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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Binary Numbers

NDA 2015 · Mathematics · Binary Numbers

If (11101011)_2 is converted decimal system, then the resulting...

If (11101011)2(11101011)_2 is converted decimal system, then the resulting number is

Options

  1. A235
  2. B175
  3. C160
  4. D126

Correct answer

A. 235

Step-by-step solution

(11101011)2=(1×27+1×26+1×25+0×24+1×23+0×22+1×21+1×20)10=(128+64+32+8+2+1)10=(235)10\begin{aligned} & (11101011)_2 \\ & =\left(1 \times 2^7+1 \times 2^6+1 \times 2^5+0 \times 2^4+1 \times 2^3\right. \\ & \left.\quad+0 \times 2^2+1 \times 2^1+1 \times 2^0\right)_{10} \\ & =(128+64+32+8+2+1)_{10} \\ & =(235)_{10} \end{aligned}\therefore \quad$ Option (A) is correct.
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