subhexadecimal

Subhexadecimal is a term that refers to a number system with a base between 7 and 15, inclusive. It is a conceptual extension of the hexadecimal system (base 16) and the decimal system (base 10). Unlike the more common decimal and hexadecimal systems, subhexadecimal bases are not widely used in practical computing or everyday life. However, they can be explored in theoretical contexts or for specific educational purposes to illustrate the principles of number representation.

When working with a subhexadecimal base, the digits used would be a combination of standard decimal digits and letters. For a base such as base 12, often called duodecimal, the digits 0-9 are used, along with two additional symbols, typically 'A' for ten and 'B' for eleven. Similarly, for a base like base 14, the digits would extend to 'A', 'B', 'C', and 'D' representing twelve, thirteen, and fourteen respectively. The choice of symbols for values greater than nine is arbitrary but follows conventions established for hexadecimal and other higher bases.

The concept of subhexadecimal systems highlights the flexibility of positional numeral systems. Any integer greater than 1 can serve as a base for a number system, allowing for unique representation of all real numbers. The practicality of these systems diminishes as the base increases beyond hexadecimal due to the increasing number of distinct symbols required.