Convert the binary number 1101.101 to its decimal (base-10) value.

Introduction / Context:Binary-to-decimal conversion requires positional weighting. Bits left of the point use powers of 2 with nonnegative exponents; bits right of the point use negative exponents. This problem includes both integer and fractional parts, so we convert each separately and then sum.

Given Data / Assumptions:

• Binary input: 1101.101
• Base: 2 (binary)
• Goal: Decimal value

Concept / Approach:For a binary value b3 b2 b1 b0 . b-1 b-2 b-3, the decimal value is sum(bi * 2^i). Compute integer and fractional contributions independently to avoid mistakes, then add them.

Step-by-Step Solution:

Verification / Alternative check:As a quick check, compare nearby options: 13.5 corresponds to .100, 13.75 corresponds to .11 (i.e., .110), and 13.875 corresponds to .111. Our fractional .101 equals 0.625, confirming 13.625.

Why Other Options Are Wrong:

• 13.5: Would require fractional part .100 (0.5), not .101.
• 13.75: Would require .11 or .110 (0.75), not .101.
• 13.875: Would require .111 (0.875), not .101.

Common Pitfalls:

• Reading .101 as 0.101 in decimal; digits are binary weights.
• Forgetting that each right-of-point bit halves the previous weight (2^-1, 2^-2, 2^-3, ...).

Final Answer:13.625