Unrooted binary tree enumeration problem on unrooted binary trees is to count the number of trees with "n" labeled leaves and unlabeled internal nodes. An unrooted binary tree on "n" labeled leaves can be formed by connecting the "n"th leaf to a new node in the middle of any of the edges of an unrooted binary tree on "n" − 1 labeled leaves. There are 2"n" − 5 edges at which the "n"th node can be attached; therefore, the number of trees on "n" leaves is larger than the number of trees on "n" − 1 leaves by a factor of 2"n" −
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