A geometric approach to presenting computer representations of integers

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 1992 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.