Convert the base 2 fractional number 110.101_2 to its equivalent value in base 10 (decimal… — JAMB UTME

Convert the base 2 fractional number $110.101_2$ to its equivalent value in base 10 (decimal). What is the decimal value?

Answer: 6.625

The decimal value of

110.101_2

6.625

To convert

110.101_2

to base 10, expand both the integer and fractional parts using powers of 2. The integer component

110_2 = (1 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) = 4 + 2 + 0 = 6

. The fractional component

0.101_2 = (1 \times 2^{-1}) + (0 \times 2^{-2}) + (1 \times 2^{-3}) = 0.5 + 0 + 0.125 = 0.625

. Summing these values gives

6 + 0.625 = 6.625

Convert the integer part

110_2

to base 10

1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 4 + 2 + 0 = 6

Each position to the left of the binary point corresponds to an increasing non-negative power of 2 (

2^0, 2^1, 2^2

Convert the fractional part

0.101_2

to base 10

1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = \frac{1}{2} + 0 + \frac{1}{8} = 0.5 + 0.125 = 0.625

Each position to the right of the binary point corresponds to a negative power of 2 (

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

Combine the integer and fractional results

6 + 0.625 = 6.625

The total value in base 10 is the sum of the expanded integer and fractional components.

Conversion of Fractional Non-Decimal Numbers to Decimal

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