Binary Fraction to Decimal — Point Positioning Convert the binary number 1001.0010 to its decimal value. Show the integer and fractional contributions clearly.

Introduction / Context:
Interpreting binary fractions requires understanding negative powers of two for positions to the right of the binary point. This conversion appears often in fixed point arithmetic and digital signal processing basics.

Given Data / Assumptions:

• Binary value: 1001.0010.
• Positions left of the point use powers 2^3, 2^2, 2^1, 2^0.
• Positions right of the point use 2^-1, 2^-2, 2^-3, 2^-4.

Concept / Approach:
Evaluate each set bit as its weight and sum them. The fractional part adds small contributions determined by negative exponents of two.

Step-by-Step Solution:
1) Integer part 1001 = 12^3 + 02^2 + 02^1 + 12^0 = 8 + 0 + 0 + 1 = 9.2) Fractional part .0010 = 02^-1 + 02^-2 + 12^-3 + 02^-4 = 0 + 0 + 0.125 + 0 = 0.125.3) Sum = 9 + 0.125 = 9.125.4) Therefore decimal value is 9.125.

Verification / Alternative check:
Multiply fractional part by 2 repeatedly to recover bits: 0.1252 = 0.25 gives 0, 0.252 = 0.5 gives 0, 0.52 = 1.0 gives 1, 0.02 gives trailing zeros, matching .0010.

Why Other Options Are Wrong:

• 90.125: Misplaced point by a factor of 10 in decimal.
• 125: Ignores the base and the point entirely.
• 12.5: Misinterprets the contribution of bits.

Common Pitfalls:
Treating binary digits as decimal weights, or reading fractional bits left to right without applying correct negative exponents.

Final Answer:
9.125