Evaluate \((111_{two})^2\) and leave your answer in base 2

  • A \(111001_{two}\)
  • B \(110001_{two}\)
  • C \(101001_{two}\)
  • D \(10010_{two}\)
waec 2007mathematics

The correct answer is B. \(110001_{two}\)

\((111_{two})^{2}=(111_{two})(111_{two})\\

=1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\\

(111_{two})^{2}=7\times 7=49\\

\begin{matrix}

2 & 49\\

2 & 24\hspace{1mm}R\hspace{1mm}1\\

2 & 12\hspace{1mm}R\hspace{1mm}0\\

2 & 6\hspace{1mm}R\hspace{1mm}0\\

2 & 3\hspace{1mm}R\hspace{1mm}0\\

2 & 1\hspace{1mm}R\hspace{1mm}1\\

& 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow

\end{matrix} \\

=110001_{2}\)

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