Convert \(47_8\) to its binary equivalent.

Data Processing WAEC 2015

Convert \(47_8\) to its binary equivalent.

  • 100111\(_2\) checkmark
  • 110011\(_2\)
  • 10001\(_2\)
  • 1111011\(_2\)

The correct answer is: A

Explanation

Convert to base 10 first.

\(47_8\) = 4 x \(8^1\) + 7 x \(8^0\) = \(39_{10}\)

Then convert \(39_{10}\) to base 2 as follows

2 39
2 19 R 1
2 9 R 1
2 4 R 1
2 2 R 0
2 1 R 0
2 0 R 1

Therefore \(47_8\) is equivalent to \(100111_2\)

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