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Modern Assembly Language Programming with the ARM Processor by Larry D. Pyeatt

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Chapter 8

Non-Integral Mathematics

Abstract

This chapter starts by demonstrating how to convert fractional numbers to radix notation in any base. It then presents a theorem that can be used to determine in which bases a given fraction will terminate rather than repeating. That theorem is then used to explain why some base ten fractional numbers cannot be represented in binary with a finite number of bits. Next fixed-point numbers are introduced. The rules for addition, subtraction, multiplication, and division are given. Division by a constant is explained in terms of fixed-point mathematics. Next, the IEEE floating point formats are explained. The chapter ends with an example showing how fixed-point mathematics can be used to write functions ...

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