Octal and Decimal tool || Table and List (Free Tool)

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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.

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:

Octal	Hexadecimal	Decimal	Binary	Text
00	0x00	0	000000	NUL
01	0x01	1	000001	SOH
02	0x02	2	000010	STX
03	0x03	3	000011	ETX
04	0x04	4	000100	EOT
05	0x05	5	000101	ENQ
06	0x06	6	000110	ACK
07	0x07	7	000111	BEL
10	0x08	8	001000	BS
11	0x09	9	001001	HT
12	0x0A	10	001010	LF
13	0x0B	11	001011	VT
14	0x0C	12	001100	FF
15	0x0D	13	001101	CR
16	0x0E	14	001110	SO
17	0x0F	15	001111	SI
20	0x10	16	010000	DLE
21	0x11	17	010001	DC1
22	0x12	18	010010	DC2
23	0x13	19	010011	DC3
24	0x14	20	010100	DC4
25	0x15	21	010101	NAK
26	0x16	22	010110	SYN
27	0x17	23	010111	ETB
30	0x18	24	011000	CAN
31	0x19	25	011001	EM
32	0x1A	26	011010	SUB
33	0x1B	27	011011	ESC
34	0x1C	28	011100	FS
35	0x1D	29	011101	GS
36	0x1E	30	011110	RS

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: Octal:

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