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