Conversions - Decimal and Octal
 

Octal to Decimal Conversion
To convert from Octal to Decimal, multiply the value in each position by its Octal weight and add each value.

 

Example 127662
























1*85 2*84 7*83 6*82 6*81 2*80
1*32768 2*4096 7*512 6*64 6*8 2*1
32768 8192 3584 384 48 2

 

32768 + 8192 + 3584 + 384 + 48 + 2 = 44978

 

Decimal to Octal Conversion
To convert decimal to octal is slightly more difficult. The typical method to convert from decimal to octal is repeated division by 8.

For this method, divide the decimal number by 8, and write the remainder on the side as the least significant digit. This process is continued by dividing he quotient by 8 and writing the remainder until the quotient is 0.

When performing the division, the remainders which will represent the octal equivalent of the decimal number are written beginning at the least significant digit (right) and each new digit is written to the next more significant digit (the left) of the previous digit.

Consider the number 44978.

 







































Division Quotient Remainder Octal Number
44978 / 8 5622 2 2
5622 / 8 702 6 62
702 / 8 87 6 662
87 / 8 10 7 7662
10 / 8 1 2 27662
1 / 8 0 1 127662

 

As you can see, we are back with the original number. That is what we should expect.

 

 

 

 

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