Octal to Decimal Conversion



Octal to Decimal Conversion

The conversion of an octal number to its equivalent decimal number is same as the binary to decimal conversion. To convert an octal number to its decimal equivalent, we multiply each digit of the octal number by its positional weight and then add all the product terms to obtain the equivalent decimal number.

The step-by-step procedure to convert an octal number to its equivalent decimal number is given below −

Step 1 − Write the positional weights for each octal digit.

Step 2 − Multiply each octal digit with its positional weight.

Step 3 − Add the product terms to obtain the equivalent decimal number.

Let us understand the conversion of octal number to decimal number with the help of examples.

Example 1

Convert (356.25)8 to its decimal equivalent.

Solution

The given octal number can be converted to equivalent decimal number as follows −

Octal Digits Positional Weights Multiply Product
3 (8)2 3 × (8)2 192
5 (8)1 5 × (8)1 40
6 (8)0 6 × (8)0 6
. . . .
2 (8)-1 2 × (8)-1 0.25
5 (8)-2 5 × (8)-2 0.078

Adding all the product terms to obtain the equivalent decimal number,

(356.25)8 = 192 + 40 + 6 + 0.25 + 0.078 = (238.328)10

Example 2

Convert (527.322)8 to its decimal equivalent.

Solution

We can convert the given octal number to its equivalent decimal number as follows −

Octal Digits Positional Weights Multiply Product
5 (8)2 5 × (8)2 320
2 (8)1 2 × (8)1 16
7 (8)0 7 × (8)0 7
. . . .
3 (8)-1 3 × (8)-1 0.375
2 (8)-2 2 × (8)-2 0.0313
2 (8)-3 2 × (8)-3 0.004

Add all the product terms to obtain the result,

(527.322)8 = 320 + 16 + 7 + 0.375 + 0.0313 + 0.004 = (343.4103)10

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