Decimal to Octal

Decimal to octal conversion is done keeping the number system in mind. A number system is a form of representation of numbers in terms of digits or symbols. There are 4 types of number systems - Octal, Binary, Decimal, and Hexadecimal. Decimal to octal conversion can be done by dividing the decimal number by the octal base number. Let us learn the steps of doing so.

Decimal to octal conversion occurs when we need to find the equivalent of any number. In this case, we need to convert the decimal number to its equivalent octal number. In the number system, each of the types has its own base number i.e.octal number has a base number of 8 and the decimal number has a base number of 10. To convert decimal to octal, we need to divide the decimal number by the octal base number 8 and write the acquired remainder in reverse to derive at the equivalent octal number. Before conversion, let us learn about the octal number system and the decimal number system.

Decimal Number System

The numbers with the base number as 10 and uses ten digits: 0,1,2,3,4,5,6,7,8 and 9 are called the decimal number system. The decimal number system is used to represent numbers in real life. If any number is represented without a base, it means that its base is 10. Decimal numbers are represented as (a)₁₀. Here are a few examples: \(23_{10}, 132_{10}, 257_{10}\)

Octal Number System

The octal number system uses eight digits: 0,1,2,3,4,5,6 and 7 with the base of 8. The advantage of this system is that it has lesser digits when compared to several other systems, hence, there would be fewer computational errors. Numbers like 8 and 9 are not included in the octal number system. Octal numbers are represented as (a)₈. Each place in an octal number is a power of eight. For example: \((151)_{8}\) = 1 x 8² + 5 x 8¹ + 1 x 8⁰.

To convert decimal to octal number, there are two methods of conversions. The first method is to convert the decimal number to another number system i.e. binary or hexadecimal and finally convert it to octal. The second method is the direct method where we convert decimal to octal directly. Let see both the methods:

Method 1: Convert Decimal to Binary to Octal

In this method, a decimal number can be converted to a binary number by dividing the given number by 2 until we obtain a quotient as 1. The numbers are written from downwards to upwards. Once the binary number is obtained, we convert that into an octal number. Let us understand this using an example. Convert the decimal number \((45)_{10}\) to an octal number.

Step 1: First, we convert the decimal number \((45)_{10}\) to a binary number. We divide 45 by the binary base number i.e. 2 until we obtain the quotient as 1.

Therefore, the decimal number \((45)_{10}\) = \((101101)_{2}\).

Step 2: Once we have obtained the binary number, we can convert this number to an octal number by using the binary to the octal conversion table.

With the help of the above table, we first write the number into its 3-bit binary number as a zero needs to be added before digits to form the 3-bit binary number. Hence, the 3-bit binary number is 101 and 101. Looking at the same table above we can convert these binary numbers to their octal numbers to derive the final number. Hence, the numbers are 5 and 5. Therefore, \((101101)_{2}\) = \((55)_{8}\).

Step 3: Once we have obtained the octal number, the conversion from decimal to octal can be written as: \((45)_{10}\) = \((55)_{8}\).

Method 2: Convert Decimal to Octal

In this method, the decimal number is divided by 8, each time a reminder is obtained from the previous digit. The first remainder obtained is the least significant digit(LSD) and the last remainder is the most significant digit(MSD). Once the quotient is less than 8, we obtain the octal number by writing the remainder in reverse order. Let us understand the conversion with the help of an example. Convert the decimal number \((350)_{10}\) to an octal number.

Step 1: Check if the decimal number is less than 8. If yes, the octal number is the same. If no, then proceed forward. In this case, 350 is more than 8 so let's go to step 2.

Step 2: Divide 350 by 8 (octal base number). Note down the quotient and the remainder in the quotient-remainder form. Repeat this process (dividing the quotient again by 8) until we get the quotient to be less than 8.

Step 3: Once we obtain the quotient to be less than 8 we stop dividing to derive at the octal number. The octal number is considered by reading all the remainders and the last quotient from bottom to top.

Therefore, \((350)_{10}\) = \((536)_{8}\).

To convert decimal to octal with a decimal point, we calculate the decimal number in two parts. First, we calculate the integer part of the decimal point by dividing the octal base number i.e. 8 until the quotient is less than 8. The second part is calculated on the fraction part of the decimal number where the number is multiplied with the base number 8 until the fractional part is equal to zero. Here, once multiplied we keep the integer part separate and the fractional part separate. The final octal number is calculated by adding both the integer and the fractional number. Let us look at an example step-wise to understand this better. Convert the decimal number \((29.45)_{10}\) to an octal number.

Step 1: Separate the decimal number into two parts - the integer and the fractional. So, 29.45 = 29 + 0.45.

Step 2: Convert the integer part of the number first. So, we begin with 29 first by dividing it by the base number 8 until the quotient is less than 8.

Hence, 29 is 35 in an octal number.

Step 3: Once the integer octal number is obtained, we proceed to the fractional part. So, 0.45 is multiplied by 8 (octal base number) where the result is again divided into its integer part and fractional part. The number is multiplied by 8 until the fractional part is equal to zero.

Write all the integer part from top to bottom that derives the octal number of the fractional number. Hence, 0.45 = 0.3463146.

Step 4: Add both the integer and the fractional part together to obtain the octal number. Hence, 35 + 0.3463146 = 35.3463146.

Therefore, \((29.45)_{10}\) = \((35.3463146)_{8}\).

Related Topics

Here are a few topics related to decimal to octal, do take a look!

• Decimal to Binary Calculator
• Decimal to Binary Formula
• Hexadecimal to Decimal
• Decimal to Hexadecimal Conversion Formula

How do you Convert from Decimal to Octal?

There are two methods to convert decimal to octal numbers. The first is by direct conversion where the decimal number is divided by the octal base number which is 8 until the quotient is less than 8. The final octal number is obtained by arranging the remainder and the last quotient from the bottom to the top. The second method to convert decimal to octal is by converting the decimal number to another number system i.e binary or hexadecimal then converting that number to an octal number.

What is Decimal to Octal Conversion?

Decimal to octal conversion helps in determining the equivalent of another number in the number system. The number system has four types: binary number system, octal number system, decimal number system, and hexadecimal number system. Each of these number types has its own base numbers. Decimal to octal conversion is based on their base numbers.

• Binary number system (Base - 2)
• Octal number system (Base - 8)
• Decimal number system (Base - 10)
• Hexadecimal number system (Base - 16)

What is a Decimal Equivalent of 12 in Octal?

To convert decimal to octal, we start by dividing 12 by the octal base number 8. Here are the steps,

• 12/8 = 1 as the quotient and 4 as the remainder
• 1/8 = 0 as the quotient and 1 as the remainder

Therefore, \((12)_{10}\) = \((14)_{8}\).

How to Convert Decimal to Octal With Decimal Point?

To convert decimal to octal with a decimal point we need to break the decimal number into two parts i.e. integer part and fractional part. The conversion begins with the integer part first by dividing the number by 8 until the quotient is less than 8. Keep aside the result and move ahead to the fractional part. The fractional part will be multiplied by 8 until the result is equal to zero. The integer part and the fractional part will be kept separately again here. The answer will be the integer part counted from top to bottom. The final number is obtained by adding the integer and the fractional part.

Can We Convert \((21.4)_{10}\) from Decimal to Octal?

To convert the decimal number 21.4 to octal here are the steps:

Step 1: Break 21.4 into the integer part and fractional part i.e. 21 and 0.4.

Step 2: Begin dividing 21 by 8. Hence, 21 = 25 in octal number.

Step 3: Multiply 0.4 with 8. Hence, 0.4 = 0.3146

Step 4: Therefore, \((21.4)_{10}\) = \((25.3146)_{8}\) (25 + 0.3146 = 25.3146)

What is the Formula to Convert a Number From Decimal to Octal?

The formula to convert a decimal to octal is mentioned below:

• Divide the number by 8 (octal base number) until the quotient is less than 8.
• Once the number the obtained, write the remainder of each of the numbers in reverse.
• The reversed remainder is the final octal number of the decimal number.