Realizing Many-Valued Logic for Computation

Abstract

This paper proposes to use many-valued logic as new potentials for improving computation speeds. To facilitate the use of many-valued logic for computation, this paper describes a simple four-step process for designing many-valued circuits to implement any many-valued functions. The aim is to design and implement digital circuits entirely within the domain of many-valued logic. In a four-valued logic circuit, each wire carries two bits at a time, each logic gate operates two bits at once, and each memory cell records two bits at one time. To be able to implement four-valued logic circuits in hardware, this paper also contributes new CMOS designs of all the necessary logic gates, including disjoint unary gates, n-input AND gates, and n-input OR gates. The many-valued circuit design methodology and the many-valued logic gates provide the necessary and sufficient tools and components for exploiting the many-valued computational paradigm.  Index Terms many-valued logic, fuzzy control, circuit design, CMOS design, fuzzy system 3 G 1 11 3

Alternative Paradigms of Computation

“…Consider a four valued logic circuit. In this circuit, "each wire carries two bits at a time, each logic gate operates two bits at once, and each memory cell records two bits at one time [97]. "…”

“…Manyvalued logic is also useful in the design of programmable logic arrays. It has the potential to improve computation speeds [97]. It will be able to increase clock-speed, which is something that is becoming increasingly difficult.…”

“…[99] Fuzzy logic flip-flops were first mentioned in "Summary of fuzzy flip-flop." [101] Many-valued logic is being used to build higher capacity flash memory, in which each memory cell contains two, three, or four bits [97]. Designs for a many-valued logic CPU can be seen in [97].…”

“…[101] Many-valued logic is being used to build higher capacity flash memory, in which each memory cell contains two, three, or four bits [97]. Designs for a many-valued logic CPU can be seen in [97]. Currently, many-valued and fuzzy systems are usually simulated or implemented by using a fuzzifier to convert inputs.…”

Designing the First Many-valued Logic Computer

“…In this paper, we focus on the design methodologies to utilize the proposed many-valued logic gates and memory cells to design many-valued logic computing systems [38] [39], in particularly to design a many-valued microprocessor.…”