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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Binary Numbers

NDA 2015 · Mathematics · Binary Numbers

What is (1000000001)_2-(0.0101)_2 equal to ?

What is (1000000001)2−(0.0101)2(1000000001)_2-(0.0101)_2 equal to ?

Options

  1. A(512.6775)10(512.6775)_{10}
  2. B(512.6875)10(512.6875)_{10}
  3. C(512.6975)10(512.6975)_{10}
  4. D(512.0909)10(512.0909)_{10}

Correct answer

B. (512.6875)10(512.6875)_{10}

Step-by-step solution

(1000000001)2=1×20+0×21+0×22+…..+1×29=1+0+0+……+512=(513)10(0.0101)2=0×2−1+1×2−2+0×2−3+1×2−4=14+116=516=(0.3125)10(1000000001)2−(0.0101)2=513−0.312=(512.6875)10\begin{aligned} & (1000000001)_2 \\ = & 1 \times 2^0+0 \times 2^1+0 \times 2^2+\ldots..+1 \times 2^9 \\ = & 1+0+0+\ldots \ldots+512 \\ = & (513)_{10} \\ & (0.0101)_2=0 \times 2^{-1}+1 \times 2^{-2}+0 \times 2^{-3}+1 \times 2^{-4} \\ = & \frac{1}{4}+\frac{1}{16}=\frac{5}{16}=(0.3125)_{10} \\ & (1000000001)_2-(0.0101)_2=513-0.312 \\ = & (512.6875)_{10}\end{aligned}
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