Chapter 3, Problem 4RQ

Program Plan Intro

Octal number system:

• Octal number system is also known as base-8 number system
• It is because eight distinct elements from 0 to 7 are used to represent a level.
• It means, in total, octal system has 8 numbers.

Binary number system:

• In binary system, the numbers “0” and “1” are only used.
• It means, in total, binary system has only 2 numbers.
• Therefore, the base used for binary numbering system is 2.

Explanation of Solution

b.

Conversion of octal number 130 to its equivalent binary number:

• Given, octal number is 130.
• Each digit of the octal number is converted into three bit binary equivalent.
• A group of three bit binary refers to its corresponding octal digit.
• Finally, the binary notation of the given octal number is noted.
• The following diagram describes the binary notation of the octal number 130...

Explanation of Solution

c.

Conversion of octal number 250 to its equivalent binary number:

• Given, octal number is 250.
• Each digit of the octal number is converted into three bit binary equivalent.
• A group of three bit binary refers to its corresponding octal digit.
• Finally, the binary notation of the given octal number is noted.
• The following diagram describes the binary notation of the octal number 250...

Explanation of Solution

d.

Conversion of octal number 1510 to its equivalent binary number:

• Given, octal number is 1510.
• Each digit of the octal number is converted into three bit binary equivalent.
• A group of three bit binary refers to its corresponding octal digit.
• Finally, the binary notation of the given octal number is noted.
• The following diagram describes the binary notation of the octal number 1510.

Explanation of Solution

e.

Conversion of octal number 2551 to its equivalent binary number:

• Given, octal number is 2551.
• Each digit of the octal number is converted into three bit binary equivalent.
• A group of three bit binary refers to its corresponding octal digit.
• Finally, the binary notation of the given octal number is noted.
• The following diagram describes the binary notation of the octal number 2551.

Explanation of Solution

f.

Conversion of octal number 2634 to its equivalent binary number:

• Given, octal number is 2634.
• Each digit of the octal number is converted into three bit binary equivalent.
• A group of three bit binary refers to its corresponding octal digit.
• Finally, the binary notation of the given octal number is noted.
• The following diagram describes the binary notation of the octal number 2634.