Question

Consider an arbitrary number system with independent digits as 0, 1, and A. If we generate the first few numbers in the sequence as 00, 01, 0A, 10, 11, 1A and if this process is continued to generate the numbers, then the position of 10A is:

• A. 15
• B. 12
• C. 9
• D. 10

Hint:

When dealing with non-standard digits in a base, assign values and proceed like normal base conversion.

Answer 1

The Correct Option is B

Step 1: Digits allowed are 0, 1, A (i.e., base 3)
Step 2: Generate numbers in increasing base-3 order (with 0,1,A)
We convert from base-10 (in 3-digit base-3 with 0,1,A): \[ {Mapping: } 0 \rightarrow 0, 1 \rightarrow 1, 2 \rightarrow A \] List of 3-digit numbers in increasing order: \[ 000, 001, 00A, 010, 011, 01A, 0A0, 0A1, 0AA, 100, 101, 10A \] Step 3: Find position of 10A
It is the 12th number in the sequence (1-based indexing)