Chapter 11 - An Introduction To Machine Calculations

Abstract

This chapter provides an overview into machine calculations in embedded systems. There are several types of machine calculations, such as integer, fixed point, and floating point, all of them differ in terms of versatility, accuracy, and speed. Binary integer arithmetic is the oldest technique used by software developers. One of the important aspects of integer type is the byte ordering. Floating-point math is a very powerful tool that conforms to IEEE 754, the standard for binary floating point math. This standard defines two sizes of floating point formats and minimum requirements for two additional sizes. A floating point number has three parts—namely, a sign bit, a mantissa, and an exponent. Fixed point math is implemented using integers and a scale factor. Instead of having the least-significant bit represent one unit, it represents a unit divided by a scale factor. The fixed-point implementations of addition and subtraction are exact. Those for multiplication and division must round the result to the nearest integer in the implementation.