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Convert (\(101.011)_2\) to base 10

Mathematics
NECO 2001

Convert (\(101.011)_2\) to base 10

  • A. 63
  • B. 43
  • C. 10
  • D. \(\frac{77}{8}\)
  • E. \(\frac{43}{8}\)
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Correct Answer: Option E
Explanation

Convert (\(101.011)_2\) to base 10

\(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 + 0 \times 2^{-1} + 1 \times 2^{-2} + 1 \times 2^{-3}\)

1 x 4 + 0 x 2 + 1 x 1 + 0 x \(\frac{1}{2}\) + 1 x \(\frac{1}{4}\) + 1 x \(\frac{1}{8}\)

4 + 1 +  \(\frac{1}{4}\) + \(\frac{1}{8}\)

=  \(\frac{43}{8}\)


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