Chapter 1, Problem 23CRP

Explanation of Solution

Convert $8$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $8$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 8& \\ 2& 4& 0\\ 2& 2& 0\\ 2& 1& 0\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $8=1000$

Therefore, ${\left(1000\right)}_2$ is the binary number for integer $8$.

Convert $9$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $9$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 9& \\ 2& 4& 1\\ 2& 2& 0\\ 2& 1& 0\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $9=1001$

Therefore, ${\left(1001\right)}_2$ is the binary number for integer $9$.

Convert $10$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $10$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 10& \\ 2& 5& 0\\ 2& 2& 1\\ 2& 1& 0\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $10=1010$

Therefore, ${\left(1010\right)}_2$ is the binary number for integer $10$.

Convert $11$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $11$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 11& \\ 2& 5& 1\\ 2& 2& 1\\ 2& 1& 0\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $11=1011$

Therefore, ${\left(1011\right)}_2$ is the binary number for integer $11$.

Convert $12$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $12$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 12& \\ 2& 6& 0\\ 2& 3& 0\\ 2& 1& 1\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $12=1100$

Therefore, ${\left(1100\right)}_2$ is the binary number for integer $12$.

Convert $13$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $13$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 13& \\ 2& 6& 1\\ 2& 3& 0\\ 2& 1& 1\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top.

  $13=1101$

Therefore, ${\left(1101\right)}_2$ is the binary number for integer $13$.

Convert $14$ to its binary number:

• To find the conversion of integer into binary notation with base $2$ number system, divide the digit $14$ by $2$ such that the quotient must be zero:

  $\begin{array}{ccc}2& 14& \\ 2& 7& 0\\ 2& 3& 1\\ 2& 1& 1\\ & 0& 1\end{array}$

• To find the binary number write the remainders in order from bottom to top