An introduction to threshold logic: a survey of present theory and practice

Abstract

The familiar logic building blocks of AND, OR, NAND, and NOR functions are practical realizations of well-known basic boolean algebraic connectives, and as such enable any two-state logic system to be constructed. however, a more powerful basic logic building block than boolean gates is the ‘threshold gate’. such a gate has binary inputs A, B, C,…, with ‘weights’ a, b, c,…associated with these respective inputs, and a binary output z. the output from such a gate is:Z = 1 if 〈a.A + b.B + c. C +…〉≥some value t1Z = 0 if 〈a.A + b.B + c.C +…≤ some value t2where normal arithmetic rules are involved in the above summations.such gates can be used to realize all the normal basic binary logic functions, and in addition can realize more complex switching functions which would otherwise require the use of several normal logic gates. thus the number of gates in a switching system may be drastically reduced by using threshold gates in place of the normal types.