✏️ Explanatory Question
Decimal সংখ্যার পূর্ণাংশ এবং ভগ্নাংশ অংশকে আলাদাভাবে Binary-তে রূপান্তর করা হয়।
পূর্ণাংশের ক্ষেত্রে ভাগশেষ নিচ থেকে উপর দিকে পড়তে হয় এবং ভগ্নাংশের ক্ষেত্রে গুণফলের পূর্ণাংশ উপর থেকে নিচে পড়তে হয়।
\[ (25.625)_{10} \]
\[ \begin{array}{r|l} 2 & 25 \\ \hline 2 & 12 \quad 1 \\ \hline 2 & 6 \quad 0 \\ \hline 2 & 3 \quad 0 \\ \hline 2 & 1 \quad 1 \\ \hline & 0 \quad 1 \\ \end{array} \]
Reading remainders from bottom to top:
\[ (25)_{10} = (11001)_2 \]
\[ 0.625 \times 2 = 1.250 \]
\[ 0.250 \times 2 = 0.500 \]
\[ 0.500 \times 2 = 1.000 \]
Reading integers from top to bottom:
\[ (0.625)_{10} = (0.101)_2 \]
\[ (25.625)_{10} = (11001.101)_2 \]
\[ (45.375)_{10} \]
\[ \begin{array}{r|l} 2 & 45 \\ \hline 2 & 22 \quad 1 \\ \hline 2 & 11 \quad 0 \\ \hline 2 & 5 \quad 1 \\ \hline 2 & 2 \quad 1 \\ \hline 2 & 1 \quad 0 \\ \hline & 0 \quad 1 \\ \end{array} \]
Reading remainders from bottom to top:
\[ (45)_{10} = (101101)_2 \]
\[ 0.375 \times 2 = 0.750 \]
\[ 0.750 \times 2 = 1.500 \]
\[ 0.500 \times 2 = 1.000 \]
Reading integers from top to bottom:
\[ (0.375)_{10} = (0.011)_2 \]
\[ (45.375)_{10} = (101101.011)_2 \]
\[ (72.75)_{10} \]
\[ \begin{array}{r|l} 2 & 72 \\ \hline 2 & 36 \quad 0 \\ \hline 2 & 18 \quad 0 \\ \hline 2 & 9 \quad 0 \\ \hline 2 & 4 \quad 1 \\ \hline 2 & 2 \quad 0 \\ \hline 2 & 1 \quad 0 \\ \hline & 0 \quad 1 \\ \end{array} \]
Reading remainders from bottom to top:
\[ (72)_{10} = (1001000)_2 \]
\[ 0.75 \times 2 = 1.50 \]
\[ 0.50 \times 2 = 1.00 \]
Reading integers from top to bottom:
\[ (0.75)_{10} = (0.11)_2 \]
\[ (72.75)_{10} = (1001000.11)_2 \]
\[ (19.125)_{10} \]
\[ \begin{array}{r|l} 2 & 19 \\ \hline 2 & 9 \quad 1 \\ \hline 2 & 4 \quad 1 \\ \hline 2 & 2 \quad 0 \\ \hline 2 & 1 \quad 0 \\ \hline & 0 \quad 1 \\ \end{array} \]
Reading remainders from bottom to top:
\[ (19)_{10} = (10011)_2 \]
\[ 0.125 \times 2 = 0.250 \]
\[ 0.250 \times 2 = 0.500 \]
\[ 0.500 \times 2 = 1.000 \]
Reading integers from top to bottom:
\[ (0.125)_{10} = (0.001)_2 \]
\[ (19.125)_{10} = (10011.001)_2 \]