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The equivalent of (10110.011)\(_2\) in base 10 is?

Mathematics
JAMB 2022

The equivalent of (10110.011)\(_2\) in base 10 is?

  • A. 26.325
  • B. 24.372
  • C. 42.443
  • D. 22.375
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Correct Answer: Option D
Explanation

Using the expansion method on (10110.011)\(_2\)

(1 * 2\(^4\)) + (0 * 2\(^3\)) + (1 * 2\(^2\)) + (1 * 2\(^1\)) (0 * 2\(^0\)) + (0 * 2\(^{-1}\)) + (1 * 2\(^{-2}\))  + (1 * 2\(^{-3}\))

(1*16) + 0 (1*4) + (1*2) + 0 + 0 + (1*\(\frac{1}{4}\)) + (1*\(\frac{1}{8}\)) 

16 + 4 + 2 + (0.25 + 0.125)

22 + 0.375

(10110.011)\(_2\) = 22.375\(_{10}\)

There is an explanation video available below.


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Explanation Video

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