Number systems: Convert the hexadecimal value 1D7F16 to its decimal (base-10) equivalent. Show the positional weights used.

Introduction / Context:
Hexadecimal-to-decimal conversion is common when interpreting addresses, error codes, and configuration values. Each hex digit corresponds to a power-of-16 weight, making manual conversion manageable for moderate-length values.

Given Data / Assumptions:

• Input: 1D7F16, where D = 13 and F = 15.
• Weights from right to left: 16^0, 16^1, 16^2, 16^3, ...
• No sign or special encoding—just an unsigned value.

Concept / Approach:
Expand by positional weights and sum: value = d316^3 + d216^2 + d116^1 + d016^0. Substitute digits and compute each term, then sum to get the decimal number.

Step-by-Step Solution:
List digits: 1, D(13), 7, F(15).Compute weights: 16^3 = 4096; 16^2 = 256; 16^1 = 16; 16^0 = 1.Multiply: 14096 = 4096; 13256 = 3328; 716 = 112; 151 = 15.Sum: 4096 + 3328 + 112 + 15 = 7551.

Verification / Alternative check:
Convert to binary then to decimal: 1 = 0001, D = 1101, 7 = 0111, F = 1111 → 0001 1101 0111 1111₂; evaluating that binary confirms 7551.

Why Other Options Are Wrong:
8771 / 5557 / 7781: sums do not match the correct positional expansion of 1D7F16.None of the above: incorrect because 7551 is correct.

Common Pitfalls:
Misreading hex digits above 9, forgetting digit weights, or adding in the wrong order.

Final Answer:
755110