If y 23 five 101 three find y leaving your answ... - WAEC Mathematics 2004 Question
If \(y = 23_{five} + 101_{three}\), find y, leaving your answer in base two
A
1110
B
10111
C
11101
D
111100
correct option: b
\(23_{five} = X_{ten}; X_{ten} = 2\times 5^1 + 3\times 5^0 = 10 + 3 = 13\
101_{three}=P_{ten}; P_{ten} = 1\times 3^2 + 0\times 3^1 + 1\times 3^0=9+0+1=10_{ten}\
Y = 13+10=23_{ten}\);
Converting to base two
\(\begin{matrix}
2 & 23\
2 & 11 &R1\
2 & 5 & R1\
2 & 2 & R1\
2 & 1 & R0\
& 0& R1 \uparrow\
\end{matrix} \
=y=10111_2\)
101_{three}=P_{ten}; P_{ten} = 1\times 3^2 + 0\times 3^1 + 1\times 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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