Page 364 - Engineering Digital Design

CHAPTER 8

Arithmetic Devices

and Arithmetic Logic Units (ALUs)

8.1 INTRODUCTION

In this chapter digital circuits will be designed with electrical capabilities that can be
interpreted as performing the basic arithmetic operations of binary numbers. The basic
operations include

• Addition
• Subtraction
• Multiplication
• Division

Now, Boolean equations are uniquely defined so as to perform specific arithmetic operations,
and the 1's and O's, which have previously been used only as logic levels, must take on a
numerical significance. The reader must keep in mind that an arithmetic circuit is only the
electrical analog of the arithmetic operation it represents. In fact, it is the interpretation of
the electrical circuit's behavior that bridges the gap between physical and logic domains.
The treatment of arithmetic circuits presented in this text is not intended to be a treatise
on the subject. Rather, the intent is to introduce the subjects at both the beginning and
intermediate-to-advanced levels utilizing, where necessary, appropriate algorithms for the
basic operations in question. The subjects of arithmetic logic units (ALUs) and the applica-
tion of dual-rail methods, which are covered in later sections, fall within the intermediate-
to-advanced level of coverage and may not be expected to be part of a first-level course in
digital design.

8.2 BINARY ADDERS

Because of the nature of binary and the requirements for arithmetic manipulation, ap-
proaches to basic adder design vary considerably depending on the form the manipulation
takes. There are ripple-carry adders, carry-save, carry select, and carry-look-ahead adders,

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