Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL

7.2 COMBINATIONAL LOGIC CIRCUITS

Building a digital system using the methods learned thus far is very possible, although very unrealistic. For simplicity, consider the NAND gate as the primitive element to design all other logic functions. A microcomputer chip such as the Motorola 68000 device comprising the equivalent of some 70,000 gates would require some 17,500 integrated-circuit (IC) packages. Designing such a complex digital system at the gate level would be a very difficult, if not impossible task. An alternative design method is to use a combination of gates as building blocks, referred to as combinational circuits.

The primary tools required to build combinational circuits include truth table design, basic knowledge of Boolean algebra, and implementation using logic gates. In some special cases the specification is given in the form of a complete truth table, but most often the procedure of designing a combinational logic circuit will start with a method to determine a truth table from a verbal or written statement, which a customer provides to the designer. A Boolean expression describes the circuit behavior required as expressed by the truth table. It is helpful to convert a Boolean expression with an arbitrary mixture of operations (AND, OR, and NOT) to a form, which is easier to implement with a combinational logic circuit.

Figure 7.1 Block Diagram of a Combinational ...