Convert the fractional binary number 0.1101_2 to its equivalent base 10 (decimal) value. W… — JAMB UTME

Convert the fractional binary number $0.1101_2$ to its equivalent base 10 (decimal) value. What is the decimal value?

Answer: 0.8125

The base 10 value of

0.1101_2

0.8125

To convert a fractional binary number to decimal, expand each digit after the radix point using decreasing negative powers of 2 (

2^{-1}, 2^{-2}, 2^{-3}, 2^{-4}

). Evaluating

1(0.5) + 1(0.25) + 0(0.125) + 1(0.0625)

yields

0.8125

Write the given binary fraction in place-value expansion using powers of 2

0.1101_2 = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3} + 1 \cdot 2^{-4}

Positions after the binary point represent negative powers of 2 starting from

2^{-1}

Evaluate each fractional component

2^{-1} = 0.5

2^{-2} = 0.25

2^{-3} = 0.125

2^{-4} = 0.0625

Calculating standard decimal values for binary fractional places.

Add the non-zero fractional terms together

0.5 + 0.25 + 0.0625 = 0.8125

Summing the decimal values gives the complete converted decimal representation.

Conversion of fractional numbers from base 2 to base 10

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