Octal Number System Practice Questions

The octal number system is a number system that uses eight digits: 0 to 7. It is also called the base-8 number system.

Example 1: What is the decimal equivalent of 1121₈?

Solution:

1121₈ = 1 × 8³ + 1 × 8² + 2 × 8¹ + 1 × 8⁰
1121₈ = 1 × 512 + 1 × 64 + 2 × 8 + 1 × 1
1121₈ = 512 + 64 + 16 + 1 = 593

Hence, 1121₈ = 593₁₀

Example 2: Convert 27₈ into the binary number.

Solution:

Write binary equivalent of each digit of 27₈

2 ---> 010
7 ---> 111

Hence 27₈ = 010111₂

Example 3: Find the octal equivalent of 1001001₂.

Solution:

Breaking 10101111 into groups of three starting from rightmost digit and adding leading zeroes we get:

001, 001, 001

Write the octal equivalent of the groups formed

001 -> 1
001 -> 1
001 -> 1

Answer is (111)8

Example 4: Represent 123₈ as a Decimal Number.

Solution:

123₈ = 1 × 8² + 2 × 8¹ + 3 × 8⁰
⇒ 123₈ = 1 × 64 + 2 × 8 + 3 × 1
⇒ 123₈ = 64 + 16 + 3
⇒ 123₈ = 83₁₀

Hence 83₁₀ is decimal representation of 123₈.

Practice Questions on Octal Number System

Question 1: Convert 121₁₀ to an octal number.

Question 2: What is Octal Value of 100010000₂?

Question 3: Find the Decimal Equivalent of 55₈.

Question 4: Convert 12F₁₆ to Octal number.

Question 5: What will be the binary value of 57₈?

Answer Key:

• 171
• 420
• 45
• 457
• 101111