Binary number digit represents. For example, the binary number 100101 is converted to decimal form as follows: Fractions in binary only terminate if the denominator has 2 as the only prime factor. As a result, 1/10 does not have a finite binary representation, and this causes 10 × 0.1 not to be precisely equal to 1 in floating point arithmetic. As an example, to interpret the binary expression for 1/3 = .010101..., this means: 1/3 = 0 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + ... = 0.3125 + ... An exact value cannot be
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