Final answer:
The largest unsigned integer with 'n' digits in base 'b' is calculated as ((b^n - 1) / (b - 1)), where every digit is the highest possible in that base (b-1).
Step-by-step explanation:
The largest unsigned integer with n digits in base b would be represented by all digits being the highest digit possible in base b, which is b-1. Each digit position contributes to the value of the number based on its place position. So, the largest number N is the sum of (b-1) multiplied by the base raised to the power of the position index, starting from 0 up to n-1.
Mathematically, this can be represented as:
- N = (b-1) + (b-1)b + (b-1)b2 + ... + (b-1)bn-1
This series is a geometric progression that can be summed up, which gives us the maximum value as:
N = ((bn - 1) / (b - 1))