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

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?

Answer 1

[Guillaume]

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.

Answer 2

[Bruno Luong]

>> I=0:9

I =

     0     1     2     3     4     5     6     7     8     9

>> n=nextpow2(I+1)

n =

     0     1     2     2     3     3     3     3     4     4

Answer 3

[Tamamo Nook]

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

Answer 4

[Walter Roberson]

 ceil(log2(X+1))

Does not work for 0, but 0 is not a positive integer.

[Bruno Luong]

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

>>