A geometric approach to presenting computer representations of integers

Abstract

The student's first serious exposure to computer arithmetic typically occurs in a sophomore course in machine architecture or assembler language. A glance at several excellent and widely used texts for these courses (for example [M], [Sh], [St], [T]) shows that this material is often presented as an unmotivated set of mechanical rules to, for example, add numbers using one's complement notation or compute the two's complement representation of a negative integer. This paper describes a way to motivate these topics by relating them to the computer's "natural " arithmetic.