# Octal to Decimal Converter

### Enter a Octal Number

Decimal number:

255

Octal to Decimal Conversion

(377)8 = (255)10

Please enter all the details correctly.

Octal and decimal are two different numeral systems used in computing and programming. Sometimes, it’s necessary to convert numbers from one system to the other. In this article, we’ll discuss how to convert from octal to decimal.

## Understanding Octal and Decimal

Before we dive into the process of converting from octal to decimal, let’s review what these numeral systems are.

### Octal

Octal is a base-8 numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit in an octal number represents a power of 8. For example, the octal number 173 can be broken down as:

• 3 x 8^0 = 3
• 7 x 8^1 = 56
• 1 x 8^2 = 64

When we add these values together, we get the decimal equivalent of 123.

### Decimal

Decimal is a base-10 numeral system that uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit in a decimal number represents a power of 10. For example, the decimal number 123 can be broken down as:

• 3 x 10^0 = 3
• 2 x 10^1 = 20
• 1 x 10^2 = 100

When we add these values together, we get 123.

## Converting from Octal to Decimal

Converting from octal to decimal is a straightforward process. Each digit in the octal number is multiplied by 8 raised to a power that corresponds to its position in the number. Then, the results are added together to get the decimal equivalent.

Let’s work through an example to illustrate the process.

### Example

Convert the octal number 647 to decimal.

1. Identify the digits of the octal number: 6, 4, and 7.
2. Assign a power of 8 to each digit, starting with 8^0 for the rightmost digit and increasing by 1 for each digit to the left. In this case, we have:
• 7 x 8^0 = 7
• 4 x 8^1 = 32
• 6 x 8^2 = 384
1. Add the results together: 7 + 32 + 384 = 423.

Therefore, the octal number 647 is equivalent to the decimal number 423.

Here’s a table showing the decimal equivalent of octal numbers from 1 to 100:

OctalDecimal
11
22
33
44
55
66
77
108
119
1210
1311
1412
1513
1614
1715
2016
2117
2218
2319
2420
2521
2622
2723
3024
3125
3226
3327
3428
3529
3630
3731
4032
4133
4234
4335
4436
4537
4638
4739
5040
5141
5242
5343
5444
5545
5646
5747
6048
6149
6250
6351
6452
6553
6654
6755
7056
7157
7258
7359
7460
7561
7662
7763
10064

Converting from octal to decimal is a simple process that involves multiplying each digit by the appropriate power of 8 and then adding the results together. This skill is useful for programmers and computer scientists who work with different numeral systems. With a little practice, you’ll be able to convert between octal and decimal numbers quickly and easily.

## FAQs

### What is the difference between octal and decimal?

Octal is a base-8 numeral system that uses eight digits to represent numbers, while decimal is a base-10 numeral system that uses ten digits to represent numbers.

### Why are octal numbers used in computing?

Octal numbers are used in computing because they can be easily converted to binary (base-2) numbers, which are used by computers to represent data.

### Can decimal numbers be converted to octal numbers?

Yes, decimal numbers can be converted to octal numbers using a similar process to the one used to convert octal numbers to decimal

### What is the purpose of converting between numeral systems?

Converting between numeral systems is useful for programmers and computer scientists who work with different numeral systems. It allows them to represent data in a more compact or efficient way.

### Is it possible to convert from octal to other numeral systems?

Yes, it’s possible to convert from octal to other numeral systems, such as binary or hexadecimal, by first converting to decimal and then to the desired system.

### How can I check my work when converting from octal to decimal?

To check your work, you can convert the decimal number back to octal and see if it matches the original octal number.

### Can I use a calculator to convert from octal to decimal?

Yes, most calculators have a function to convert between numeral systems, including octal and decimal.

### Are there any other numeral systems used in computing?

Yes, there are several other numeral systems used in computing, including binary (base-2), hexadecimal (base-16), and base-64. Each system has its own advantages and disadvantages, depending on the specific application.