How can I check that a bit is set (without bitwise operation)?

Question

Looking at the int 44 — I need Math.CEIL (log(2) 44) of binary places to represent 44. (answer is 6 places)

6 places :

___  ___  ___  ___  ___   ___
32   16    8    4    2     1

But how can I check that (for example) the bit of 8 is checked or not ?

A simple solution will be do to :

((1<<3) & 44)>0 so this will check if the bit is set.

But please notice that behind the scenes the computer translates 44 to its binary representation and just check if bit is set via bitwise operation.

Another solution is just to build the binary myself via toString(2) or mod%2 in a loop

Question

Mathematically Via which formula, I can test if n'th bit is set ?

(I would prefer a non loop operation but pure single math phrase)

Answer 1

Divide by the value of the bit that you want to check and test if the first bit is set (this can be tested with x mod 2 == 1)

Math expression:

floor(value/(2^bitPos)) mod 2 = 1

As JS function:

function isSet(value, bitPos) {
   var result =   Math.floor(value / Math.pow(2, bitPos)) % 2;
   return result == 1;
}

Note: bitPos starts with 0 (bit representing the nr 1)