Octal to Hexadecimal Matching (Base Conversion Practice) Convert each octal value in List I to its correct hexadecimal equivalent in List II and select the correct mapping.

Introduction / Context:Digital design frequently requires base conversions between octal, decimal, and hexadecimal. This problem tests the ability to convert octal numbers to their hexadecimal forms accurately and then perform a correct matching.

Given Data / Assumptions:

• List I (Octal): A = 66, B = 77, C = 55, D = 47.
• List II (Hex): 1 = 3F, 2 = 36, 3 = 27, 4 = 2D.
• All numbers are unsigned positive integers.

Concept / Approach:

Convert octal to decimal, then decimal to hexadecimal. Alternatively, group binary triples for octal and quadruples for hex; however, the decimal bridge is straightforward and less error-prone for small values.

Step-by-Step Solution:

Verification / Alternative check:

Binary method: 66(oct) → 110 110(b) → 0011 0110(b) = 0x36; 77(oct) → 111 111(b) → 0011 1111(b) = 0x3F; 55(oct) → 101 101(b) → 0010 1101(b) = 0x2D; 47(oct) → 100 111(b) → 0010 0111(b) = 0x27.

Why Other Options Are Wrong:

Any alternative pairing misrepresents at least one conversion and fails a quick decimal cross-check.

Common Pitfalls:

Arithmetic slips with base-8 multiplication, or confusing the hex pairs (e.g., mixing 0x2D and 0x27).

Final Answer:

A-2, B-1, C-4, D-3