Binary number 1197. Note that the first Prior Value of 0 is simply an initial decimal value. This method is an application of the Horner scheme. The fractional parts of a number are converted with similar methods. They are again based on the equivalence of shifting with doubling or halving. In a fractional binary number such as 0.11010110101, the first digit is formula_7, the second formula_8, etc. So if there is a 1 in the first place after the decimal, then the number is at least formula_7, and vice versa. Double that number is at least 1. This suggests the algorithm: Repeatedly
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