Table of Contents

Last modified on March 28th, 2023

‘Octal’ means eight. The octal number system uses numbers from 0 to 7. The octal number represents numbers with 8 as the base.

Since the octal system uses only 0 to 7, we can memorize the decimal equivalents for each octal number by referring to the **octal to the decimal table**. The conversion chart is tabulated below.

Octal (Base 8) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 20 | 30 | 40 | 50 | 60 | 70 | 100 |

Decimal (Base 10) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 24 | 32 | 40 | 48 | 56 | 64 |

Converting an octal number to a decimal number means changing it to its decimal equivalent. We can do it in two different ways.

The formula for decimal to octal is:

Decimal number_{10} = (d_{0} × 8^{0}) + (d_{1} × 8^{1}) + … + (d_{r – 1 }× 8^{n – 1})

Here, n = number of digits, r = place of the digit

Let us take the number 1725.43 to convert it to octal using the above formula. The fractional part is .43. It will be easier to demonstrate how we can convert a number having a fractional part from octal to decimal.

Let us summarize the steps for the standard method of the converting octal to decimal:

- Let us summarize the steps for the standard method of converting octal to decimal:
- Let a digit have the n
^{th}position from right to left in the given octal number. So, the position of each digit has an increasing power of 8 from right to left. - Multiply each digit with 8
^{n-1}, where n = position of each digit. - Add each value from the multiplication. The final result after addition will be the decimal equivalent of the octal number given.

**Convert the number 362 from octal to decimal.**

Solution:

362 = (3 × 8^{2}) + (6 × 8^{1}) + (2 × 8^{0}) = 242

∴(362)_{8} = (242)_{10}

**(245.54) _{8} = (?)_{10}**

Solution:

245.54 = (2 × 8²) + (4 × 8¹) + (5 × 8⁰) + (5 × 8⁻¹) + (4 × 8⁻²) = 165.6875

∴ (245.54)_{8} = (165.6875)_{10}

Using an **Alternative Method** to convert **OCTAL TO DECIMAL**

**Convert 2676 from octal to decimal.**

Solution:

Here the most significant digit is 2. So we will focus on removing the significant digits from left to right until we reach the last digit.

∴(2676)_{8} =

0 + 2 = 2 (removing 2)

2 × 8 = 16

16 + 6 = 22 (removing 6)

22 × 8 = 176

176 + 7 = 183 (removing 7)

183 × 8 = 1464

1464 + 6 = 1470 (6 is the last significant digit. So we stop the process here and consider the final result as the decimal equivalent)

Hence, (2676)_{8} = (1470)_{10}

**Convert 561 from octal to decimal using the alternative method.**

Solution:

0 + 5 = 5

5 × 8 = 40

40 + 6 = 46

46 × 8 = 368

368 + 1 = 369

∴(561)_{8}= (369)_{10}

Last modified on March 28th, 2023