# Octal to Decimal

## Converting octal to decimal is a simple yet powerful concept that can make all the difference in technical fields.

Have you ever wondered what octal numbers are and how they relate to the decimal system? Octal numbers, which use a base of 8, are used in computer programming and other technical fields. Octal to decimal conversion takes place when we want to know the equivalent of a number in the number system. In this article, we will delve deeper into the concept of octal to decimal conversion and solve some examples to make it easier to understand.

## What is Octal Number System?

Octal is a number system that uses a base of 8, unlike the decimal system that uses a base of 10. In the octal system, we use 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. The place values of the digits in the octal system are as follows:

Octal place values: 8^0, 8^1, 8^2, 8^3, and so on.

For instance, the number 234 in the octal system can be represented as follows:

2 x 8^2 + 3 x 8^1 + 4 x 8^0 = 128 + 24 + 4 = 156

## What is Decimal Number System?

Decimal is a number system that uses a base of 10, and it is the most commonly used system in our daily life. In the decimal system, we use 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The place values of the digits in the decimal system are as follows:

Decimal place values: 10^0, 10^1, 10^2, 10^3, and so on.

For instance, the number 234 in the decimal system can be represented as follows:

2 x 10^2 + 3 x 10^1 + 4 x 10^0 = 200 + 30 + 4 = 234

## Octal to Decimal Conversion

To convert a number from octal to decimal, we need to multiply each digit of the octal number by the corresponding power of 8 and then add up the results.

Let's consider an example: Convert octal number 345 to decimal.

3 x 8^2 + 4 x 8^1 + 5 x 8^0 = 192 + 32 + 5 = 229

Therefore, the decimal equivalent of octal number 345 is 229.

It is important to note that when the octal number contains a decimal point, we use the same formula for the whole part of the number, and then add the decimal part as follows:

Example: Convert octal number 34.72 to decimal.

3 x 8^1 + 4 x 8^0 = 24 + 4 = 28

0 x 8^-1 + 7 x 8^-2 + 2 x 8^-3 = 0 + 0.0859375 + 0.015625 = 0.1015625

34.72 (octal) = 28.1015625 (decimal)

## Octal to Decimal Conversion Chart

For convenience, you can use a chart to convert octal numbers to decimal numbers quickly. The chart lists the octal digits from 0 to 7 and their decimal equivalents.

Octal Decimal 0 0 1 1 2 2 3 3 4 4 5 5 6 6

## Solving Examples

Now that we understand the concept of octal to decimal conversion, let's solve some examples to solidify our understanding.

### Example 1: Convert octal number 123 to decimal.

1 x 8^2 + 2 x 8^1 + 3 x 8^0 = 64 + 16 + 3 = 83

Therefore, the decimal equivalent of octal number 123 is 83.

### Example 2: Convert octal number 763 to decimal.

7 x 8^2 + 6 x 8^1 + 3 x 8^0 = 448 + 48 + 3 = 499

Therefore, the decimal equivalent of octal number 763 is 499.

### Example 3: Convert octal number 56.72 to decimal.

5 x 8^1 + 6 x 8^0 = 40 + 6 = 46

7 x 8^-1 + 2 x 8^-2 = 0.875 + 0.03125 = 0.90625

56.72 (octal) = 46.90625 (decimal)

Therefore, the decimal equivalent of octal number 56.72 is 46.90625.

In conclusion, octal to decimal conversion is a useful concept in computer programming and other technical fields. To convert an octal number to a decimal number, we need to multiply each digit of the octal number by the corresponding power of 8 and then add up the results. We can also use a chart for quick conversion. By solving examples, we can understand the concept better and apply it to real-world problems. Therefore, understanding octal to decimal conversion is crucial for those working in technical fields.

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