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Find out number of bits needed to represent a positive integer in binary?

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Mohsin Shah
Mohsin Shah on 16 Aug 2017
Edited: Bruno Luong on 9 Jan 2021
How to compute the bit length of a positive integer-the number of bits to represent a positive integer. For example, we have:
integer bits
0 1
1 1
2 2
3 2
4 3
5 3
6 3
7 3
8 4
9 4
How to compute the bit length of an arbitrary large integer?

Accepted Answer

Guillaume
Guillaume on 16 Aug 2017
Edited: Guillaume on 16 Aug 2017
trivially with log2 (and ceil).
I have no idea what from the cryptographic perspective mean. It's the same from any perspective. It's just basic maths.

More Answers (3)


Tamamo Nook
Tamamo Nook on 9 Jan 2021
Try this
integer=5; % Integer that you wanna calculate the binary bits
bits=log2(integer);
if integer==0;
bits=1
elseif bits==floor(bits);
bits=bits+1
else
bits=ceil(bits)
end%if

Walter Roberson
Walter Roberson on 9 Jan 2021
ceil(log2(X+1))
Does not work for 0, but 0 is not a positive integer.
  1 Comment
Bruno Luong
Bruno Luong on 9 Jan 2021
I would argue it is still correct. You need no more than 0 bit to store 0. After all the bits are implicit to be 0s beyong the explcit interval.
>> polyval([],2) % 0 byte
ans =
0
>> polyval([1],2)
ans =
1
>> polyval([1 0],2)
ans =
2
>> polyval([1 1],2)
ans =
3
>>

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