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 length), adding 1 will result in the number 1 followed by a string of zeros. That concept follows, logically, just as in the decimal system, where adding 1 to a string of 9s will result in the number 1 followed by a string of 0s: