Page 108 - Engineering Digital Design

CHAPTER 3

Background for Digital Design

3.1 INTRODUCTION
The contents of this chapter are considered all important to the reader's understanding of
the remainder of this text and, hence, to an understanding of modern digital design methods.
In this chapter the reader will learn mixed logic notation and symbology, Boolean algebra,
and the reading and construction of logic circuits. Besides becoming the industrial standard,
mixed logic notation and symbology, once learned, offers a remarkably simple, direct means
of reading and constructing logic circuits and timing diagrams. Use will be made of the
CMOS logic family to develop this symbology. Other logic families, such as NMOS and
TTL, are discussed in Appendix A.
This chapter goes beyond the usual treatment of Boolean algebra to present what is
called XOR algebra, an extension of Boolean algebra that deals with functions that have
become very important in circuit design, particularly in arithmetic circuit design. CMOS
realizations of XOR functions have, in a special sense, revolutionized thinking along these
lines, making the use of such functions much more appealing to the logic designer.

3.2 BINARY STATE TERMINOLOGY AND MIXED LOGIC NOTATION
Digital systems are switching devices that operate in only one of two possible states at any
given time, but that can be switched back and forth from one state to another at very high
speed (millions of times per second). The two states are high voltage (HV) and low voltage
(LV). The LV and HV levels are usually taken as 0 V and 2 to 5 V, respectively, for common
CMOS logic circuits.
To design a useful digital device, meaningful logic names must be assigned to the inputs
and outputs of a logic circuit so that their physical interpretation in terms of voltage levels
can be made unambiguously. This requires the use of a notation that can easily bridge the gap
between the logic domain in which the device is designed, and the physical domain in which
the device is to be operated. The following subsection defines this notation.

3.2.1 Binary State Terminology
A state is said to be active if it is the condition for causing something to happen. And for
every active state there must exist one that is inactive. In the binary (base 2) system of 1's

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