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Decimal number:

255

Octal to Decimal Conversion

(377)_{8} = (255)_{10}

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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.

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

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 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 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.

Convert the octal number 647 to decimal.

- Identify the digits of the octal number: 6, 4, and 7.
- 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

- 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:

Octal | Decimal |
---|---|

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

10 | 8 |

11 | 9 |

12 | 10 |

13 | 11 |

14 | 12 |

15 | 13 |

16 | 14 |

17 | 15 |

20 | 16 |

21 | 17 |

22 | 18 |

23 | 19 |

24 | 20 |

25 | 21 |

26 | 22 |

27 | 23 |

30 | 24 |

31 | 25 |

32 | 26 |

33 | 27 |

34 | 28 |

35 | 29 |

36 | 30 |

37 | 31 |

40 | 32 |

41 | 33 |

42 | 34 |

43 | 35 |

44 | 36 |

45 | 37 |

46 | 38 |

47 | 39 |

50 | 40 |

51 | 41 |

52 | 42 |

53 | 43 |

54 | 44 |

55 | 45 |

56 | 46 |

57 | 47 |

60 | 48 |

61 | 49 |

62 | 50 |

63 | 51 |

64 | 52 |

65 | 53 |

66 | 54 |

67 | 55 |

70 | 56 |

71 | 57 |

72 | 58 |

73 | 59 |

74 | 60 |

75 | 61 |

76 | 62 |

77 | 63 |

100 | 64 |

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.

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.

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.

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

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.

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.

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

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

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.