Binary fractions to decimal conversion Convert the fractional binary number 0001.0010₂ to its decimal (base-10) value.

Introduction / Context:Binary numbers can include fractional parts. Converting binary fixed-point values to decimal is essential for interpreting ADC outputs, fixed-point arithmetic in embedded systems, and digital signal processing where fractional precision matters.

Given Data / Assumptions:

• Binary value: 0001.0010₂.
• Point location: four bits integer part, four bits fractional part.
• We need a base-10 decimal equivalent.

Concept / Approach:Binary place values to the left of the point are powers of 2: …, 8, 4, 2, 1. To the right, they are fractional powers: 1/2, 1/4, 1/8, 1/16, etc. Sum the weighted contributions of bits that are 1. Leading zeros do not change the value.

Step-by-Step Solution:

Verification / Alternative check:Multiply the fractional part by 10 is not valid in base-2; instead, verify by converting back: 1.125 decimal = 1 + 1/8 = 1.0010₂, which matches the given binary form.

Why Other Options Are Wrong:

• 1.40 / 1.20 / 1.80: These decimals are not equal to 1 + 1/8. They imply different fractional sums like 0.4, 0.2, or 0.8, which do not correspond to .0010₂.

Common Pitfalls:Misplacing fractional weights (confusing 1/2 with 1/8), or reading the binary fraction as if it were decimal digits. Always apply powers of two for each fractional bit position.

Final Answer:1.125