Page 13 - Digital Electronics by harish

Octal to decimal conversion

i) Integer numbers

The given octal number can be converted to decimal number by using the following
procedure:

Step 1 : Write the octal number
Step 2 : Write the place value (weight) directly under the octal number
Step 3 : Multiply the octal number by the place value
Step 4 : Add the values to get the decimal number.

Example: To convert the octal number 257 to decimal number

Step 1 : 2 5 7 (Octal number)
Step 2 : 64 8 1 (Place value)
Step 3 : 128 40 7 (Multiply)
Step 4 : 175 (Add, to get the Decimal number)

Therefore, 257 8 = 175 10

ii) Fractional numbers

The same procedure used for the integer numbers can be used for fractional numbers also.

Example: To convert the octal number 0.41 to decimal number

Step 1 : 4 1 (Octal number)
Step 2 : 0.125 0.015625 (Place value)
Step 3 : 0.5 0.015625 (Multiply)
Step 4 : 0.515625175 (Add, to get the Decimal number)

Therefore, 0.41 8 = 0.515625175 10

Octal to binary conversion

The following procedure can be used for converting the octal number to binary number:

Step 1 : Write the octal number
Step 2 : Write the three digit equivalent binary number

Example: To convert the octal number 34.56 to binary number

Step 1 : 3 4 . 5 6 (Octal number)
Step 2 : 011 100 . 101 110 (Binary equivalent)

Therefore, 34.56 8 = 11100.10111 2

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