What mathematical computation does the octal numbering system rely on?

The octal numbering system is based on powers of eight. This means that each digit in an octal number represents a power of eight, reflecting the base of the system. For example, the rightmost digit represents 8^0 (which is 1), the next digit to the left represents 8^1 (which is 8), the next one represents 8^2 (which is 64), and so on. This structure allows for a compact representation of binary numbers, which is particularly useful in computing where data is often expressed in binary form.

In this context, the other options can be understood as follows: the powers of two relate to the binary system, where numbers are expressed using two digits (0 and 1); powers of ten characterize the decimal system commonly used in daily life; and powers of sixteen pertain to the hexadecimal system utilized in computing for a more compact representation than binary. Each numeral system has its own unique base, which dictates how numbers are represented and calculated within that system. In the case of octal, the focus is strictly on powers of eight.