Chapter 14 - IEEE 754 Floating Point Numbers

Abstract

This chapter focuses on IEEE 754 floating point numbers. These numbers are the most common representation today for real numbers on computers. Floating point represent real numbers using a base number and an exponent. For example,123.456 could be represented as 1.23456 x 102. In hexadecimal, the number 123.abc might be represented as 1.23abc x 162. IEEE floating point numbers have three components: the sign, the exponent (also known as the characteristic), and the mantissa. The mantissa is composed of the fraction and an implicit leading digit (explained below). The exponent is always applied to an implied 2, so is really 2exponent. The sign bit is a 0 to denote a positive number; 1 is a negative number. To support both negative and positive exponents a bias is added to the actual—127 for single-precision floats. The mantissa represents the number itself, without exponent. It is composed of an implied leading bit and the fraction bits. The IEEE-754 standard supports some special values such as zero is represented as all zeroes in the mantissa and exponent, with a zero or one in the sign bit. Moreover, some computations generate undefined results—defined as Not a Number (NAN).