Decimal to Octal Converter

Convert between decimal (base-10) and octal (base-8) number systems with step-by-step conversion process

Number System Converter

Range: 0 to 2,147,483,647

Use digits 0-7 only

Example Conversions

Decimal to Octal Examples:

810=108
1810=228
6410=1008
25510=3778
51210=10008
652110=145718

Octal to Decimal Examples:

108=810
228=1810
1008=6410
3778=25510
10008=51210
32418=169710

Decimal to Octal Reference Table

DecimalOctalBinary
00000
11001
22010
33011
44100
55101
66110
77111
810001 000
911001 001
1012001 010
1113001 011
1214001 100
1315001 101
1416001 110
1517001 111

Each octal digit represents 3 binary digits (bits)

Quick Tips

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Decimal uses base 10 (digits 0-9)

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Octal uses base 8 (digits 0-7)

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Divide by 8 and collect remainders

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Used in computing and digital systems

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Each octal digit = 3 binary bits

Understanding Decimal and Octal Number Systems

What is the Octal System?

The octal number system uses base 8, meaning it has eight unique digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each position in an octal number represents a power of 8, just like decimal uses powers of 10.

Applications of Octal

  • Computer programming and digital systems
  • Unix file permissions
  • Compact representation of binary data
  • Error-prone binary calculations

Conversion Methods

Decimal to Octal:

  1. 1. Divide the decimal number by 8
  2. 2. Record the remainder (0-7)
  3. 3. Use the quotient as the new number
  4. 4. Repeat until quotient is 0
  5. 5. Read remainders from bottom to top

Octal to Decimal:

  1. 1. Start from the rightmost digit (position 0)
  2. 2. Multiply each digit by 8^position
  3. 3. Sum all the products
  4. 4. The result is the decimal equivalent

Quick Formula: For octal digit d at position p: d × 8^p. Sum all products for the final decimal value.