Chapter 3, Problem 3RQ

a.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 36.
• • First, multiply the given octal number 36 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 36.

$\begin{array}{l}36=8^1*3+8^0*6\\ =8*3+1*6\\ =24+6\\ =30\end{array}$

• • Therefore, the decimal notation of octal number ${\left(36\right)}_8$ is “${\left(30\right)}_{10}$”.

b.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 104.
• • First, multiply the given octal number 104 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 104.

$\begin{array}{l}104=8^2*1+8^1*0+8^0*4\\ =64*1+8*0+1*4\\ =64+0+4\\ =68\end{array}$

• • Therefore, the decimal notation of octal number ${\left(104\right)}_8$ is “${\left(68\right)}_{10}$”.

c.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 120.
• • First, multiply the given octal number 120 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 120.

$\begin{array}{l}120=8^2*1+8^1*2+8^0*0\\ =64*1+8*2+1*0\\ =64+16+0\\ =80\end{array}$

• • Therefore, the decimal notation of octal number ${\left(120\right)}_8$ is “${\left(80\right)}_{10}$”.

d.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 216.
• • First, multiply the given octal number 216 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 216.

$\begin{array}{l}216=8^2*2+8^1*1+8^0*6\\ =64*2+8*1+1*6\\ =128+8+6\\ =142\end{array}$

• • Therefore, the decimal notation of octal number ${\left(216\right)}_8$ is “${\left(142\right)}_{10}$”.

e.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 360.
• • First, multiply the given octal number 360 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 360.

$\begin{array}{l}360=8^2*3+8^1*6+8^0*0\\ =64*3+8*6+1*0\\ =192+48+0\\ =240\end{array}$

• • Therefore, the decimal notation of octal number ${\left(360\right)}_8$ is “${\left(240\right)}_{10}$”.

Explanation of Solution

Conversion of octal numbers to decimal numbers:

• • Given, octal number is 1516.
• • First, multiply the given octal number 1516 with multiples of 8, with respect to their positions and then, add all the values to get the final answer.
• • The following calculation describes the decimal notation of the octal number 1516.

$\begin{array}{l}1516=8^3*1+8^2*5+8^1*1+8^0*6\\ =512*1+64*5+8*1+1*6\\ =512+320+8+6\\ =846\end{array}$

• • Therefore, the decimal notation of octal number ${\left(1516\right)}_8$ is “${\left(846\right)}_{10}$”.