Convert the fractional binary number 10010.0100₂ to its decimal (base-10) equivalent.

Introduction / Context:
Binary numbers with fractional parts occur in fixed-point arithmetic, digital signal processing, and fractional addressing. Converting such values to decimal requires understanding positional weights on both sides of the binary point.

Given Data / Assumptions:

• Binary value: 10010.0100₂.
• Left of the binary point uses positive powers of two; right uses negative powers.
• No scaling or bias is applied beyond pure binary weighting.

Concept / Approach:
For a binary string a₄a₃a₂a₁a₀.b₁b₂b₃b₄, the decimal value is Σ aᵢ * 2^i + Σ bⱼ * 2^(−j). Only positions with bit 1 contribute to the sum.

Step-by-Step Solution:
Integer part 10010₂: weights are 2^4=16, 2^3=8, 2^2=4, 2^1=2, 2^0=1.Bits = 1 0 0 1 0 ⇒ contributions 16 + 2 = 18.Fractional part .0100₂: weights are 2^(−1)=0.5, 2^(−2)=0.25, 2^(−3)=0.125, 2^(−4)=0.0625.Bits = 0 1 0 0 ⇒ contribution 0.25 only.Total = 18 + 0.25 = 18.25.

Verification / Alternative check:
Convert the fractional portion by fraction: 0.0100₂ = 1/4 = 0.25. Add to the integer 18 to confirm 18.25. A calculator that accepts binary input or a spreadsheet using powers can reproduce the result exactly.

Why Other Options Are Wrong:

• 24.50 and 16.25 use incorrect integer weights.
• 18.40 incorrectly treats 0.0100₂ as 0.40 decimal; binary fractions are not decimal tenths.

Common Pitfalls:

• Confusing binary place values with decimal tenths and hundredths; in binary, the first fractional place is 1/2, then 1/4, 1/8, 1/16, etc.
• Reading the bit order from left to right without applying the correct weights for each position.

Final Answer:
18.25