Hex to Decimal — Positional Weights Convert the hexadecimal number 1CF16 to its decimal value by expanding each digit with powers of sixteen.

Introduction / Context:
Hexadecimal to decimal conversion relies on positional weights where each position represents a power of sixteen. Understanding this expansion is necessary for interpreting addresses, constants, and register values in documentation and code.

Given Data / Assumptions:

• Hex input: 1CF16.
• Digit values: 1=1, C=12, F=15.
• Rightmost position is 16^0, moving left increases the exponent by one.

Concept / Approach:
Multiply each hex digit value by its positional weight and sum. The formula is value = d216^2 + d116^1 + d016^0 for a three digit hex number d2 d1 d0.

Step-by-Step Solution:
1) Write weights: 16^2 = 256, 16^1 = 16, 16^0 = 1.2) Map digits: 1→1, C→12, F→15.3) Compute partials: 1256 = 256; 1216 = 192; 151 = 15.4) Sum: 256 + 192 + 15 = 463.

Verification / Alternative check:
Convert 463 back to hex by repeated division by 16: 463 / 16 = 28 remainder 15 (F); 28 / 16 = 1 remainder 12 (C); 1 / 16 = 0 remainder 1. Reading remainders in reverse yields 1CF16.

Why Other Options Are Wrong:

• 4033, 4049, 479: Each results from incorrect weights or arithmetic mistakes, not from the exact expansion of 1CF16.

Common Pitfalls:
Confusing C with 13 rather than 12, or using powers of 10 instead of 16 for the place values.

Final Answer:
463