Application of Ternary Algebra to the Study of Static Hazards

Abstract

This paper is concerned with the study of static hazards in combinational switching circuits by means of a suitable ternary switching algebra. Techniques for hazard detection and elimination are developed which are analogous to the Huffman-McCluskey procedures. However, gate and series-parallel contact networks are treated by algebraic methods exclusively, whereas a topological approach is applied to non-series-parallel contact networks only. Moreover, the paper derives necessary and sufficient conditions for a ternary function to adequately describe the steady-state and static hazard behavior of a combinational network. The sufficiency of these conditions is proved constructively leading to a method for the synthesis of combinational networks containing static hazards as specified. The section on non-series-parallel contact networks also includes a brief discussion of the applicability of lattice matrix theory to hazard detection. Finally, hazard prevention in contact networks by suitable contact sequencing techniques is discussed and a ternary map method for the synthesis of such networks is explained.