Number Systems and Arithmetic

Publisher Summary This chapter discusses number systems and arithmetic for machine calculation. It presents techniques, concepts, and models that are relevant to the development of improved machine arithmetic processes. An attempt is made to present the important basic concepts and the essential flavor of each item discussed. The chapter also presents definitions, basic concepts, and the general properties and characteristics of machine number systems. Emphasis is placed on the distinction between a representation in a machine number system and the interpretation, which may be given to a representation. The manner in which a machine designer restricts interpretation is also considered for fixed point number system. The consideration of number systems for digital computer applications may be restricted to finite number systems. The most important characteristics of machine number systems, contrary to the most prevalent opinion, are finitude rather than the fact that binary logic employed. Overflows, underflows, scaling, and complement coding that characterize machine number systems are direct consequences of finitude and, in fact, illustrate both the detrimental and beneficial consequences of finitude.

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