Brookhouse Method of Binary Addition

The Long Carry Method of Addition or Brookhouse Method of Binary Addition is a simplification of adding binary numbers in computations. The basic concept is that any string of binary "1's" May Be added to a "1" with the lowest place value of the string, and the result will be a "1" one place larger than the original length and followed by all "0's".

For Example:

   1   and    1 1 1    and   1 1 1 0
 + 1        + 0 0 1        + 0 0 1 0
-----       --------       ----------
 1 0        1 0 0 0        1 0 0 0 0

Therefore This method is GeneRally useful in any binary addition where one of the numbers has a long string of “1” digits. For example the following large binary numbers can be added in two simple steps without multiple carries from one place to the next.

  1 1 1   1 1 1 1 1   (carried digits)                   (Long Carry Method)
    1 1 1 0 1 1 1 1 1 0                              1 1 1 0 1 1 1 1 1 0
+   1 0 1 0 1 1 0 0 1 1            Versus:       +   1 0 1 0 1 1 0 0 1 1  
-----------------------                          + 1 0 0 0 1 0 0 0 0 0 0  sum of crossed out digits
= 1 0 0 0 1 1 1 0 0 0 1                          -----------------------  now add remaining digits
                                                   1 1 0 0 1 1 1 0 0 0 1

In this example, two numerals are being added together: 1 1 1 0 1 1 1 1 1 0₂ (958₁₀) and 1 0 1 0 1 1 0 0 1 1₂ (691₁₀). The top row shows the carry bits used. Instead of the standard carry from one column to the next, the lowest place-valued "1" with a "1" in the corresponding place value beneath it may be added and a "1" may be carried to one digit past the end of the series. These numbers must be crossed off since they are already added. Then simply add that result to the uncanceled digits in the second row. Proceeding like this gives the final answer 1 1 0 0 1 1 1 0 0 0 1₂ (1649₁₀).