Number systems conversion (binary fraction to decimal): Convert the fractional binary number 0000.1010 to its decimal (base-10) value.

Introduction / Context:
Binary fractions use negative powers of 2 to represent values to the right of the binary point. Proficiency with these conversions is essential for fixed-point arithmetic, digital signal processing, and interpreting DAC/ADC resolutions.

Given Data / Assumptions:

• Binary value: 0000.1010 (leading zeros do not affect magnitude).
• We use positional weights 2^−1, 2^−2, 2^−3, 2^−4 ... for fractional bits.

Concept / Approach:
Sum contributions of each bit multiplied by its positional weight. For a binary fraction b1 b2 b3 b4 after the point: value = b12^−1 + b22^−2 + b32^−3 + b42^−4.

Step-by-Step Solution:
Bits after point: 1 0 1 0.Compute contributions: 12^−1 = 0.5, 02^−2 = 0, 12^−3 = 0.125, 02^−4 = 0.Sum = 0.5 + 0.125 = 0.625.

Verification / Alternative check:
Convert 0.625 to binary by repeated multiplication by 2: 0.6252=1.25 → 1; .252=0.5 → 0; .52=1.0 → 1; .02=0 → 0. Thus .1010, confirming the result.

Why Other Options Are Wrong:
0.50: corresponds to .1000.0.55: not a power-of-two fractional combination.0.10: decimal 0.10 is not equal to binary .1010.0.375: corresponds to .0110.

Common Pitfalls:
Interpreting 0.1010 as a decimal fraction with place values 10^−1, 10^−2, etc., instead of powers of 2.

Final Answer:
0.625