Lets convert decimal base 10 number 273 to binary 
 and store those bits as a String of 1s and 0s

  base case: if n == 0  just return "" (empty string)

#1 Dimension an array of chars with exact number of bits
   to store the binary number. Each char will either be a 1 or a 0
   
  ? How to calculate number of bits needed to represent n in binary ?
  A It's (log2 of n) + 1.  That how big to make your char array.
  hint: Use java's Math.log(x) function. 
        use identity => log2N = log(N) / log(2)
  You want the FLOOR of this value not rounded, not ceil so you'll have
  to use the int cast operator (int) around the entire quotient above.

  the floor or (int) of log2N is 8 and adding one you get nine.

#2 fill your array of 9 chars '0' chars
     index           0 1 2 3 4 5 6 7 8
                     -----------------
   the array is now  0 0 0 0 0 0 0 0 0
                     -----------------
     how much        2 1
     that bit ==>    5 2 6 3 1
     worth           6 8 4 2 6 8 4 2 1

#3 convert this process into a loop until n == 0

   ? what is the largest power p of 2 such that 2^p <= 273
     well, n is 273 and 256 is the largest power of 2
     that does not exceed 273 so the largest power p is 8
     p == 8 so overwrite a '1' into the array at the slot
     representing the 256's. That would be index [0]

   array now =>  1 0 0 0 0 0 0 0 0

   now subtract 2^p (i.e. 256) from n
   i.e. n = n - 256  or n == 17

   DO AGAIN  with n == 17

   ? what is the largest power p of 2 such that 2^p <= 17
   p is 4 and 2^4 == 16 so overwrite a 1 into the bit that 
   represents the 16s. That would be the bit at index [4]

   array now =>  1 0 0 0 1 0 0 0 0

   now subtract 16 from 17
   i.e. n = n - 16 so n now == 1 

   DO AGAIN  with n == 1

   largest power of 2 where 2^p <= 1 is 1
   overwrite a '1' into the array at the index of the ones
   that would be index [8]

   array now =>  1 0 0 0 1 0 0 0 1
                256    + 16    + 1  = 273

   now subtract 1 from n ( 1 from 1 ) and n == 0

   YOU ARE DONE.

   return a new string constructed on this char array