Evaluate 111 two 2 and leave your answer in bas... - WAEC Mathematics 2007 Question
Evaluate \((111_{two})^2\) and leave your answer in base 2
A
\(111001_{two}\)
B
\(110001_{two}\)
C
\(101001_{two}\)
D
\(10010_{two}\)
correct option: b
\((111_{two})^{2}=(111_{two})(111_{two})\
=1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\
(111_{two})^{2}=7\times 7=49\
\begin{matrix}
2 & 49\
2 & 24\hspace{1mm}R\hspace{1mm}1\
2 & 12\hspace{1mm}R\hspace{1mm}0\
2 & 6\hspace{1mm}R\hspace{1mm}0\
2 & 3\hspace{1mm}R\hspace{1mm}0\
2 & 1\hspace{1mm}R\hspace{1mm}1\
& 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow
\end{matrix} \
=110001_{2}\)
=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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