Numbers and Computers

This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second examines several other number representations. Details are explained thoroughly, with clarity and specificity. Each chapter ends with a summary, recommendations, carefully selected references, and exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, big integers and rational arithmetic. This new edition has three new chapters: Pitfalls of Floating-Point Numbers (and How to Avoid Them), Arbitrary Precision Floating Point, and Other Number Systems. This book is for anyone who develops software including software engineers, scientists, computer science students, engineering students and anyone who programs for fun. "This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, floating point numbers, big integers and rational arithmetic. This book is for anyone who develops software including software engineerings, scientists, computer science students, engineering students and anyone who programs for fun." -- Publisher's website This is a book about numbers and how those numbers are represented in and operated on by computers. Of course, numbers are fundamental to how computers operate because, in the end, everything a computer works with is a number. It is crucial that people who develop a code understand this area becasue the numerical operations allowed by computers and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to help by exploring, in sufficient, but not overwhelming, detail, just what it is that computers do with numbers. From preface This book is about numbers and how they are represented and manipulated by computers. In this second edition, we expand on the coverage of the first edition by adding three new chapters and new material to several sections.