Octal To Decimal Converter

8
10

How to convert an octal number to decimal

To convert octal to decimal, multiply each octal digit by the matching power of 8, then add the results together. The rightmost whole-number digit uses 80, the next uses 81, and so on: Convert each octal digit to its decimal equivalent and multiply it by the corresponding positional value. Sum up these products to obtain the decimal equivalent of the entire octal number. This method provides a clear step-by-step approach for manual conversion, allowing for a better understanding of the positional values associated with each octal digit.

For each octal digit d, n is the position of that digit:

dn-1 .... d4 d3 d3 d2 d1 d0 . d-1 d-2 d-3

The decimal number is equal to the sum of octal digits (dn) times their power of (8n):

decimal = dn-1 x 8n-1 + .... + d1 x 81 + d0 x 80 + d-1 x 8-1 + .... + d-n x 8-n

Octal to Decimal Conversion

Example of octal to decimal conversion.

Convert (57.62)8 to decimal.

octal number: 5 7 . 6 2
power of 8: 81 80   8-1 8-2

(57.62)8= (?) 10
= 5 x 81 + 7 x 80 + 6 x 8-1 + 2 x 8-2
= 40 + 7 + 0.75 + 0.03125
= (47.78125)10

Binary to decimal conversion table:

Octal Decimal
0 0
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

Octal to decimal guide

Octal to decimal conversion uses powers of 8. Multiply each octal digit by the matching power of 8, then add the results.

Best uses

  • Translate base-8 values into ordinary decimal numbers.
  • Check programming or file-permission examples.
  • Practice positional number systems.

Quality checks

  • Start the rightmost whole-number digit at 8^0.
  • Move left with 8^1, 8^2, and so on.
  • Reject digits 8 and 9 because they are not octal digits.

Common mistakes

  • Treating octal digits as base-10 place values.
  • Starting the rightmost power at 8^1.
  • Using invalid digits such as 8 or 9.

Quick answers

What is 322 octal in decimal?

322 in octal equals 210 in decimal because it is 3x64 + 2x8 + 2.

Why is the rightmost digit multiplied by 1?

Any base raised to the power 0 equals 1, so the rightmost whole-number place is 8^0.