's width is the integral part of $log_{2}(n)+1$

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I think they should use floor value instead using simply using log₂n

because for 4 digit number it is 15

and if we use log₂15 then it is 3.9068 and its floor value is 3 adding 1 will give 4.