Base conversion — convert the binary number to decimal. Task: Evaluate the decimal value of binary 1110₂ using positional weights.

Introduction / Context:Binary-to-decimal conversion reinforces understanding of bit weights (1, 2, 4, 8, …). This is essential when reading register dumps, flags, and immediate constants in low-level code.

Given Data / Assumptions:

• Binary number: 1110₂
• No sign bit or fraction; simple unsigned conversion

Concept / Approach:Sum the weights corresponding to the 1 bits. For 4-bit numbers, the weights from most to least significant are 8, 4, 2, 1.

Step-by-Step Solution:

Verification / Alternative check:Using polynomial expansion: 12^3 + 12^2 + 12^1 + 02^0 = 8 + 4 + 2 + 0 = 14. Converting 14 back to binary gives 1110₂, confirming the round-trip.

Why Other Options Are Wrong:

• 3, 1, 7, 12: each omits one or more active bit weights.

Common Pitfalls:

• Reading bits right-to-left and misassigning weights (e.g., adding the 1′s place when it is 0).

Final Answer:14