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.

Methods and examples of decimal-to-octal conversion are given below.

1. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

Decimal Fraction to Octal Conversion

Decimal fractions (numbers with decimal points) can also be converted into octal form using a multiplication-based method. This is important in computer science when working with base-8 representations of real numbers.

Algorithm for Multiplication by 8 Method (Fractional Part)

This method converts decimal fractions into octal by repeatedly multiplying by 8 and extracting integer parts.

Step 1: Take the decimal fractional number (for example, 0.x)
Step 2: Multiply the fractional number by 8
Step 3: Note the integer part of the result (0 to 7)
Step 4: Keep only the fractional part of the result
Step 5: Repeat Steps 2 to 4 with the new fractional part
Step 6: Continue until the fraction becomes 0 or required precision (3–4 digits) is achieved
Step 7: Write all recorded integer parts in the same order

Example 01: Convert (0.625)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (0.625)₁₀ into its equivalent octal

Description:

0.625 is multiplied by 8 and the result is 5.0, so the integer part is 5

Octal fraction = 0.5₈

Example 02: Convert (0.375)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (0.375)₁₀ into its equivalent octal

Description:

0.375 is multiplied by 8 and the result is 3.0, so the integer part is 3

Octal fraction = 0.3₈

Example 03: Convert (0.8125)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (0.8125)₁₀ into its equivalent octal

Description:

0.8125 is multiplied by 8 and the result is 6.5, so the integer part is 6
0.5 is multiplied by 8 and the result is 4.0, so the integer part is 4

Octal fraction = 0.64₈

Example 04: Convert (0.1)₁₀ to Octal (Approximate)

Solution:

The following diagram shows the conversion of the decimal number (0.1)₁₀ into its equivalent octal

Description:

0.1 is multiplied by 8 and the result is 0.8, so the integer part is 0
0.8 is multiplied by 8 and the result is 6.4, so the integer part is 6
0.4 is multiplied by 8 and the result is 3.2, so the integer part is 3
0.2 is multiplied by 8 and the result is 1.6, so the integer part is 1
0.6 is multiplied by 8 and the result is 4.8, so the integer part is 4

(Octal starts repeating)

Octal fraction ≈ 0.06314₈

Example 05: Convert (0.45)₁₀ to Octal (Approximate up to 4 digits)

Solution:

The following diagram shows the conversion of the decimal number (0.45)₁₀ into its equivalent octal

Description:

0.45 is multiplied by 8 and the result is 3.6, so the integer part is 3
0.6 is multiplied by 8 and the result is 4.8, so the integer part is 4
0.8 is multiplied by 8 and the result is 6.4, so the integer part is 6
0.4 is multiplied by 8 and the result is 3.2, so the integer part is 3

Octal fraction ≈ 0.3463₈

Decimal (Integer + Fraction) to Octal Conversion

When a decimal number has both integer and fractional parts, convert each separately.

• Step 01: Convert integer part using division by 8
• Step 02: Convert fractional part using multiplication by 8
• Step 03: Combine both results

Example 01: Convert (16.625)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (16.625)₁₀ into its equivalent octal

 

Integer Part Description:

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

Binary integer part = 20₈

Fraction Part Description:

0.625 is multiplied by 8 and the result is 5.0, so the integer part is 5

Octal fraction = 0.5₈

Final Answer:

(16.625)₁₀ = (20.5)₈

Example 02: Convert (25.375)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (25.375)₁₀ into its equivalent octal

Integer Part 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

Octal integer part = 31₈

Fraction Part Description:

0.375 is multiplied by 8 and the result is 3.0, so the integer part is 3

Octal fraction = 0.3₈

Final Answer:

(25.375)₁₀ = (31.3)₈

Example 03: Convert (56.8125)₁₀ to Octal

Solution:

The following diagram shows the conversion of the decimal number (56.8125)₁₀ into its equivalent octal

Integer Part Description:

56 is divided by 8 and the quotient is 7 with a remainder of 0
7 is divided by 8 and the quotient is 0 with a remainder of 7

Octal integer part = 70₈

Fraction Part Description:

0.8125 is multiplied by 8 and the result is 6.5, so the integer part is 6
0.5 is multiplied by 8 and the result is 4.0, so the integer part is 4

Octal fraction = 0.64₈

Final Answer:

(56.8125)₁₀ = (70.64)₈

Example 04: Convert (100.1)₁₀ to Octal (Approximate)

Solution:

The following diagram shows the conversion of the decimal number (100.1)₁₀ into its equivalent octal

Integer Part 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

Octal integer part = 144₈

Fraction Part Description:

0.1 is multiplied by 8 and the result is 0.8, so the integer part is 0
0.8 is multiplied by 8 and the result is 6.4, so the integer part is 6
0.4 is multiplied by 8 and the result is 3.2, so the integer part is 3
0.2 is multiplied by 8 and the result is 1.6, so the integer part is 1

Octal fraction ≈ 0.0631₈

Final Answer:

(100.1)₁₀ ≈ (144.0631)₈

Example 05: Convert (255.45)₁₀ to Octal (Approximate up to 4 digits)

Solution:

The following diagram shows the conversion of the decimal number (255.45)₁₀ into its equivalent octal

Integer Part 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

Octal integer part = 377₈

Fraction Part Description:

0.45 is multiplied by 8 and the result is 3.6, so the integer part is 3
0.6 is multiplied by 8 and the result is 4.8, so the integer part is 4
0.8 is multiplied by 8 and the result is 6.4, so the integer part is 6
0.4 is multiplied by 8 and the result is 3.2, so the integer part is 3

Octal fraction ≈ 0.3463₈

Final Answer:

(255.45)₁₀ ≈ (377.3463)₈

This method is widely used in computer systems where base-8 representation is required, especially in low-level computing and digital systems.

Decimal to Octal Conversion Examples for Quick Practice

Practicing different decimal values improves speed and accuracy in conversions. A list of decimal to octal examples is given below.

Decimal	Octal	Decimal	Octal	Decimal	Octal	Decimal	Octal
0	0	25	31	50	62	75	113
1	1	26	32	51	63	76	114
2	2	27	33	52	64	77	115
3	3	28	34	53	65	78	116
4	4	29	35	54	66	79	117
5	5	30	36	55	67	80	120
6	6	31	37	56	70	81	121
7	7	32	40	57	71	82	122
8	10	33	41	58	72	83	123
9	11	34	42	59	73	84	124
10	12	35	43	60	74	85	125
11	13	36	44	61	75	86	126
12	14	37	45	62	76	87	127
13	15	38	46	63	77	88	130
14	16	39	47	64	100	89	131
15	17	40	50	65	101	90	132
16	20	41	51	66	102	91	133
17	21	42	52	67	103	92	134
18	22	43	53	68	104	93	135
19	23	44	54	69	105	94	136
20	24	45	55	70	106	95	137
21	25	46	56	71	107	96	140
22	26	47	57	72	110	97	141
23	27	48	60	73	111	98	142
24	30	49	61	74	112	99	143

Common Mistakes in Decimal to Octal Conversion

Avoiding common mistakes in decimal to octal conversion is essential for achieving accurate results in exams and practical applications.

1. Writing Remainders in Wrong Order

In the division-by-8 method, remainders must be written from bottom to top. Writing them in the same order leads to incorrect results.

• Example: Correct: 25 → 31 . Incorrect: 25 → 13
• Tip: Always reverse the order of remainders before writing the final answer.

2. Skipping Steps in Division

Each division step contributes one octal digit. Skipping steps results in missing digits.

• Example: Missing an intermediate step while converting 50 can give an incorrect octal value.
• Tip: Write all steps clearly to avoid calculation errors.

3. Confusing Base Values

Octal uses base 8 (digits 0–7), but students sometimes mistakenly use base 10 or base 2 logic.

• Example: Using powers of 2 instead of 8 leads to incorrect answers.
• Tip: Remember: Octal = base 8 → use powers of 8 (1, 8, 64, 512, …).

4. Incorrect Handling of Fractions

Fractional parts must be converted using multiplication by 8, not division.

• Example: 0.625 should be multiplied by 8 repeatedly, not divided.
• Tip: Separate integer and fractional parts, then combine results.

5. Ignoring Digit Limits (0–7)

Octal digits range only from 0 to 7. Writing 8 or 9 in octal is invalid.

• Example: Incorrect: 128₈ . Correct representation must not contain digits ≥ 8
• Tip: Always verify that all digits are between 0 and 7.

Applications of Decimal to Octal Conversion

1. Digital Systems

Octal is sometimes used as a compact representation of binary numbers. Each octal digit represents exactly 3 binary bits, making it easier to read large binary values.

Use Cases:

• Embedded systems
• Digital design
• Microprocessor operations

2. Computer Programming

Octal is used in certain programming contexts. Some languages allow octal literals for representing numbers.

Use Cases:

• File permission systems (like Unix/Linux)
• Low-level programming

3. Data Representation

Octal provides a shorter way to represent binary data. Large binary numbers can be simplified using octal grouping.

Use Cases:

• Debugging
• Memory representation

4. Networking and Encoding

Octal may be used in encoding schemes and legacy systems. Helps simplify binary-based data transmission.

Use Cases:

• Communication protocols
• Data encoding

5. Computer Architecture Learning

Octal helps beginners understand number systems and base conversions. Acts as a bridge between binary and decimal systems.

Use Cases:

• Academic learning
• Competitive exams

Conclusion

Decimal to octal conversion is an important concept in number systems that helps simplify binary representation and supports various computing applications. By practicing conversion tables, avoiding common mistakes, and understanding real-world uses, students can build strong problem-solving skills and improve accuracy in exams and technical tasks.