Octal to Decimal

Octal to Decimal conversion is just like the other conversions in the number system such as decimal to octal, octal to hexadecimal, octal to binary, and so on. Octal to decimal conversion occurs when an octal number with the base of 8 has to be converted to a decimal number with the base of 10. Let us learn more about the conversion methods and solve a few examples for a better understanding.

Octal to decimal conversion takes place when we want to know the equivalent of a number in the number system. The number system is of four types - Binary number system, Octal number system, Decimal number system, and Hexadecimal number system. Each number system has its own base numbers that help in identifying which type of number it is. These base numbers also help in the octal to decimal conversion. The base number for octal numbers is 8 and the base number for decimal numbers is 10.

Octal Number System

A number system with its base as 8 and uses digits from 0 to 7 is called Octal Number System. The word octal is used to represent the numbers that have eight as the base. The octal numbers have many applications and importance such as it is used in computers and digital numbering systems. In the number system, octal numbers can be converted to binary numbers, decimal numbers, and to hexadecimal numbers. Some of the examples of octal numbers are \((47)_{8}\), \((120)_{8}\). The octal numbers are represented with a power of 8. For example: \((547)_{8}\) = 5 × 8² + 4 × 8¹ + 7 × 8⁰.

Decimal Number System

The number system with its base as 10 and uses ten digits: 0,1,2,3,4,5,6,7,8 and 9 are called decimal number system. The decimal number system is the system that we generally use to represent numbers in real life. If any number is represented without a base, it means that its base is 10. For example: \(65_{10}, 687_{10}, 4198_{10}\) are some examples of numbers in the decimal number system.

As with any other conversion in the number system, octal to decimal conversion is also done by using its base number. To convert octal to decimal, we need to multiply the octal digits with the power of 8 starting from the right-hand side and gradually decreasing to zero to sum up, all the products. Here are the steps to convert a number from octal to decimal:

• Step 1: Since an octal number only uses digits from 0 to 7, we first arrange the octal number with the power of 8.
• Step 2: We evaluate all the power of 8 values such as 8⁰ is 1, 8¹ is 8, etc., and write down the value of each octal number.
• Step 3: Once the value is obtained, we multiply each number.
• Step 4: Final step is to add the product of all the numbers to obtain the decimal number.

Let us look at an example, convert \((140)_{8}\) into a decimal number.

Step 1: Write 140 with the power of 8. Start from the right-hand side.

1 × 8² + 4 × 8¹ + 0 × 8⁰

Step 2: Evaluate the power of 8 values for each octal number.

8² = 64, 8¹ = 8, 8⁰ = 1

Step 3: Multiply each of the power of 8 numbers with the respective numbers.

1 × 64 + 4 × 8 + 0 × 1 = 64 + 32 + 0

Step 4: Add the values to obtain the decimal number.

64 + 32 + 0 = 96.

Therefore, \((140)_{8}\) = \((96)_{10}\).

To convert octal to decimal number with a decimal point, we need to follow the same procedure as did in the previous section. However, the power or the exponents of 8 will vary after the decimal point. Since we are moving towards the right-hand side with the exponents increasing, the exponents after the decimal point will decrease or be negative. Let us look at an example.

Convert \((246.28)_{8}\) into a decimal number. We will follow the same steps as before.

Step 1: Write 140 with the power of 8. Start from the right-hand side. Here, the power of 8 will be negative after the decimal point.

2 × 8² + 4 × 8¹ + 6 × 8⁰ + 2 × 8^-1 + 8 × 8^-2

Step 2: Evaluate the power of 8 values for each octal number.

8² = 64, 8¹ = 8, 8⁰ = 1, 8^-1 = 1/8, 8^-2 = 1/8² or 1/64

Step 3: Multiply each of the power of 8 numbers with the respective numbers.

2 × 64 + 4 × 8 + 6 × 1 + 2 × 1/8 + 8 × 1/64 = 128 + 32 + 6 + 0.25 + 0.125

Step 4: Add the values to obtain the decimal number.

128 + 32 + 6 + 0.25 + 0.125 = 166.375.

Therefore, \((246.28)_{8}\) = \((166.375)_{10}\).

Related Topics:

Here are a few topics related to the octal to decimal conversion, take a look.

• Multiplication
• Decimal to Octal
• Binary to Decimal Calculator
• Binary to Decimal

What is Octal to Decimal Conversion?

Octal to decimal conversion helps in obtaining the equivalent of a number. Each of the number systems (binary number system, octal number system, decimal number system, and hexadecimal number system) has its own base number through which the conversions are taken place. The octal to decimal conversion uses the base number of 8 which is the octal base number.

How to Convert Octal to Decimal?

Mentioned below are the steps to convert octal to decimal:

• Arrange the octal number with the power of 8.
• Find the value of each of the numbers with exponents i.e. 8⁰ is 1, 8¹ is 8, etc.
• Multiply each number.
• Add the product of all numbers to obtain the decimal number.

What Does the Octal Number 150 Represent in the Decimal System?

The decimal equivalent of 150 is 104 in the decimal system. Here are the steps to reach the answer:

150 = 1 × 8² + 5 × 8¹ + 0 × 8⁰ = 1 x 64 + 5 x 8 + 0 x 1 = 104.

Hence, \((150)_{8}\) = \((104)_{10}\).

What is the Octal Equivalent of 30?

The octal equivalent of 30 is 24 in decimal numbers.

What is the Base Number of the Octal Number System?

The base number of the octal number system is 8 in the number system and uses digits from 0 to 7. The octal numbers have many applications and importance such as it is used in computers and digital numbering systems.

What is the Base Number of the Decimal Number System?

The base number of the decimal number system is 10 and uses ten digits: 0,1,2,3,4,5,6,7,8 and 9. The decimal number system is the system that we generally use to represent numbers in real life.