Logic Design of Elementary Functional Operators in Quaternary Algebra

Abstract

Abstract-Multivalued logic is an extension of Boolean algebra with high radix approaches and is preferable over conventional binary logic operations for reduction in interconnection cost, chip area both on-chip and between chips and high information handing capability. This paper includes the design of elementary combinational quaternary operators that have sufficient representative capability to efficiently implement in intricate quaternary arithmetic circuits. Design of several combinational logic circuits have been presented which can function individually and in logic blocks for designing further complex circuits resulting in a reduction of circuit complexity and better speed processing in integrated circuit technology.Index Terms-Cycle gate, max and min gate, multivalued logic, quaternary algebra. I. INTRODUCTIONBinary logic has been predominant in embedded system and a fundamental for computer programming and mathematical logic due to its easy accessibility and widespread use in logic circuits. Operating with binary logic implies to controlling the real world with computers and that an alternative improved approach with a better usage of transmission path, storage and processing of large amount of information in digital signal processing even exist seems somewhat impossible. Yet, Moore's law states that, the number of transistors on integrated circuits doubles approximately every two years. As this law has been by far proven accurate, it is high time we considered alternative approaches to reduce this tremendous positive rate of elements used in integrated circuits. It has been suggested that by increasing the processing speed, memory capacity, sensors or memory states, this significant rate can be inhibited to an exponential rate. But, due to the inherent limitation data representation system of only two distinct levels {0, 1}, binary logic impedes the scope for multiple states and lacks high speed and information handling capacity. On the other hand, multivalued number systems, such as ternary and quaternary systems with a radix more than '2' (p>2) emerges with the immediate benefit of larger information handling and storage capacities.Multivalued logic system introduces new operators in addition to binary values {0, 1} and is a proposed extension of the idea that n valued logic can be used instead of two logical values (that is, true or false, logic high or low) where n>2 [1].Perhaps one of the most tangible immediate benefits of Manuscript received September 9, 2014; revised January 5, 2015.The authors were with the Ahsanullah University of Science and Technology, Dhaka, Bangladesh (e-mail: asif.faiyaz@gmail.com).higher-radix approaches like quaternary logic lies in their potential for reduction of the wiring congestion and interconnection cost [2]. Using a single conductor to transmit three or more discrete voltage or current values allows for greater information content per wire and thus results in a circuit with reduced conductors and logic gates than the binary-valued counterpart. Furthermore model...