Chapter 2, Problem 4E

Explanation of Solution

a)

Converting 20101 base 3 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 3.

$\begin{array}{l}{\text{1 x 3}}^{\text{0}}\text{= 1}\\ {\text{0 x 3}}^1\text{= 0}\\ {\text{1 x 3}}^2\text{= 9}\\ {\text{0 x 3}}^3\text{= 0}\end{array}$

${\text{2 x 3}}^{}$

Explanation of Solution

b)

Converting 2302 base 5 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 5.

$\begin{array}{l}{\text{2 x 5}}^{\text{0}}\text{= 2}\\ {\text{0 x 5}}^1\text{= 0}\\ {\text{3 x 5}}^2\text{= 75}\\ {\text{2 x 5}}^3\text{= 250}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value

Explanation of Solution

c)

Converting 1605 base 7 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 7.

$\begin{array}{l}{\text{5 x 7}}^{\text{0}}\text{= 5}\\ {\text{0 x 7}}^1\text{= 0}\\ {\text{6 x 7}}^2\text{= 294}\\ {\text{1 x 7}}^3\text{= 343}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value

Explanation of Solution

d)

Converting 687 base 9 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 9.

$\begin{array}{l}{\text{7 x 9}}^{\text{0}}\text{= 7}\\ {\text{8 x 9}}^1\text{= 72}\\ {\text{6 x 9}}^2\text{= 486}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value