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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binary Numbers

NDA 2022 · Mathematics · Binary Numbers

What is (1110011)_2 (10111)_2 equal to?

What is (1110011)2÷(10111)2(1110011)_2 \div(10111)_2 equal to?

Options

  1. A(101)2(101)_2
  2. B(1001)2(1001)_2
  3. C(111)2(111)_2
  4. D(1011)2(1011)_2

Correct answer

A. (101)2(101)_2

Step-by-step solution

(1110011)2=1×26+1×25+1×24+21+20=64+32+16+2+1=115(10111)2=1×24+1×22+1×21+1×20=16+4+2+1=23∴(1110011)2÷(10111)2=115÷23=5\begin{aligned} & (1110011)_2=1 \times 2^6+1 \times 2^5+1 \times 2^4+2^1+2^0 \\ & =64+32+16+2+1=115 \\ & (10111)_2=1 \times 2^4+1 \times 2^2+1 \times 2^1+1 \times 2^0 \\ & =16+4+2+1=23 \\ & \therefore(1110011)_2 \div(10111)_2=115 \div 23=5\end{aligned}
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