A Symbolic Analysis of Relay and Switching Circuits

SHANNON, Claude Elwood

Edité par American Institute of Electrical Engineers [AIEE], New York, 1938

A propos de cet article

Boolean Algebra and the Design of Switching Circuits. First edition, in the form Shannon's own department circulated three months before the bound journal reached its subscribers, of the paper that made the design of switching circuits a deductive science. In the summer of 1937 Claude Shannon, a twenty-one-year-old research assistant at MIT, was running Vannevar Bush's differential analyser - a room-sized analog computer whose motions were governed by a control circuit of about a hundred relays - when he saw that the open-and-closed behaviour of those relays mapped exactly onto the true-and-false of Boolean logic. The observation looked elementary; its consequence was that the design of switching networks could be lifted out of intuitive cut-and-try and carried out within a rigorous algebra. He worked it up over that summer at Bell Telephone Laboratories and over the following year as his MIT master's thesis. The paper appeared in 1938 in three closely related forms; the present item is the second of them - the typeset offprint the American Institute of Electrical Engineers supplied to MIT's Electrical Engineering Department on 16 September 1938 for redistribution within the department, three months ahead of the bound Transactions. In its eleven typeset pages the paper opens with four postulates now found in some form in every text on switching theory: 0 0 = 0; 1 + 1 = 1; 1 + 0 = 0 + 1 = 1; 0 1 = 1 0 = 0; and 'at any given time either X = 0 or X = 1'. From these, with a single convention - Xab the hindrance between terminals a and b, 0 the closed circuit and 1 the open one - Shannon builds, across thirty-six figures, a complete calculus for relay networks: the canonical series-parallel form, the expansion of a switching function in any subset of its variables, the equivalence transformations, the duality theorem for planar networks, and the realisation of symmetric functions. The paper's fifth section then turns the calculus to engineering, in five worked examples: a selective relay that responds to one, three, or four of its inputs but not to two; an electric combination lock that opens only to its buttons pressed in the right order; a vote-counter; a base-translator; and - the example for which the paper is most remembered - a binary full-adder, the first published electrical circuit derived from a symbolic-Boolean framework, and the schematic germ of every digital computer that followed. What gave the algebra its force was economy as much as rigour. Shannon framed the problem in his opening sentence as that of the automatic telephone exchange, and set two explicit goals: to find, for a required behaviour, a circuit equivalent to any other that realised it, and to find the one needing the fewest relay contacts. The second answered to the largest engineering enterprise of the age. A telephone exchange was a machine built almost wholly of relays - by mid-century a single automatic exchange might operate more than a thousand of them to set up one call, and the Bell System counted its relays in the hundreds of millions - so that a method for proving two contact networks equivalent, and for choosing the leaner, turned every contact saved into a cost not paid across tens of thousands of installations. The algebra gave the exchange engineer, for the first time, a way to prove a circuit minimal rather than merely workable. The paper exists in three states, each in a different physical form. The earliest is the AIEE Advance Copy preprint of June 1938, twenty-eight typewritten quarto leaves with Shannon's thirty-six figures drawn by hand, distributed to delegates of the Summer Convention; the latest is the bound Transactions volume 57 of December 1938, the normal journal channel. The present copy is the state between the two: a properly typeset offprint, pulled from the same plates as the bound journal - the verso carries the AIEE's 'Preprinted from TRANSACTIONS' legend and the dated stamp 9/16/38 - which the AIEE supplied to MIT's El.

N° de réf. du vendeur 5553

Détails bibliographiques

• Titre: A Symbolic Analysis of Relay and Switching Circuits
• Éditeur: American Institute of Electrical Engineers [AIEE], New York
• Date de parution: 1938
• Édition: First edition.
• Catalogues du vendeur:
  • Computers, Numerical Methods