問題の解答
検索用コード（LaTeX）
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% 例題A4.2.13：$n$進法の四則計算（One More）★
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次の計算をせよ．
(1) $11011_{(2)}+1101_{(2)}$
(2) $102_{(3)}\times 21_{(3)}$
(3) $432_{(6)}-231_{(6)}$
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% 例題A4.2.13の解答（One More）★
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(1) $11011_{(2)},1101_{(2)}$をそれぞれ10進法で表すと，
\begin{align*}
&11011_{(2)}=1\times 2^4+1\times 2^3+0\times 2^2+1\times 2^1+1=27,\\
&1101_{(2)}=1\times 2^3+1\times 2^2+0\times 2^1+1=13
\end{align*}
よって，
\begin{align*}
11011_{(2)}+1101_{(2)}&=27+13=40\\
&=1\times 2^5+0\times 2^4+1\times 2^3+0\times 2^2+0\times 2^1+0\\
&=101000_{(2)}
\end{align*}
(2) $102_{(3)},21_{(3)}$をそれぞれ10進法で表すと，
\begin{align*}
&102_{(3)}=1\times 3^2+0\times 3^1+2=9+2=11,\\
&21_{(3)}=2\times 3^1+1=6+1=7
\end{align*}
よって，
\begin{align*}
102_{(3)}\times 21_{(3)}&=11\times 7=77\\
&=2\times 3^3+2\times 3^2+1\times 3^1+2\\
&=2212_{(3)}
\end{align*}
(3) $432_{(6)},231_{(6)}$をそれぞれ10進法で表すと，
\begin{align*}
&432_{(6)}=4\times 6^2+3\times 6^1+2=144+18+2=164,\\
&231_{(6)}=2\times 6^2+3\times 6^1+1=72+18+1=91
\end{align*}
よって，
\[
432_{(6)}-231_{(6)}=164-91=73=2\times 6^2+0\times 6+1=201_{(6)}
\]
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% 問題A4.2.13：$n$進法の四則計算（One More）★
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次の計算をせよ．
(1) $10101_{(2)}+1110_{(2)}$
(2) $210_{(3)}\times 12_{(3)}$
(3) $543_{(6)}-312_{(6)}$
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% 問題A4.2.13の解答（One More）★
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(1) $10101_{(2)},1110_{(2)}$をそれぞれ10進法で表すと，
\begin{align*}
&10101_{(2)}=1\times 2^4+0\times 2^3+1\times 2^2+0\times 2^1+1=21,\\
&1110_{(2)}=1\times 2^3+1\times 2^2+1\times 2^1+0=14
\end{align*}
よって，
\begin{align*}
10101_{(2)}+1110_{(2)}&=21+14=35\\
&=1\times 2^5+0\times 2^4+0\times 2^3+0\times 2^2+1\times 2^1+1\\
&=100011_{(2)}
\end{align*}
(2) $210_{(3)},12_{(3)}$をそれぞれ10進法で表すと，
\begin{align*}
&210_{(3)}=2\times 3^2+1\times 3^1+0=18+3+0=21,\\
&12_{(3)}=1\times 3^1+2=3+2=5
\end{align*}
よって，
\begin{align*}
210_{(3)}\times 12_{(3)}&=21\times 5=105\\
&=1\times 3^4+0\times 3^3+2\times 3^2+2\times 3^1+0\\
&=10220_{(3)}
\end{align*}
(3) $543_{(6)},312_{(6)}$をそれぞれ10進法で表すと，
\begin{align*}
&543_{(6)}=5\times 6^2+4\times 6^1+3=180+24+3=207,\\
&312_{(6)}=3\times 6^2+1\times 6^1+2=108+6+2=116
\end{align*}
よって，$543_{(6)}-312_{(6)}=207-116=91=2\times 6^2+3\times 6^1+1=231_{(6)}$
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