1.4 Numeral systems

Representations of memory will require proficiency in numeral systems, so in preparation for section 1.5 on memory, we will review positional numeral systems in this section. Before we begin the serious consideration of positional numeral systems, let's pause for a whimsical story exploring the motivation and requirements for representing numbers in positional numeral systems.

1.4.1 The myth of Niles and Pepper

Niles was an unusual boy with great hair, living in a time before numeral systems. Quantities were familiar, but symbolic representations of them were not. Niles lived in a grove of trees. A grove on the other side of the hill was home to his friend Pepper, a sassy, no-nonsense girl.

One day, Niles and Pepper were walking together and, as children do, began arguing about whose grove had more trees. If the argument had been about who had …