Main Answer:
The value of the largest digit in the base-X number system, where X is any positive integer, is (X-1). This is because in base-X, digits are represented from 0 to (X-1). Therefore, the largest digit is (X-1).
Step-by-step explanation:
In any base-X number system, each digit can take values from 0 to (X-1). For example, in base-10, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Similarly, in base-8, the digits are 0, 1, 2, 3, 4, 5, 6, and 7.
The largest possible digit in the base-X system is (X-1). This is because the digits start from 0 and go up to (X-1), so (X-1) represents the highest value a digit can take in that base.
For instance, in base-6, the digits are 0, 1, 2, 3, 4, and 5. The largest digit is 5. In base-16 (hexadecimal), the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The largest digit is F, which represents 15 in base-10. This pattern holds for any positive integer X.