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The decimal number corresponding to the binary number ${(111000.0101)}_{2}$ is

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{(5631.25)}_{10}

{(5.63125)}_{10}

{(56312.5)}_{10}

{(56.3125)}_{10}

answer is D.

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Detailed Solution

1 \times 2^{5} + 1 \times 2^{4} + 1 \times 2^{3} + 0 \times 2^{2} + 0 \times 2^{0} + 0 \times 2^{- 1} + 1 \times 2^{- 2} + 0 \times 2^{- 3} + 1 \times 2^{- 4}

$= 32 + 16 + 8 + 0 + 0 + 0 + 0 + 0.25 + 0 + 0.0625$

$= {(56.3125)}_{10}$

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