AN ALGEBRAIC-GEOMETRIC TECHNIQUE FOR THE REALIZATION OF SWITCHING FUNCTIONS WITH M-OUTOF-N DECISION GATES,
Abstract
An algebraic-geometric technique is presented for the realization of binary switching functions with networks composed of m-out-of-n decision gates. An m-out-of-n decision gate is defined as a device that may be described by a threshold function whose weights and threshold are positive integers. An expansion theorem is proved that can produce a variety of gate configurations ranging between the two extremes of 2(n-1) stages of 3-input majority gates, and a 2-stage form composed of gates having a much greater number of inputs. For realization with two stages, the terms of the expansion theorem may be mapped on to one-half of a Karnaugh diagram. The map displays all possible combinations of terms which may be combined according to the m-out-of-n decision logic, and provides a basis for formalizing the initial step in a reduction procedure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1964
- Accession Number
- AD0609505
Entities
People
- Manush Raship
Organizations
- New York University