Hexadecimal to decimal — evaluate 777₁₆. Compute the decimal value of the hex number 0x777 using positional weights.

Introduction / Context:Hexadecimal expands by powers of 16. Rewriting multi-digit hex numbers into decimal clarifies positional weighting and strengthens mental math for address offsets and constants in code.

Given Data / Assumptions:

• Hex number: 777₁₆
• Each digit 7 represents decimal 7

Concept / Approach:Apply place values: value = d216^2 + d116^1 + d016^0. With d2=d1=d0=7, the computation is straightforward.

Step-by-Step Solution:

Verification / Alternative check:Convert to binary: 7 → 0111, so 777₁₆ = 0111 0111 0111₂. Evaluate in decimal: (4+2+1)16^2 + (4+2+1)16 + (4+2+1) = 7256 + 716 + 7, same result 1911₁₀.

Why Other Options Are Wrong:

• 191 and 19: undercount by ignoring higher place values.
• 19111: overcount by an extra digit place.
• 2071: arithmetic mismatch of the 16-based expansion.

Common Pitfalls:

• Treating base-16 digits as base-10 and adding 7+7+7=21 (incorrect).

Final Answer:1911