Trinary Logic Operations and Circuitry with Communication Systems Applications

Abstract

This paper begins with a general discussion of numbering system properties including the concepts of ambipolarity and radix. A classic derivation of the optimumly efficient radix is given. This leads to the consideration of a trinary number system as an advantageous alternative to the binary system. There follows a discussion of the practical economies of the trinary system in hardware realization and operational speed of digital systems. A family of functional, combinatorial, and sequential logic operations is developed with associated truth tables. Synthesis of complex functions from these elementary operations is illustrated for data storage, data movement, and arithmetic processes. A practical scheme for realizing trinary system circuitry using CMOS technology is presented. Trinary digital-to-analog (D-A) and analog-to-digital (A-D) circuits and algorithms are considered. The paper includes discussions of applications of the trinary system to communication formats and carrier modulation schemes, including the use of pseudo-noise (PN) trinary coding for continuous and pulsed spread-spectrum modems.