12 - Significance, Double Precision, Complex Numbers

Abstract

Constants are stored in the computer's memory as binary digits. To highlight the way in which the contents of a word translate into decimal, this chapter describes the way to convert a binary number to a decimal number. In any number system, the largest digit that can be used in a number is the value of the base minus one. Therefore, the largest digit that can be used in the decimal system is nine. As the binary system uses two as its base, the largest digit that can be used in a binary number is one. Therefore, a binary number consists of zeros and ones. A maximum of approximately seven decimal digits can be used in writing a REAL constant on the IBM 360. The chapter explains why the maximum number of digits depends on the computer's hardware. A word that stores a REAL constant is subdivided into a sign bit, an exponent part, and a mantissa. The mantissa contains the fractional part of the REAL constant.