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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Binary Numbers

NDA 2020 · Mathematics · Binary Numbers

The number (1101101+1011011)_2 can be written in decimal system as

The number (1101101+1011011)2(1101101+1011011)_2 can be written in decimal system as

Options

  1. A(198)10(198)_{10}
  2. B(199)10(199)_{10}
  3. C(200)10(200)_{10}
  4. D(201)10(201)_{10}

Correct answer

C. (200)10(200)_{10}

Step-by-step solution

(1101101)2+(1011011)2(1101101)_2+(1011011)_2=(1×26+1×25+0+1×23+1×22+0+1×20)10+(1×26+0+1×24+1×23+0+1×21+1×20)10\begin{aligned}=(1 \times & \left.2^6+1 \times 2^5+0+1 \times 2^3+1 \times 2^2+0+1 \times 2^0\right)_{10} \\ & \quad+\left(1 \times 2^6+0+1 \times 2^4+1 \times 2^3+0+1 \times 2^1+1 \times 2^0\right)_{10}\end{aligned}$\begin{aligned} & =(64+32+8+4+1)_{10}+(64+0+16+8+2+1)_{10} \\ & =(109+91)_{10}=(200)_{10}.\end{aligned}
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