Some of the recent digital systems have a serious clock skew problem due to huge hardware implementation and high-speed operation in VLSI's. To overcome this problem, clock distribution techniques and, more notably, asynchronous system design methodologies have been investigated. Since the latest asynchronous digital systems use two-rail logic with two-phase data transfer manner, more than two-fold hardware is required in comparison with the synchronous system. In this article, we present a design of asynchronous digital system which is based on B-ternary logic that can process binary data. The system which is based on speed-independent mode consists of data-path and its controller. Then we provide B-ternary two-phase binary data processing in the data-path and its control procedure with hand-shake protocol. To implement the system some functional elements are presented, that is, a ternary-in/binary-out register with request/acknowledge circuits and a control unit. These functional elements are fabricated with ternary NOR, NAND, INV gates and ternary-in/binary-out D-FF (D-elements). The B-ternary based asynchronous circuit has less interconnections, achives race-free operations and makes use of conventional binary powerful design tools. Particularly, we extend the speed-independent delay model to relativity delays in order to reduce hardware overhead of checking memory stability in the system. As a concrete example, a carry-completion type asynchronous adder system is demonstrated under extended speed-independent mode to show the validity of the extension.

Regular ternary logic functions are one of the most useful special classes of Kleenean functions, and a lot of research has been done on them. However, there has been little work done on incompletely specified regular ternary logic functions. This paper describes the following points: (1) Minimization of incompletely specified regular ternary logic functions. (2) A new definition of incompletely specified fuzzy switching functions and their minimization. (Concretely speaking, minimal disjunctive forms of incompletely specified fuzzy switching functions are represented in formulas of regular ternary logic functions. ) (3) Their application to fuzzy logic circuits such as fuzzy PLAs of AND-OR type.

Three types of ternary decision diagrams (TDDs) are considered: AND -TDDs, EXOR-TDDs, and Kleene-TDDs. Kleene-TDDs are useful for logic simulation in the presence of unknown inputs. Let N(BDD:f), N(AND-TDD:f), and N(EXOR-TDD:f) be the number of non-terminal nodes in the BDD, the AND-TDD, and the EXOR-TDD for f, respectively. Let N(Kleene-TDD:) be the number of non-terminal nodes in the Kleene -TDD for , where is the regular ternary function corresponding to f. Then N(BDD:f) N(TDD:f). For parity functions, N(BDD:f)=N(AND-TDD:f)=N(EXOR-TDD:f)=N(Kleene-TDD:). For unate functions,N(BDD:f)=N(AND-TDD:f). The sizes of Kleene-TDDs are O(3n/n), and O(n3) for arbitrary functions, and symmetric functions, respectively. There exist a 2n-variable function, where Kleene-TDDs require O(n) nodes with the best order, while O(3n) nodes in the worst order.

A new design methodology is proposed and analyzed for the design of ternary logic systems. In the new ternary logic systems, no conversions among radices are required and only the two-state ternary literals associated with the ternary signals are transmitted in the whole system. With the new design methodology, the ternary systems can be realized by the dynamic CMOS logic circuits which are simple and fully compatible with those of the conventional binary logic circuits in process, power supply, and logic levels. A new dynamic differential logic called the CMOS Redundant Differential Logic (CRDL) is also developed to increase the logic flexibility and the circuit performance. Using the new design methodology and the CRDL circuits, the multiplier with redundant binary addition tree is designed in both non-pipelined and pipelined systems. The experimental chip has been fabricated and measured, which successfully verifies the correctness of the logic functions and the speed performance of the designed circuits.