Chapter 1.4, Problem 6QE

a.

Explanation of Solution

Convert $6$ to its equivalent binary form:

• To find the equivalent binary form of $6$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$, the binary form of the original value is the remainders listed from bottom to top in the reverse order

b.

Explanation of Solution

Convert $13$ to its equivalent binary form:

• To find the equivalent binary form of $13$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$, the binary form of the original value is the remainders listed from bottom to top in the reverse order

c.

Explanation of Solution

Convert $11$ to its equivalent binary form:

• To find the equivalent binary form of $11$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$,  the binary form of the original value is the remainders listed from bottom to top in the reverse order

d.

Explanation of Solution

Convert $18$ to its equivalent binary form:

• To find the equivalent binary form of $18$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$, the binary form of the original value is the remainders listed from bottom to top in the reverse order.

$\begin{array}{ccc}2& 18& \\ \end{array}$

e.

Explanation of Solution

Convert $27$ to its equivalent binary form:

• To find the equivalent binary form of $27$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$, the binary form of the original value is the remainders listed from bottom to top in the reverse order.

$\begin{array}{ccc}2& 27& \\ 2\end{array}$

f.

Explanation of Solution

Convert $4$ to its equivalent binary form:

• To find the equivalent binary form of $4$, divide the number by $2$ and record the remainder. As long as the quotient is not obtained as $0$, continue the division of the newest quotient by two and record the remainder.
• When the obtained quotient is $0$, the binary form of the original value is the remainders listed from bottom to top in the reverse order