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

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

Evaluate ((111_{two})^2) and leave your answer in base 2
  • A.
    (111001_{two})
  • B.
    (110001_{two})
  • C.
    (101001_{two})
  • D.
    (10010_{two})
Correct Answer: Option B
Explanation

((111_{two})^{2}=(111_{two})(111_{two})\
=1 times 2^{2}+1times2^{1}+1times 2^{0}=4+2+1=7_{_{ten}}\
(111_{two})^{2}=7times 7=49\
begin{matrix}
2 & 49\
2 & 24hspace{1mm}Rhspace{1mm}1\
2 & 12hspace{1mm}Rhspace{1mm}0\
2 & 6hspace{1mm}Rhspace{1mm}0\
2 & 3hspace{1mm}Rhspace{1mm}0\
2 & 1hspace{1mm}Rhspace{1mm}1\
& 0hspace{1mm}Rhspace{1mm}1hspace{1mm}uparrow
end{matrix} \
=110001_{2})

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