How to Convert Octal to Binary

"Octal" and "binary" are both expressions of the base for a counting system. Counting base describes the number at which a system adds a second digit. For example our current counting system adds a second digit at 10 and is thus described as a base ten, or "Decimal" counting system. Octal is a base 8 system and binary is a base 2 system. People convert octal to binary either to simplify computer programming or as an exercise in number theory. In both cases, it's easiest to convert the octal to decimal, then the decimal to binary.

Instructions

Octal to Decimal

1. Multiply the last digit of the octal number by one (8 to the zeroth power). In this and the following steps, write down the result in a column.

2. Multiply the second to last digit of the octal number by 8 (8 to the first power).

3. Multiply the third to last digit of the octal number by 64 (eight to the second power).

4. Multiply the fourth to last digit of the octal number by 512 (8 to the third power).

5. Continue applying this pattern until you have processed the entire number.

6. Add the results from each step. The total is the octal number expressed as a decimal.

Decimal to Binary

1. Follow the steps below, writing down the remainders for each step in a row from right to left.

2. Divide the total from section 1, step 6, by two. Note the remainder.

3. Divide the result of step 1 by two. Note the remainder.

4. Divide the result of step 2 by two. Note the remainder.

5. Continue the pattern until you reach the answer 0. Note the remainder.

6. The string of 1s and 0s you wrote, following directions from step one, is the binary version of your decimal number.

Tips & Warnings

• Example: Octal number 1234.

• Converting Octal to Decimal

• 1*4=4, 3*8=24, 2*64=128, 1*512=512. Octal 1234= Decimal (512+128+24+1=)665

• Converting Decimal to Binary

• 665/2=332, remainder 1

• 332/2=166, remainder 0

• 166/2=83, remainder 0

• 83/2=41, remainder 1

• 41/2=20, remainder 1

• 20/2=10, remainder 0

• 10/2=5, remainder 0

• 5/2=2, remainder 1

• 2/2=1, remainder 0

• 1/2=0, remainder 1

• Decimal 665= Binary 1010011001

• Thus, Octal 1234=Binary 1010011001

References

• Evergreen College: Converting Between Integer Representation