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If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
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3 Answers

Best answer
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12 votes

Answer: $3$ 

This conversion is just

$\frac{1}{2} + \frac{1}{4} + \frac{1}{16} = \frac{8 + 4 + 1}{16} = \frac{13}{16} = 0.8125$

On comparison we get $x = 1$ and $y = 2.$ Hence, $x+y= 3.$

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Answer $= 3$

  1. $(0.1)_2 = (0.5)_{10}$
  2. $(0.01)_2 = (0.25)_{10}$
  3. $(0.001)_2 = (0.125)_{10}$
  4. $(0.0001)_2 = (0.0625)_{10}$

$A + B + D \implies (0.1101)_2 = 0.8125$

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