Convert the following number systems from base 10 to base 2: 1) 19 101 247 99

Repeatedly divide the number by 2 and record the remainders (read remainders from last to first).

$$\begin{align*} 310 &\div 2 = 155 \ remainder\ 0, \\ 155 &\div 2 = 77 \ remainder\ 1, \\ 77 &\div 2 = 38 \ remainder\ 1, \\ 38 &\div 2 = 19 \ remainder\ 0, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $100110110_2$.
\textbf{$310_{10} = 100110110_2$
100110110_2

$$\begin{align*} 310 &\div 8 = 38 \ remainder\ 6, \\ 38 &\div 8 = 4 \ remainder\ 6, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}$$

Remainders from bottom to top: $466_8$.
\textbf{$310_{10} = 466_8$
466_8

$$\begin{align*} 310 &\div 16 = 19 \ remainder\ 6, \\ 19 &\div 16 = 1 \ remainder\ 3, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $136_{16}$.
\textbf{$310_{10} = 136_{16}$
136_{16}

$$\begin{align*} 2510 &\div 2 = 1255 \ remainder\ 0, \\ 1255 &\div 2 = 627 \ remainder\ 1, \\ 627 &\div 2 = 313 \ remainder\ 1, \\ 313 &\div 2 = 156 \ remainder\ 1, \\ 156 &\div 2 = 78 \ remainder\ 0, \\ 78 &\div 2 = 39 \ remainder\ 0, \\ 39 &\div 2 = 19 \ remainder\ 1, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $100111001110_2$.
\textbf{$2510_{10} = 100111001110_2$
100111001110_2

$$\begin{align*} 2510 &\div 8 = 313 \ remainder\ 6, \\ 313 &\div 8 = 39 \ remainder\ 1, \\ 39 &\div 8 = 4 \ remainder\ 7, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}$$

Remainders from bottom to top: $4716_8$.
\textbf{$2510_{10} = 4716_8$
4716_8

$$\begin{align*} 2510 &\div 16 = 156 \ remainder\ 14 \ (E), \\ 156 &\div 16 = 9 \ remainder\ 12 \ (C), \\ 9 &\div 16 = 0 \ remainder\ 9. \end{align*}$$

Remainders from bottom to top: $9CE_{16}$.
\textbf{$2510_{10} = 9CE_{16}$
9CE_{16}

$$\begin{align*} 282 &\div 2 = 141 \ remainder\ 0, \\ 141 &\div 2 = 70 \ remainder\ 1, \\ 70 &\div 2 = 35 \ remainder\ 0, \\ 35 &\div 2 = 17 \ remainder\ 1, \\ 17 &\div 2 = 8 \ remainder\ 1, \\ 8 &\div 2 = 4 \ remainder\ 0, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $100011010_2$.
\textbf{$282_{10} = 100011010_2$
100011010_2

$$\begin{align*} 282 &\div 8 = 35 \ remainder\ 2, \\ 35 &\div 8 = 4 \ remainder\ 3, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}$$

Remainders from bottom to top: $432_8$.
\textbf{$282_{10} = 432_8$
432_8

$$\begin{align*} 282 &\div 16 = 17 \ remainder\ 10 \ (A), \\ 17 &\div 16 = 1 \ remainder\ 1, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $11A_{16}$.
\textbf{$282_{10} = 11A_{16}$
11A_{16}

$$\begin{align*} 4990 &\div 2 = 2495 \ remainder\ 0, \\ 2495 &\div 2 = 1247 \ remainder\ 1, \\ 1247 &\div 2 = 623 \ remainder\ 1, \\ 623 &\div 2 = 311 \ remainder\ 1, \\ 311 &\div 2 = 155 \ remainder\ 1, \\ 155 &\div 2 = 77 \ remainder\ 1, \\ 77 &\div 2 = 38 \ remainder\ 1, \\ 38 &\div 2 = 19 \ remainder\ 0, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $1001101111110_2$.
\textbf{$4990_{10} = 1001101111110_2$
1001101111110_2

$$\begin{align*} 4990 &\div 8 = 623 \ remainder\ 6, \\ 623 &\div 8 = 77 \ remainder\ 7, \\ 77 &\div 8 = 9 \ remainder\ 5, \\ 9 &\div 8 = 1 \ remainder\ 1, \\ 1 &\div 8 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $11576_8$.
\textbf{$4990_{10} = 11576_8$
11576_8

$$\begin{align*} 4990 &\div 16 = 311 \ remainder\ 14 \ (E), \\ 311 &\div 16 = 19 \ remainder\ 7, \\ 19 &\div 16 = 1 \ remainder\ 3, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}$$

Remainders from bottom to top: $137E_{16}$.
\textbf{$4990_{10} = 137E_{16}$
137E_{16}