Digital Electronics: Principles, Devices and Applications

234 Digital Electronics'n'InputsCombinationalLogic'm'OutputsFigure 7.1Generalized combinational circuit.n, there are 2 n possible combinations of bits at the input. Each output can be expressed in terms ofinput variables by a Boolean expression, with the result that the generalized system of Fig. 7.1 can beexpressed by m Boolean expressions. As an illustration, Boolean expressions describing the functionof a four-input OR/NOR gate are given asY 1 OR output = A + B + C + D and Y 2 NOR output = A + B + C + DAlso, each of the input variables may be available as only the normal input on the input linedesignated for the purpose. In that case, the complemented input, if desired, can be generated by usingan inverter, as shown in Fig. 7.2(a), which illustrates the case of a four-input, two-output combinationalfunction. Also, each of the input variables may appear in two wires, one representing the normal literaland the other representing the complemented one, as shown in Fig. 7.2(b).In combinational circuits, input variables come from an external source and output variables feed anexternal destination. Both source and destination in the majority of cases are storage registers, and theseCombinationalLogic(a)CombinationalLogic(b)Figure 7.2Combinational circuit with normal and complemented inputs.