# Arithmetic Operations in Digital Computers

## Excerpt

Among the first things that are learned in a study of mathematics are rules and procedures for performing basic arithmetic operations, notably addition, subtraction, multiplication, and division. The rules and procedures taught in school are, for the most part, aimed at making the operations as simple and speedy as possible when a pencil and a piece of paper are the only tools. In the design of more elaborate arithmetical tools, it is usually found necessary or at least highly desirable to devise new methods for executing the various arithmetic operations.

This text has been written to point out the shortcomings of pencil-andpaper rules and procedures when applied to computing machinery and to explain the more important of the schemes which have been worked out for executing arithmetic operations in that class of machinery generally known as "digital computers." Of course, to appreciate the features of the different schemes, many other points must be considered, and these range all the way from the systems of symbols which are to be used to the ideas involved in causing a computer to proceed through a long sequence of arithmetic operations in an automatic fashion. In other words, it might be said that the text has been prepared as an answer to the question: "How does a digital computer work?"

In the design of computers, not only the methods of performing arithmetic operations, but also the fundamental concepts with regard to symbolic representation of quantities have been subjected to critical review. For this reason, the explanation of computer functioning has been started with a discussion of systems of symbols which have been invented for representing the numbers entering into the computations. Relatively little attention is given to actual components, circuits, and other engineering details which must be considered when designing a computer. However, these details have been a great influence in the selection of the arithmetic methods to be presented, and the advantages and disadvantages of the various schemes from an engineering standpoint are pointed out throughout the text. Most of the means for performing arithmetic operations are explained through the use of "functional block diagrams," where it is understood that any set of physical components which pro-

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