Editing Binary number (section)

===Square root===
The process of [[Methods of computing square roots#Binary numeral system (base 2)|taking a binary square root]] digit by digit is essentially the same as for a decimal square root but much simpler, due to the binary nature.  First group the digits in pairs, using a leading 0 if necessary so there are an even number of digits.  Now at each step, consider the answer so far, extended with the digits 01.  If this can be subtracted from the current remainder, do so.  Then extend the remainder with the next pair of digits.  If you subtracted, the next digit of the answer is 1, otherwise it's 0.

                              1                          1  1                       1  1  0                   1  1  0  1
  -------------             -------------              -------------              -------------             -------------
 √ 10 10 10 01             √ 10 10 10 01              √ 10 10 10 01              √ 10 10 10 01             √ 10 10 10 01
                            - 1                        - 1                        - 1                       - 1         
 Answer so far is 0,        ----                       ----                       ----                      ----        
 extended by 01 is 001,       1 10                       1 10                       1 10                      1 10
 this CAN be subtracted                                - 1 01                     - 1 01                    - 1 01
 from first pair 10,       Answer so far is 1,         -------                    -------                   -------
 so first digit of         extended by 01 is 101,           1 10                       1 10 01                   1 10 01
 answer is 1.              this CAN be subtracted                                                              - 1 10 01
                           from remainder 110, so     Answer so far is 11,       Answer so far is 110,         ----------
                           next answer digit is 1.    extended by 01 is 1101,    extended by 01 is 11001,              0
                                                      this is TOO BIG to         this CAN be subtracted
                                                      subtract from remainder    from remainder 11001, so           Done!
                                                      110, so next digit of      next digit of answer is 1.
                                                      answer is 0.