How to convert octal to decimal? Step by step guide

How to convert octal to decimal?

Octal to Decimal conversion is also like other numbers conversions such as decimal to octal, octal to hexadecimal, octal to binary and so on. An octal to decimal conversion is carried out when an octal number with a base of 8 needs to be transformed into a decimal number with a base of 10. We'll learn more on conversion methods and figure out some examples to help us understand.

What is Octal to Decimal Conversion?

If we want to know the equivalent of a number in the numbering system Octal to decimal conversion will take place. There are four types of number system in the form of Binary, Octal, Decimal and Hexadecimal numbers. Each number scheme has its own basic numbers which help you to determine the type of number it is. The octal to digit conversion is assisted by those base numbers. For octal base number is 8 and for decimal numbers it's 10.

What is Octal Number System?

The Octal Number System is a system of numbers with a base of 8 and uses digits from 0 to 7. The numbers with eights as the base are represented in octal. The octal number has many uses such as being used by computers and digital numbering systems. Octal numbers can be converted to binary, decimal, and hexadecimal numbers in the number system. Some of examples of octal numbers are (63)₈, (245)₈. Octal numbers are represented using powers of 8. For example (367)₈ can be expressed as 3 × 8² + 6 × 8¹ + 7 × 8⁰.

What is Decimal Number System?

A decimal number system is called a number system with a base of 10 and uses ten digits 0,1,2,3,4,5,6,7,8 and 9. We generally use decimal system to represent numbers in real life. If a number is represented without a base it means that its base is 10. For example 123₁₀, 892₉₁₀ and 5674₁₀ are some instances of numbers in decimal number system.

How to Convert Octal to Decimal step by step:

The octal to decimal conversion is also done using the base number as with any other conversion in number system. For converting octal to decimal we need to multiply octal numbers with power of 8 starting from the right hand side and gradually decreasing to zero to sum up all products. The steps for converting a number from octal to decimal are listed below:

• Step 1: Since octal numbers are composed of digits from 0 to 7 we first draw an octal number with 8 power.
• Step 2: We're going to evaluate power of 8 values like 80 is 1, 81 is 8, etc. and write down value of each octal number. 
• Step 3: We multiply each number as soon as value is obtained. 
• Step 4: In order to obtain decimal number product of all the numbers must be added.

Examples of Octal to Decimal Conversion

Let's consider octal number (256)₈ and we are going to convert it into a decimal number.

Step 1: Write 256 with the powers of 8 starting from right hand side.

2 × 8² + 5 × 8¹ + 6 × 8⁰

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

8² = 64, 8¹ = 8, 8⁰ = 1

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

2 × 64 + 5 × 8 + 6 × 1 = 128 + 40 + 6

Step 4: Add values to obtain decimal number.

128 + 40 + 6 = 174.

Therefore (256)₈ = (174)₁₀.

Let us take another example convert (347)₈ into a decimal number by following same steps.

Step 1: Write 347 with the powers of 8.

3 × 8² + 4 × 8¹ + 7 × 8⁰

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

8² = 64, 8¹ = 8, 8⁰ = 1

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

3 × 64 + 4 × 8 + 7 × 1 = 192 + 32 + 7

Step 4: Add the values to obtain decimal number.

192 + 32 + 7 = 231.

Therefore, (347)₈ = (231)₁₀.

Another example let's convert (53)₈ into a decimal number.

Step 1: Write 53 with powers of 8.

5 × 8¹ + 3 × 8⁰

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

8¹ = 8, 8⁰ = 1

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

5 × 8 + 3 × 1 = 40 + 3

Step 4: Add values to obtain decimal number.

40 + 3 = 43.

Therefore, (53)₈ = (43)₁₀.

How to Convert Octal to Decimal with Decimal Point?

We must follow same procedure as in previous section to convert octal to decimal number with decimal point. After the decimal point however, power or exponent of 8 will change. The exponents after decimal point will decrease or be negative as we move to right hand side with exponents increasing.

Conclusion

It is an essential skill to understand how octal can be converted into a Decimal when dealing with various numbers systems. It is possible to convert October numbers based on a system of eight digits into decimals with bases of ten. The conversion involves systematic multiplication of each octal digit by corresponding power of 8 and sum of products. This procedure provides an easy way of expressing octal values in a decimal format.
We have been able to gain an insight into the process of converting octal numbers and illustrate how 8 values can be used to convert octal numbers for their decimal equivalents thanks to our step by step guide and examples. It is possible for anyone to convert octal numbers to decimals by following specified steps such as evaluation of powers of 8 and necessary multiplications.