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

Explanation

\(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\)