Design of combinational circuits

The design of combinational circuits is perhaps the most important topic in logic design, and a thorough understanding of the principles of combinational design is an essential prerequisite to the design of more complex sequential systems. A combinational logic circuit has the characteristic that the steady-state output obtained from the circuit is dependent only upon the present state of the input. Therefore, if the input and output signals are denoted by X and Y respectively, then Y = f(X). Combinational circuits may be single-output or multiple-output, and while in the latter case an m-output circuit may always be considered as m single-output circuits, this precludes any form of circuit minimization in which components are used in the generation of more than one output. This chapter is primarily concerned with fundamental logic design principles, based around the optimal use of ‘gate-level’ components. The classical objective of logic design is to produce a circuit having the required input—output function while utilizing the minimum number of components. Obviously no designer will argue against this as an example of standard engineering practice, but we will examine this point again in later chapters when it will be seen in a wider context, as only one of a number of factors which contribute to the total cost of system design and manufacture.