Chapter 2 - COMPUTER ARITHMETIC

Abstract

This chapter discusses some basic ideas about number bases and number representations. Any integer can be used as a base for a number system. The most commonly used number bases are 10, 2, 8, and recently 16. Numbers expressed with these bases are called decimal, binary, octal, and hexadecimal numbers, respectively. Most computers use the binary number system because of the fact that in this system only two digits are needed for representing numbers. If a closed switch or a positive polarity denotes the digit 1, and an open switch or negative polarity denotes the digit 0, then any binary number can be represented by a series of opened and closed switches, or positive and negative polarities. However, a major drawback with the binary number system is that it requires a many binary digits to represent even rather small numbers. The data for a problem given as decimal numbers must be converted into suitable binary numbers for use by the computer.