Binary number 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: Such long strings are quite common in the binary system. From that one finds that large binary numbers can be added using two simple steps, without excessive carry operations. In the following example, two numerals are being added together: 1 1 1 0 1 1 1 1 1 0 (958) and 1 0 1 0
Binary GCD algorithm Binary GCD algorithm The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programmer Josef Stein in 1967, it may have been known in 1st-century China. The algorithm reduces the problem of finding the GCD by repeatedly applying these identities: The algorithm requires O(n) worst-case time, where n is the number of bits in the larger of