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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Binary Numbers

NDA 2019 · Mathematics · Binary Numbers

A binary number is represented by (c d c c d d c c c d d d)_2 ,...

A binary number is represented by (cdccddcccddd)2(c d c c d d c c c d d d)_2, where c>dc > d. What is its decimal equivalent?

Options

  1. A1848
  2. B2048
  3. C2842
  4. D2872

Correct answer

D. 2872

Step-by-step solution

(cdccddcccddd)2∵c>d∴c=1 and d=0∴ no =(101100111000)2∴ decimal equivalent =211+29+28+25+24+23=2048+512+256+32+16+8=2872\begin{aligned} & (c d c c d d c c c d d d)_2 \\ & \because c > d \\ & \therefore c=1 \text{ and } d=0 \\ & \therefore \text{ no }=(101100111000)_2 \\ & \therefore \text{ decimal equivalent }= \\ & 2^{11}+2^9+2^8+2^5+2^4+2^3 \\ & =2048+512+256+32+16+8 \\ & =2872\end{aligned}
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