Skew binary number system non-zero digits, a form called the sparse representations of numbers by Okasaki, incrementation and decrementation can be performed in constant time. Other arithmetic operations are performed by switching between the skew binary representation and the binary representation. Given a skew binary number, its value can be computed by a loop, computing the successive values of formula_4 and adding it once or twice for each formula_5 such that the formula_5th digit is 1 or 2 respectively. A more efficient method is now given, with only bit representation and one substraction. The skew binary number of the form formula_7 without 2 and
Binary number British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry. In 1937, Claude Shannon produced his master's thesis at MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history. Entitled "A Symbolic Analysis of Relay and Switching Circuits", Shannon's thesis essentially founded practical digital circuit design. In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer he dubbed the "Model K" (for