Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols.
-base $b$, eight distinct symbols (where $b$ is any counting number 2 or greater)
A) $8 ^ { b } - 1$
B) $b ^ { 8 } - 1$
C) $b ^ { 8 }$
D) $8 \mathrm {~b} - 1$

Question

Quizplus · Accepted Answer

The largest number expressible in a base $b$ system with eight distinct symbols is $b^8 - 1$, because you can use all symbols in each of the eight positions, from $0$ to $b-1$, and the highest value is when all positions are at their maximum ($b-1$), leading to the formula $b^8 - 1$.

Identify the Largest Number Expressible in a Simple Grouping System bbb

Identify the Largest Number Expressible in a Simple Grouping System $b$