Editing Binary number (section)

===Division===
{{See also|Division algorithm#Integer division (unsigned) with remainder}}

[[Long division]] in binary is again similar to its decimal counterpart.

In the example below, the [[divisor]] is 101<sub>2</sub>, or 5 in decimal, while the [[Division (mathematics)|dividend]] is 11011<sub>2</sub>, or 27 in decimal. The procedure is the same as that of decimal [[long division]]; here, the divisor 101<sub>2</sub> goes into the first three digits 110<sub>2</sub> of the dividend one time, so a "1" is written on the top line. This result is multiplied by the divisor, and subtracted from the first three digits of the dividend; the next digit (a "1") is included to obtain a new three-digit sequence:

               1
         ___________
 1 0 1   ) 1 1 0 1 1
         − 1 0 1
           -----
           0 0 1

The procedure is then repeated with the new sequence, continuing until the digits in the dividend have been exhausted:

              1 0 1
        ___________
 1 0 1  ) 1 1 0 1 1
        − 1 0 1
          -----
              1 1 1
          −   1 0 1
              -----
              0 1 0

Thus, the [[quotient]] of 11011<sub>2</sub> divided by 101<sub>2</sub> is 101<sub>2</sub>, as shown on the top line, while the remainder, shown on the bottom line, is 10<sub>2</sub>. In decimal, this corresponds to the fact that 27 divided by 5 is 5, with a remainder of 2.

Aside from long division, one can also devise the procedure so as to allow for over-subtracting from the partial remainder at each iteration, thereby leading to alternative methods which are less systematic, but more flexible as a result.