Decimal to Octal Converter

Omni's decimal to octal converter allows you to convert numbers between the decimal and octal number systems.

Continue reading this article to know what an octal number system is and how to convert octal to decimal number systems and vice-versa. You will also see some examples of octal to decimal conversion and learn about the use of octal number systems.

Let us first try to understand what the octal number system is.

You must be well familiar with the decimal number system. After all, we have been using it since we first started learning to count. But have you noticed that each position in a decimal number system can be expressed as a power of $10$? For example, we can write $13$ as:

$13 = 1 \times 10^1 + 3 \times 10^0$

Hence, we can also say that the base of the decimal number system is $10$ and it contains ten unique symbols from $0$ to $9$.

The octal number system has $8$ as its base. We can express each place as a power of $8$. The digits of an octal number can be a number between $0$ and $7$. Examples of numbers in the octal system are $(321)_8$, $(10)_8$, etc.

We can express these numbers as:

$(321)_8 = 3 \times 8^2 + 2 \times 8^1 + 1 \times 8^0$

$(10)_8 = 1 \times 8^1 + 0 \times 8^0$

In the following sections, we will see how we can convert a number from decimal to the octal system and vice-versa.

To convert a number from the decimal system to the octal system, we will use a very simple approach:

1. Divide the number by $8$.

2. Take note of the remainder. It can be any number between $0$ to $7$. This number will be the last digit of the octal number, i.e., the rightmost digit.

3. Use the quotient from step 1 as your new initial number.

4. Repeat steps 1-3, and keep adding the remainder to the left of the previously obtained digits.

Let us understand this using an example. We will convert the number $(6521)_{10}$ to octal representation:

1. Divide by $8$, i.e., $6521/8 = 815$, remainder is $1$.
2. Now, we will use the quotient from step 1, i.e., $815$ as the new number, and repeat step 1.
3. We will continue repeating the above steps until we get $0$ as the quotient. The results are shown in the table below.

Reading upwards, i.e., from bottom to top, the number $(6521)_{10}$ is $(14571)_8$ in octal representation.

If you have understood how to convert decimal to octal, then you must have realized by now how we can go the other way, i.e., convert a number from the octal to decimal system. Just reverse the algorithm explained above:

1. Start with the last digit (i.e., the rightmost one) and count the positions of digits as 0, 1, 2, 3, .... We will denote the digit at position 0 as $D_0$, position 1 as $D_1$, ..., and so on.

2. Now use the following algorithm to get the number ($N_{10}$) in the decimal system:
   $N_{10}= D_0(8^0) + D_1(8^1) + D_2(8^2) + ...$

For example, let us convert $(3241)_8$ to decimal.

1. First, we will count the position of each digit starting from the last one.

2. Now using the algorithm,
   $N_{10}= D_0(8^0) + D_1(8^1) + D_2(8^2) + D_3(8^3)$

   we will get:

   $N_{10}= 1\times(8^0) + 4\times(8^1) + 2\times(8^2) + 3\times(8^3)$

   $N_{10} = 1697$

Hence, the number $3241$ corresponds to $(1697)_{10}$ in the decimal representation.

You can also check our binary to octal converter to convert between binary and octal numbers.

Now let us see how we can use our decimal to octal converter to solve the same octal to decimal conversion examples:

1. Using the drop-down menu, choose the option decimal to octal.

2. Type the number you want to convert, i.e., 6521.

3. The tool will display the result in the octal number system, i.e., 14571.

4. You can also convert octal to decimal by choosing it as the option.

The base of the octal number system is 8. That means that it has eight possible symbols (or digits) from 0 to 7. There are no 8's or 9's in the octal number system.

The octal number system is widely used in computers as it is more convenient and efficient to express numbers in octal rather than in binary representation. While dealing with binary numbers involving several bits converting them into octal makes the data handling and computation less prone to error.

To convert 18 into the octal number system, follow the given instructions:

1. Divide 18 by 8. The quotient is 2, and the remainder is 2. This remainder will be the last digit of the octal number.

2. Now divide the quotient from step 1, i.e., 2 by 8. You will get 0 as the quotient and 2 as the remainder. This remainder will be the first digit of the octal number.

3. Arranging the remainders from steps 1 and 2, you will get 22, which is the octal representation of 18.

10. If we divide 10 by 8, the remainder is 0, and the quotient is 1. Similarly, when we divide 1 by 8, the remainder is 1, and the quotient is 0. Arranging the two remainders, we will get 10, which is the octal equivalent of decimal number 8.