Floating-Point Systems

This chapter introduces the concept of floating-point numbers and how to build systems that use floating-point representations to perform mathematical operations. Floating-point numbers represent real numbers (i.e., ones that have a fractional component) using an encoding technique that first converts the original number into scientific notation (SN) and then encodes the three distinct fields of the notation with binary codes (e.g., the sign, the mantissa, and the exponent). The standard that guides the encoding/decoding of floating-point numbers is IEEE 754. This standard is used in all modern computers. This chapter begins with a detailed explanation of the IEEE 754 encoding approach including the anatomy, the algorithms for converting between decimal and floating-point formats, range, and precision. The chapter then discusses arithmetic using floating-point numbers and then moves into Verilog modeling for floating-point systems. The goal of this chapter is to provide an understanding of floating-point numbers and the basic principles of how to begin building digital systems that use floating-point numbers in Verilog.