Chapter Summary

The main purpose of this chapter is to acquaint you with the basic concepts involved in logic design and to give you a general understanding of the basic circuit configurations used to construct computer systems. This level of familiarity will not enable you to design these components; rather, it gives you a much better understanding of the architectural concepts discussed in the following chapters.

In this chapter we examined the behaviors of the standard logical operators AND, OR, and NOT and looked at the logic gates that implement them. Any Boolean function can be represented as a truth table, which can then be transformed into a logic diagram, indicating the components necessary to implement the digital circuit for that function. Thus, truth tables provide us with a means to express the characteristics of Boolean functions as well as logic circuits. In practice, these simple logic circuits are combined to create components such as adders, ALUs, decoders, multiplexers, registers, and memory.

There is a one-to-one correspondence between a Boolean function and its digital representation. Boolean identities can be used to reduce Boolean expressions, and thus, to minimize both combinational and sequential circuits. Minimization is extremely important in circuit design. From a chip designer's point of view, the two most important factors are speed and cost: minimizing the circuits helps to both lower the cost and increase performance.

Digital logic is divided into two categories: combinational logic and sequential logic. Combinational logic devices, such as adders, decoders, and multiplexers, produce outputs that are based strictly on the current inputs. The AND, OR, and NOT gates are the building blocks for combinational logic circuits, although universal gates, such as NAND and NOR, could also be used. Sequential logic devices, such as registers, counters, and memory, produce outputs based on the combination of current inputs and the current state of the circuit. These circuits are built using SR, D, and JK flip-flops.

These logic circuits are the building blocks necessary for computer systems. In the next chapter we put these blocks together and take a closer, more detailed look at how a computer actually functions.

If you are interested in learning more about Kmaps, there is a special section that focuses on Kmaps located at the end of this chapter, after the exercises.