Home » If (y = 23_{five} + 101_{three}), find y, leaving your answer in base two

If (y = 23_{five} + 101_{three}), find y, leaving your answer in base two

If (y = 23_{five} + 101_{three}), find y, leaving your answer in base two
  • A.
    1110
  • B.
    10111
  • C.
    11101
  • D.
    111100
Correct Answer: Option B
Explanation

(23_{five} = X_{ten}; X_{ten} = 2times 5^1 + 3times 5^0 = 10 + 3 = 13\
101_{three}=P_{ten}; P_{ten} = 1times 3^2 + 0times 3^1 + 1times 3^0=9+0+1=10_{ten}\
Y = 13+10=23_{ten});
Converting to base two
(begin{matrix}
2 & 23\
2 & 11 &R1\
2 & 5 & R1\
2 & 2 & R1\
2 & 1 & R0\
& 0& R1 uparrow\
end{matrix} \
=y=10111_2)

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