Multi-Valued Logic Circuit Design and Implementation

Abstract

To further increase the speed of computation, this paper aims to design and implement digital circuits entirely within the domain of multi-valued logic. In a fourvalued 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 make the multi-valued computation possible, this paper describes a simple fourstep process for designing multi-valued circuits to implement any multi-valued functions. The design of a fourvalued adder is provided as an example. This paper also contributes new designs for multi-valued memory and flipflops, which can be extended to be used for infinite-valued or Fuzzy logic circuits, for fully exploiting many-valued logic and fuzzy paradigm in hardware. The multi-valued circuit design methodology and the multi-valued memory provide the necessary and sufficient tools and components for designing multi-valued systems entirely within the domain of multi-valued logic. 

Fuzzy Hold Flip-Flop and Flip-Flops Hardware Realizations

“…In a simulated case, the state of Lukasiewicz H flip-flop is increasing by the difference S À R and Zadeh H flip-flop holds the value of S. It is worth to notice that all of fuzzy H flip-flops are stable (in contrast to fuzzy JK flip-flop [2]). Fuzzy flip-flops were considered to be a part of a neural network used to produce transfer function [10] A fuzzy H flip-flops allow the building of fuzzy register.…”

Ferroelectric multiple-valued logic units

“…The first level is connected to the memory of PLA to read the coefficients. x2 x1 a (0) a (1) a (2) a (3) a (4) a (5) a (6) a (7) a (8) a (9) a (10) a (11) a (12) a (13) a (14) a (15) a (16) a (17) a (18) a (19) a (20) a (21) a (22) a (23) a (24) a (25) a (26) M L Figure 4. The detailed structure of the PLA for implementation of 3-valued function on 3 variables…”

Symbolic checking of Fuzzy CTL on Fuzzy Program Graph

“…According to (8) it is obvious g ≤ e Δ , because in each iteration there exists at least one v j whose value is incremented by a minimum of Δ. In order to store all members of S we use all variables U and W , consequently e = O(2 h ) and g = O(2 h+d ).…”

“…The concept of fuzzy flip-flops was first proposed by Hirota et al and then studied in [8,13,14,19,20]. They presented the idea of designing fuzzy logic hardware systems using fuzzy flip-flops.…”

“…Ben Choi and Kankana Shulka proposed a multi-valued D flip-flop in [8]. Although they investigated the validity of their proposed circuit via computer simulations, under certain conditions gate delays lead to dynamic hazards.…”