Decimal to Octal Conversion Examples

Decimal-to-octal conversion is an important concept in computer science and digital electronics. It helps students understand how numbers are represented in base-8 systems, which are often used to simplify binary data. This conversion transforms numbers from base 10 (decimal system) into base 8 (octal system), making it easier to work with grouped binary values. This concept is widely used in programming, memory representation, and digital system design.

Method and examples of decimal to octal conversion are given below.

Repeated Division by 8 Method

This is the most common and fundamental method used to convert decimal numbers into octal form. It involves dividing the number repeatedly by 8 and recording remainders.

Algorithm for Repeated Division by 8 Method

This algorithm clearly defines each step to ensure accuracy and avoid common mistakes during conversion.

• Step 1: Start with the given decimal number N
• Step 2: Divide N by 8
• Step 3: Record the remainder (it will always be between 0 and 7)
• Step 4: Update the quotient obtained from the division
• Step 5: Repeat Steps 2 to 4 until N = 0
• Step 6: Write all recorded remainders in reverse order (from last to first)
• Step 7: The resulting sequence is the octal equivalent

The following diagram explains the entire algorithm of decimal to octal conversion

Decimal to Octal Conversion Examples

Below are 30 solved examples of decimal to octal conversion using the repeated division by 8 method. Each example follows the same structured format for better understanding.

Example 1: Convert Decimal (10)₁₀ to Octal

This example demonstrates how a small decimal number is converted into octal using repeated division.

Solution

The following diagram shows the conversion of the decimal number (10)₁₀ into its equivalent octal

Description

• 10 is divided by 8, and the quotient is 1 with a remainder of 2.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (10)₁₀ is (12)₈.

Example 2: Convert Decimal (15)₁₀ to Octal

This example explains conversion of another small decimal number.

Solution

The following diagram shows the conversion of the decimal number (15)₁₀ into its equivalent octal

Description

• 15 is divided by 8, and the quotient is 1 with a remainder of 7.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (15)₁₀ is (17)₈.

Example 3: Convert Decimal (20)₁₀ to Octal

This example demonstrates conversion of a moderate decimal value.

Solution

The following diagram shows the conversion of the decimal number (20)₁₀ into its equivalent octal

Description

• 20 is divided by 8, and the quotient is 2 with a remainder of 4.
• 2 is divided by 8, and the quotient is 0 with a remainder of 2.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (20)₁₀ is (24)₈.

Example 4: Convert Decimal (25)₁₀ to Octal

This example shows conversion of a commonly used number.

Solution

The following diagram shows the conversion of the decimal number (25)₁₀ into its equivalent octal

Description

• 25 is divided by 8, and the quotient is 3 with a remainder of 1.
• 3 is divided by 8, and the quotient is 0 with a remainder of 3.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (25)₁₀ is (31)₈.

Example 5: Convert Decimal (32)₁₀ to Octal

This example highlights conversion of a power-related number.

Solution

The following diagram shows the conversion of the decimal number (32)₁₀ into its equivalent octal

Description

• 32 is divided by 8, and the quotient is 4 with a remainder of 0.
• 4 is divided by 8, and the quotient is 0 with a remainder of 4.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (32)₁₀ is (40)₈.

Example 6: Convert Decimal (45)₁₀ to Octal

This example demonstrates conversion of a two-digit decimal number.

Solution

The following diagram shows the conversion of the decimal number (45)₁₀ into its equivalent octal

Description

• 45 is divided by 8, and the quotient is 5 with a remainder of 5.
• 5 is divided by 8, and the quotient is 0 with a remainder of 5.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (45)₁₀ is (55)₈.

Example 7: Convert Decimal (50)₁₀ to Octal

This example shows the conversion of a round number.

Solution

The following diagram shows the conversion of the decimal number (50)₁₀ into its equivalent octal

Description

• 50 is divided by 8, and the quotient is 6 with a remainder of 2.
• 6 is divided by 8, and the quotient is 0 with a remainder of 6.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (50)₁₀ is (62)₈.

Example 8: Convert Decimal (64)₁₀ to Octal

This example explains conversion of a power of 8.

Solution

The following diagram shows the conversion of the decimal number (64)₁₀ into its equivalent octal

Description

• 64 is divided by 8, and the quotient is 8 with a remainder of 0.
• 8 is divided by 8, and the quotient is 1 with a remainder of 0.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (64)₁₀ is (100)₈.

Example 9: Convert Decimal (75)₁₀ to Octal

This example demonstrates conversion of a larger number.

Solution

The following diagram shows the conversion of the decimal number (75)₁₀ into its equivalent octal

Description

• 75 is divided by 8, and the quotient is 9 with a remainder of 3.
• 9 is divided by 8, and the quotient is 1 with a remainder of 1.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (75)₁₀ is (113)₈.

Example 10: Convert Decimal (80)₁₀ to Octal

This example shows conversion near a multiple of 8.

Solution

The following diagram shows the conversion of the decimal number (80)₁₀ into its equivalent octal

Description

• 80 is divided by 8, and the quotient is 10 with a remainder of 0.
• 10 is divided by 8, and the quotient is 1 with a remainder of 2.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (80)₁₀ is (120)₈.

Example 11: Convert Decimal (100)₁₀ to Octal

This example demonstrates the conversion of a three-digit decimal number.

Solution

The following diagram shows the conversion of the decimal number (100)₁₀ into its equivalent octal

Description

• 100 is divided by 8, and the quotient is 12 with a remainder of 4.
• 12 is divided by 8, and the quotient is 1 with a remainder of 4.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (100)₁₀ is (144)₈.

Example 12: Convert Decimal (120)₁₀ to Octal

This example shows conversion of a larger value.

Solution

The following diagram shows the conversion of the decimal number (120)₁₀ into its equivalent octal

Description

• 120 is divided by 8, and the quotient is 15 with a remainder of 0.
• 15 is divided by 8, and the quotient is 1 with a remainder of 7.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (120)₁₀ is (170)₈.

Example 13: Convert Decimal (150)₁₀ to Octal

This example demonstrates conversion of a mid-range number.

Solution

The following diagram shows the conversion of the decimal number (150)₁₀ into its equivalent octal

Description

• 150 is divided by 8, and the quotient is 18 with a remainder of 6.
• 18 is divided by 8, and the quotient is 2 with a remainder of 2.
• 2 is divided by 8, and the quotient is 0 with a remainder of 2.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (150)₁₀ is (226)₈.

Example 14: Convert Decimal (200)₁₀ to Octal

This example explains conversion of a round number.

Solution

The following diagram shows the conversion of the decimal number (200)₁₀ into its equivalent octal

Description

• 200 is divided by 8, and the quotient is 25 with a remainder of 0.
• 25 is divided by 8, and the quotient is 3 with a remainder of 1.
• 3 is divided by 8, and the quotient is 0 with a remainder of 3.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (200)₁₀ is (310)₈.

Example 15: Convert Decimal (255)₁₀ to Octal

This example shows conversion of a commonly used number.

Solution

The following diagram shows the conversion of the decimal number (255)₁₀ into its equivalent octal

Description

• 255 is divided by 8, and the quotient is 31 with a remainder of 7.
• 31 is divided by 8, and the quotient is 3 with a remainder of 7.
• 3 is divided by 8, and the quotient is 0 with a remainder of 3.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (255)₁₀ is (377)₈.

Example 16: Convert Decimal (300)₁₀ to Octal

This example demonstrates conversion of a larger number.

Solution

The following diagram shows the conversion of the decimal number (300)₁₀ into its equivalent octal

Description

• 300 is divided by 8, and the quotient is 37 with a remainder of 4.
• 37 is divided by 8, and the quotient is 4 with a remainder of 5.
• 4 is divided by 8, and the quotient is 0 with a remainder of 4.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (300)₁₀ is (454)₈.

Example 17: Convert Decimal (400)₁₀ to Octal

This example explains conversion of a higher value.

Solution

The following diagram shows the conversion of the decimal number (400)₁₀ into its equivalent octal

Description

• 400 is divided by 8, and the quotient is 50 with a remainder of 0.
• 50 is divided by 8, and the quotient is 6 with a remainder of 2.
• 6 is divided by 8, and the quotient is 0 with a remainder of 6.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (400)₁₀ is (620)₈.

Example 18: Convert Decimal (512)₁₀ to Octal

This example shows conversion of a power of 2.

Solution

The following diagram shows the conversion of the decimal number (512)₁₀ into its equivalent octal

Description

• 512 is divided by 8, and the quotient is 64 with a remainder of 0.
• 64 is divided by 8, and the quotient is 8 with a remainder of 0.
• 8 is divided by 8, and the quotient is 1 with a remainder of 0.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (512)₁₀ is (1000)₈.

Example 19: Convert Decimal (750)₁₀ to Octal

This example demonstrates conversion of a large number.

Solution

The following diagram shows the conversion of the decimal number (750)₁₀ into its equivalent octal

Description

• 750 is divided by 8, and the quotient is 93 with a remainder of 6.
• 93 is divided by 8, and the quotient is 11 with a remainder of 5.
• 11 is divided by 8, and the quotient is 1 with a remainder of 3.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (750)₁₀ is (1356)₈.

Example 20: Convert Decimal (1024)₁₀ to Octal

This example explains conversion of a very large number used in computing.

Solution

The following diagram shows the conversion of the decimal number (1024)₁₀ into its equivalent octal

Description

• 1024 is divided by 8, and the quotient is 128 with a remainder of 0.
• 128 is divided by 8, and the quotient is 16 with a remainder of 0.
• 16 is divided by 8, and the quotient is 2 with a remainder of 0.
• 2 is divided by 8, and the quotient is 0 with a remainder of 2.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (1024)₁₀ is (2000)₈.

Example 21: Convert Decimal (1500)₁₀ to Octal

This example demonstrates conversion of a larger decimal number into octal using repeated division.

Solution

The following diagram shows the conversion of the decimal number (1500)₁₀ into its equivalent octal

Description

• 1500 is divided by 8, and the quotient is 187 with a remainder of 4.
• 187 is divided by 8, and the quotient is 23 with a remainder of 3.
• 23 is divided by 8, and the quotient is 2 with a remainder of 7.
• 2 is divided by 8, and the quotient is 0 with a remainder of 2.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (1500)₁₀ is (2734)₈.

Example 22: Convert Decimal (5200)₁₀ to Octal

This example explains conversion of a four-digit decimal number.

Solution

The following diagram shows the conversion of the decimal number (5200)₁₀ into its equivalent octal

Description

• 5200 is divided by 8, and the quotient is 650 with a remainder of 0.
• 650 is divided by 8, and the quotient is 81 with a remainder of 2.
• 81 is divided by 8, and the quotient is 10 with a remainder of 1.
• 10 is divided by 8, and the quotient is 1 with a remainder of 2.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (5200)₁₀ is (12120)₈.

Example 23: Convert Decimal (10800)₁₀ to Octal

This example shows conversion of a large decimal value.

Solution

The following diagram shows the conversion of the decimal number (10800)₁₀ into its equivalent octal

Description

• 10800 is divided by 8, and the quotient is 1350 with a remainder of 0.
• 1350 is divided by 8, and the quotient is 168 with a remainder of 6.
• 168 is divided by 8, and the quotient is 21 with a remainder of 0.
• 21 is divided by 8, and the quotient is 2 with a remainder of 5.
• 2 is divided by 8, and the quotient is 0 with a remainder of 2.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (10800)₁₀ is (25060)₈.

Example 24: Convert Decimal (17189)₁₀ to Octal

This example demonstrates conversion of a complex decimal number.

Solution

The following diagram shows the conversion of the decimal number (17189)₁₀ into its equivalent octal

Description

• 17189 is divided by 8, and the quotient is 2148 with a remainder of 5.
• 2148 is divided by 8, and the quotient is 268 with a remainder of 4.
• 268 is divided by 8, and the quotient is 33 with a remainder of 4.
• 33 is divided by 8, and the quotient is 4 with a remainder of 1.
• 4 is divided by 8, and the quotient is 0 with a remainder of 4.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (17189)₁₀ is (41445)₈.

Example 25: Convert Decimal (24688)₁₀ to Octal

This example explains conversion of another large decimal number.

Solution

The following diagram shows the conversion of the decimal number (24688)₁₀ into its equivalent octal

Description

• 24688 is divided by 8, and the quotient is 3086 with a remainder of 0.
• 3086 is divided by 8, and the quotient is 385 with a remainder of 6.
• 385 is divided by 8, and the quotient is 48 with a remainder of 1.
• 48 is divided by 8, and the quotient is 6 with a remainder of 0.
• 6 is divided by 8, and the quotient is 0 with a remainder of 6.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (24688)₁₀ is (60160)₈.

Example 26: Convert Decimal (35474)₁₀ to Octal

This example demonstrates conversion of a high-value decimal number.

Solution

The following diagram shows the conversion of the decimal number (35474)₁₀ into its equivalent octal

Description

• 35474 is divided by 8, and the quotient is 4434 with a remainder of 2.
• 4434 is divided by 8, and the quotient is 554 with a remainder of 2.
• 554 is divided by 8, and the quotient is 69 with a remainder of 2.
• 69 is divided by 8, and the quotient is 8 with a remainder of 5.
• 8 is divided by 8, and the quotient is 1 with a remainder of 0.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (35474)₁₀ is (105222)₈.

Example 27: Convert Decimal (48000)₁₀ to Octal

This example shows conversion of a very large decimal number.

Solution

The following diagram shows the conversion of the decimal number (48000)₁₀ into its equivalent octal

Description

• 48000 is divided by 8, and the quotient is 6000 with a remainder of 0.
• 6000 is divided by 8, and the quotient is 750 with a remainder of 0.
• 750 is divided by 8, and the quotient is 93 with a remainder of 6.
• 93 is divided by 8, and the quotient is 11 with a remainder of 5.
• 11 is divided by 8, and the quotient is 1 with a remainder of 3.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (48000)₁₀ is (135600)₈.

Example 28: Convert Decimal (65535)₁₀ to Octal

This example demonstrates conversion of a commonly used large number in computing.

Solution

The following diagram shows the conversion of the decimal number (65535)₁₀ into its equivalent octal

Description

• 65535 is divided by 8, and the quotient is 8191 with a remainder of 7.
• 8191 is divided by 8, and the quotient is 1023 with a remainder of 7.
• 1023 is divided by 8, and the quotient is 127 with a remainder of 7.
• 127 is divided by 8, and the quotient is 15 with a remainder of 7.
• 15 is divided by 8, and the quotient is 1 with a remainder of 7.
• 1 is divided by 8, and the quotient is 0 with a remainder of 1.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (65535)₁₀ is (177777)₈.

Example 29: Convert Decimal (99999)₁₀ to Octal

This example explains conversion of a very large decimal number.

Solution

The following diagram shows the conversion of the decimal number (99999)₁₀ into its equivalent octal

Description

• 99999 is divided by 8, and the quotient is 12499 with a remainder of 7.
• 12499 is divided by 8, and the quotient is 1562 with a remainder of 3.
• 1562 is divided by 8, and the quotient is 195 with a remainder of 2.
• 195 is divided by 8, and the quotient is 24 with a remainder of 3.
• 24 is divided by 8, and the quotient is 3 with a remainder of 0.
• 3 is divided by 8, and the quotient is 0 with a remainder of 3.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (99999)₁₀ is (303237)₈.

Example 30: Convert Decimal (123456)₁₀ to Octal

This example demonstrates conversion of a large real-world number.

Solution

The following diagram shows the conversion of the decimal number (123456)₁₀ into its equivalent octal

Description

• 123456 is divided by 8, and the quotient is 15432 with a remainder of 0.
• 15432 is divided by 8, and the quotient is 1929 with a remainder of 0.
• 1929 is divided by 8, and the quotient is 241 with a remainder of 1.
• 241 is divided by 8, and the quotient is 30 with a remainder of 1.
• 30 is divided by 8, and the quotient is 3 with a remainder of 6.
• 3 is divided by 8, and the quotient is 0 with a remainder of 3.

Now, we write all remainders from bottom to top to get the final octal number. The octal representation of the decimal number (123456)₁₀ is (361100)₈.

Conclusion

Decimal to octal conversion is a simple yet powerful technique that helps students understand number systems used in computing. By mastering the repeated division by 8 method and practicing these examples, students can easily convert any decimal number into its octal equivalent. This concept also builds a strong foundation for learning binary and hexadecimal number systems.