Binary number 100100 (36 decimal). When computers must add two numbers, the rule that: x xor y = (x + y) mod 2 for any two bits x and y allows for very fast calculation, as well. A simplification for many binary addition problems is the Long Carry Method or Brookhouse Method of Binary Addition. This method is generally useful in any binary addition in which one of the numbers contains a long "string" of ones. It is based on the simple premise that under the binary system, when given a "string" of digits composed entirely of ones ("where:" is any integer
Skew binary number system with formula_8 1s is equal to the binary number formula_9 minus formula_8. Let formula_11 represents the digit formula_12 repeated formula_13 times. The skew binary number of the form formula_14 with formula_8 1s is equal to the binary number formula_16 minus formula_8. Similarly to the preceding section, the binary number formula_18 of the form formula_7 with formula_8 1s equals the skew binary number formula_21 plus formula_8. Note that since addition is not defined, adding formula_8 corresponds to incrementing the number formula_8 times. However, formula_8 is bounded by the logarithm of formula_18 and incrementation takes constant time. Hence transforming a binary number