The field of computer arithmetic is a fascinating subject, and not at all the drudgery that most of us experienced with our first exposure to the third r of the three r’s at school. The first two r’s are related as requirements of the processes required to become literate. The third r relates to numeracy, the understanding and implementation of computation which is a basic requirement for “technical literacy,” as important a skill in today’s world as was traditional literacy in the past. In this introductory chapter, we provide a brief history and introduction to number systems and machine calculation; we emphasize special applications that drive the search for efficient machine arithmetic given the requirements of the applications and the available technology.