Binary-to-decimal conversion: determine the decimal (base-10) value of the 5-bit binary number 10010.

Introduction / Context:Converting between binary and decimal is a foundational skill for interpreting addresses, register contents, and configuration fields in digital systems. Short binary words can be converted mentally by weighting each bit position by powers of two.

Given Data / Assumptions:

• Binary number: 10010(2).
• Bit positions from LSB to MSB carry weights 2^0, 2^1, 2^2, 2^3, 2^4.
• We want the base-10 value.

Concept / Approach:Each binary 1 contributes its positional weight; zeros contribute nothing. Sum all active weights to obtain the decimal value.

Step-by-Step Solution:Write weights: from right to left: 2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16.Map bits: 1 0 0 1 0 corresponds to 2^4 + 2^1 = 16 + 2.Add contributions: 16 + 2 = 18.Therefore, 10010(2) = 18(10).

Verification / Alternative check:Convert back: 18 / 2 gives remainders 0,1,0,0,1 (in reverse), yielding 10010(2), confirming the result.

Why Other Options Are Wrong:

• 6 and 9 misplace bit weights.
• 20 adds an extra 2^2 or 2^0 weight that is not present.

Common Pitfalls:

• Reading bit order right-to-left incorrectly.
• Forgetting that a zero bit contributes nothing regardless of position.

Final Answer:18₁₀