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Decimal and octal are two numbering systems used to represent numerical values. The decimal system is widely used in everyday life and is a base 10 numbering system, while the octal system is less common and is a base 8 numbering system.

In this article, we will explore the basics of decimal and octal numbering systems, their relationship, and provide examples of how to convert between the two. I have placed the tool at the end of the article.

Tool Tech

Decimal Number System:

The decimal number system is a base 10 numbering system, meaning it uses ten digits (0-9) to represent numbers. The rightmost digit represents the ones place, the next digit to the left represents the tens place, and so on, with each digit representing a power of ten.

For example, the number 123 can be broken down as follows:

1 x 10^2 + 2 x 10^1 + 3 x 10^0 = 100 + 20 + 3 = 123

The decimal system is commonly used in everyday life for counting and arithmetic operations, such as addition, subtraction, multiplication, and division.

Octal Number System:

The octal number system is a base 8 numbering system, meaning it uses eight digits (0-7) to represent numbers. The rightmost digit represents the ones place, the next digit to the left represents the eights place, and so on, with each digit representing a power of eight.

For example, the number 173 can be broken down as follows:

1 x 8^2 + 7 x 8^1 + 3 x 8^0 = 64 + 56 + 3 = 123

The octal system is less commonly used in everyday life, but it is often used in computer programming and other technical fields.

Relationship between Decimal and Octal Number Systems:

The relationship between the decimal and octal number systems is based on the fact that 8 is a power of 2, and 2 is a factor of 10. This means that any octal number can be converted to a decimal number by multiplying each digit by the appropriate power of 8 and then adding the results.

For example, the octal number 173 can be converted to decimal as follows:

1 x 8^2 + 7 x 8^1 + 3 x 8^0 = 64 + 56 + 3 = 123

Conversely, any decimal number can be converted to octal by repeatedly dividing the number by 8 and recording the remainders.

For example, the decimal number 123 can be converted to octal as follows:

123 ÷ 8 = 15 remainder 3
15 ÷ 8 = 1 remainder 7
1 ÷ 8 = 0 remainder 1

Therefore, the octal representation of 123 is 173.

Converting between Decimal and Octal:

To convert a decimal number to octal, you can use the repeated division method described above. Alternatively, you can use the following algorithm:

Divide the decimal number by 8.
Record the remainder.
Divide the quotient by 8 and repeat step 2 until the quotient is 0.
The octal representation of the decimal number is the remainders in reverse order.
For example, to convert the decimal number 275 to octal, we can use the following algorithm:

275 ÷ 8 = 34 remainder 3
34 ÷ 8 = 4 remainder 2
4 ÷ 8 = 0 remainder 4

Therefore, the octal representation of 275 is 423.

To convert an octal number to decimal, you can use the following algorithm:

Write the octal number as a sum of powers of 8, starting with the rightmost digit as the first power.

For example, to convert the octal number 423 to decimal, we can use the following algorithm:

4 x 8^2 + 2 x 8^1 + 3 x 8^0 = 256 + 16 + 3 = 275

Therefore, the decimal representation of 423 is 275.

Advantages and Disadvantages of Decimal and Octal Number Systems:

The decimal system is easy to understand and widely used in everyday life. It is also easy to perform arithmetic operations such as addition, subtraction, multiplication, and division in the decimal system.

The octal system is less commonly used in everyday life but is often used in computer programming and other technical fields. The octal system has the advantage of being easy to convert to binary, another important numbering system used in computing. This is because each octal digit can be represented by three binary digits, making it easy to convert between the two.

However, the octal system can be more difficult to use for arithmetic operations than the decimal system, and it is less intuitive for most people.

Table of Octal and decimal:

Here's a table showing the correspondence of octal 0 to 50 in hexadecimal, decimal, binary, and text:

OctalHexadecimalDecimalBinaryText
000x000000000NUL
010x011000001SOH
020x022000010STX
030x033000011ETX
040x044000100EOT
050x055000101ENQ
060x066000110ACK
070x077000111BEL
100x088001000BS
110x099001001HT
120x0A10001010LF
130x0B11001011VT
140x0C12001100FF
150x0D13001101CR
160x0E14001110SO
170x0F15001111SI
200x1016010000DLE
210x1117010001DC1
220x1218010010DC2
230x1319010011DC3
240x1420010100DC4
250x1521010101NAK
260x1622010110SYN
270x1723010111ETB
300x1824011000CAN
310x1925011001EM
320x1A26011010SUB
330x1B27011011ESC
340x1C28011100FS
350x1D29011101GS
360x1E30011110RS


List of Octal:

Here's a list of octal numbers from 0 to 77:

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77.

Note: that each octal digit represents three bits in binary notation.


How to use


If you are finding it difficult to use this tool, no problem, you can easily use this tool by following the instructions below:
  • First, you have to enter any decimal or Octal number that you want to convert to Octal or Decimal and then click the convert button.
  • As soon as you click the convert button, your data will be displayed below.
  • You can copy any data you want to copy by pressing the copy button below the tool.
Decimal to Octal and Octal to Decimal Conversion Tool

Decimal to Octal and Octal to Decimal Conversion Tool

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