The implementation and applications of multiple-valued logic

Multiple-Valued Logic (MVL) takes two major forms. Multiple-valued circuits can implement the logic directly by using multiple-valued signals, or the logic can be implemented indirectly with binary circuits, by using more than one binary signal to represent a single multiple-valued signal. Techniques such as carry-save addition can be viewed as indirectly implemented MVL. Both direct and indirect techniques have been shown in the past to provide advantages over conventional arithmetic and logic techniques in algorithms required widely in computing for applications such as image and signal processing. It is possible to implement basic MVL building blocks at the transistor level. However, these circuits are difficult to design due to their non binary nature. In the design stage they are more like analogue circuits than binary circuits. Current integrated circuit technologies are biased towards binary circuitry. However, in spite of this, there is potential for power and area savings from MVL circuits, especially in technologies such as BiCMOS. This thesis shows that the use of voltage mode MVL will, in general not provide bandwidth increases on circuit buses because the buses become slower as the number of signal levels increases. Current mode MVL circuits however do have potential to reduce power and area requirements of arithmetic circuitry. The design of transistor level circuits is investigated in terms of a modern production technology. A novel methodology for the design of current mode MVL circuits is developed. The methodology is based upon the novel concept of the use of non-linear current encoding of signals, providing the opportunity for the efficient design of many previously unimplemented circuits in current mode MVL. This methodology is used to design a useful set of basic MVL building blocks, and fabrication results are reported. The creation of libraries of MVL circuits is also discussed. The CORDIC algorithm for two dimensional vector rotation is examined in detail as an example for indirect MVL implementation. The algorithm is extended to a set of three dimensional vector rotators using conventional arithmetic, redundant radix four arithmetic, and Taylor's series expansions. These algorithms can be used for two dimensional vector rotations in which no scale factor corrections are needed. The new algorithms are compared in terms of basic VLSI criteria against previously reported algorithms. A pipelined version of the redundant arithmetic algorithm is floorplanned and partially laid out to give indications of wiring overheads, and layout densities. An indirectly implemented MVL algorithm such as the CORDIC algorithm described in this thesis would clearly benefit from direct implementation in MVL