Decimal to Octal

A Decimal to Octal Converter is a tool that transforms numbers from the decimal system (base-10) into the octal system (base-8). The decimal system is the standard number system used in everyday life, while the octal system is widely used in computer science, digital electronics, and low-level programming.

The decimal system uses digits 0–9, whereas the octal system uses digits 0–7.

Conversion Principle:

To convert decimal to octal:

• Divide the decimal number by 8 repeatedly.
• Record the remainders.
• Read the remainders in reverse order to get the octal equivalent.

Example:

Decimal: 83

→ 83 ÷ 8 = 10 remainder 3

→ 10 ÷ 8 = 1 remainder 2

→ 1 ÷ 8 = 0 remainder 1

→ Octal = 123

Common Uses for Decimal to Octal Conversion:

• Computer Programming: Simplifies binary patterns in permissions, addresses, and instructions.
• Digital Systems: Octal representation eases memory mapping and register configurations.
• Microcontrollers & Embedded Systems: Often rely on octal formats for compact binary representation.
• Educational Applications: Helps students understand base conversions and number systems.
• Networking: Sometimes used in file permissions and configuration data

Key Features of Decimal to Octal Converter:

• Accurate Division Logic: Converts decimal to octal using standard base-8 conversion.
• Handles Integers and Fractions: Converts whole numbers and decimal fractions.
• Real-Time Output: Instant conversion as you type.
• Supports Large Inputs: Handles values with multiple digits.
• Beginner-Friendly Interface: Ideal for students and professionals alike.
• Copy-Ready Format: Clean output ready for programming or documentation.

This tool is essential for converting standard base-10 numbers into octal format for use in low-level system design, education, and programming.

Enter a Decimal Number:

Example: 100, 254, or 45.625.

Click Convert or Get Instant Result:

The tool performs division by 8 and generates the octal equivalent.

Read the Octal Output:

View the result instantly (e.g., 100 → 144).

Use in Your Application:

Ideal for low-level code, permissions, or system design.

Formula (Integer Part):

Divide the decimal number by 8, keep the remainder, and repeat until the quotient is 0.

Example 1: Decimal: 56

→ 56 ÷ 8 = 7 remainder 0

→ 7 ÷ 8 = 0 remainder 7

→ Octal = 70

Example 2: Decimal: 255

→ 255 ÷ 8 = 31 remainder 7

→ 31 ÷ 8 = 3 remainder 7

→ 3 ÷ 8 = 0 remainder 3

→ Octal = 377



Example 3 (with fraction): Decimal: 45.625

→ Integer Part: 45 → Octal = 55

→ Fractional Part:

0.625 × 8 = 5.0 → take 5

→ Octal = 55.5

Decimal

Octal

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

10

10

12

15

17

20

24

64

100

128

200

255

377

Steps to Convert Decimal to Octal:

For Integer Part:

1. Divide the decimal number by 8.
2. Note the remainder.
3. Continue dividing the quotient by 8 until you reach 0.
4. Read the remainders in reverse order.

For Fractional Part:

1. Multiply the fraction by 8.
2. Take the integer part as the next digit.
3. Repeat with the fractional part until it becomes 0 or repeats.

Formula:



Octal = Integer Conversion + Fractional Conversion