Convert Decimal to Octal

Decimal to Octal is a simple math topic. Decimal to Octal converter helps you to convert decimal number to octal number. It is very simple and easy to use. In this topic we are going to divide the number by 8 and write the remainders down to get the answer. It is useful in computer science, and number systems. This topic is easy to understand and practice for the students after learning it.

Table of Content

• Definition
• What is Decimal?
• What is Octal?
• How to Convert Decimal to Octal
• Decimal to Octal Table
• Solved Examples on Decimal to Octal
• Practice Questions on Decimal to Octal
• Real Life Examples on Decimal to Octal

Definition

Changing a number from base-10 (decimal) to base-8 (octal) is known as conversion from decimal to octal. Because octal representations are shorter than binary and simpler for humans to read, this is helpful in computing.

What is Decimal?

The standard method for identifying both integer and non-integer numbers is the decimal number system. Because it is based on ten digits - 0 through 9 - it is also referred to as the base-10 system. A power of 10 is represented by each position in a decimal number.

For example:

• 524 in decimal = 5 x 10^2 + 2 x 10^1 + 4 x 10^0 = 500 + 20 + 4

What is Octal?

Base-8, another name for the octal number system, has eight digits: 0 through 7. A power of eight is represented by each place value. Because each octal digit precisely corresponds to three binary digits, octal numbers are frequently used in computing as a more readable representation of binary code.

For example:

• Octal number 725 = 7 x 8^2 + 2 x 8^1 + 5 x 8^0 = 448 + 16 + 5 = 469 in decimal

How to Convert Decimal to Octal

Use these procedures to change a decimal number to an octal number:

Step 1: Divide the decimal number by eight.

Step 2: Write down what's left.

Step 3: Divide by 8 once more using the quotient from Step 1.

Step 4: Continue until the quotient equals zero.

Step 5: Write the remainders from last to first in reverse order. The octal number will be this.

Decimal to Octal Table

 

 

Solved Examples on Decimal to Octal

Example 1: Convert 45 to octal.

• 45 ÷ 8 = 5 remainder 5

• 5 ÷ 8 = 0 remainder 5

• Read remainders from bottom to top: 55

Answer: 45 in decimal = 55 in octal

Example 2: Convert 100 to octal.

• 100 ÷ 8 = 12 remainder 4

• 12 ÷ 8 = 1 remainder 4

• 1 ÷ 8 = 0 remainder 1

• Read remainders: 144

Answer: 100 in decimal = 144 in octal

Example 3: Convert 255 to octal.

• 255 ÷ 8 = 31 remainder 7

• 31 ÷ 8 = 3 remainder 7

• 3 ÷ 8 = 0 remainder 3

• Read remainders: 377

Answer: 255 in decimal = 377 in octal

Example 4: Convert 64 to octal

• 64 ÷ 8 = 8 remainder 0

• 8 ÷ 8 = 1 remainder 0

• 1 ÷ 8 = 0 remainder 1

• Read remainders: 100

Answer: 64 in decimal = 100 in octal

Example 5: Convert 128 to octal

• 128 ÷ 8 = 16 remainder 0

• 16 ÷ 8 = 2 remainder 0

• 2 ÷ 8 = 0 remainder 2

• Read remainders: 200

Answer: 128 in decimal = 200 in octal

Example 6: Convert 300 to octal

• 300 ÷ 8 = 37 remainder 4

• 37 ÷ 8 = 4 remainder 5

• 4 ÷ 8 = 0 remainder 4

• Read remainders: 454

Answer: 300 in decimal = 454 in octal

Example 7: Convert 512 to octal

• 512 ÷ 8 = 64 remainder 0

• 64 ÷ 8 = 8 remainder 0

• 8 ÷ 8 = 1 remainder 0

• 1 ÷ 8 = 0 remainder 1

• Read remainders: 1000

Answer: 512 in decimal = 1000 in octal

Example 8: Convert 90 to octal

• 90 ÷ 8 = 11 remainder 2

• 11 ÷ 8 = 1 remainder 3

• 1 ÷ 8 = 0 remainder 1

• Read remainders: 132

Answer: 90 in decimal = 132 in octal

Practice Questions on Decimal to Octal

1. Convert 64 to octal

2. Convert 128 to octal

3. Convert 75 to octal

4. Convert 200 to octal

5. Convert 300 to octal

6. Convert 512 to octal

7. Convert 350 to octal

8. Convert 23 to octal

9. Convert 90 to octal

10. Convert 1000 to octal

Real Life Examples on Decimal to Octal

• Digital Clocks and Timers: When working with bits and binary-coded formats, embedded system programming occasionally uses octal values.

• Unix File Permissions: Octal numbers (such as chmod 755) are used by Unix and Linux file permission systems to indicate read, write, and execute permissions.

• Programming in Assembly Language: Octal representations make it easier to understand machine instructions in low-level programming.

• Old Computers and Hardware: Memory addresses and instructions were frequently represented in octal rather than hexadecimal by earlier computing systems.

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