Binary number converted to binary, whereupon the first converted piece is multiplied by 10 and added to the second converted piece, where "k" is the number of decimal digits in the second, least-significant piece before conversion. Binary may be converted to and from hexadecimal more easily. This is because the radix of the hexadecimal system (16) is a power of the radix of the binary system (2). More specifically, 16 = 2, so it takes four digits of binary to represent one digit of hexadecimal, as shown in the adjacent table. To convert a hexadecimal number into its binary equivalent, simply substitute
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