Octal Addition Solved Examples

This is my first article on octal arithmetic. In this post I am going to explain the two different methods of adding octal numbers.

Key Questions:

• How to perform addition in octal number system?
• How to perform fractional octal numbers addition?
• Draw octal addition table
• Discuss two methods of octal addition

Octal Numbers Addition Technique:

There are two methods of adding octal numbers. I will solve each example by using methods for better understanding. You can check your results using this online calculator for octal addition.

Method#1:

In this method you should remember these points:

• Think each number as a decimal number and add them as decimal numbers.
• After adding each column if the sum of a column exceeds to 7 divide the result by 8 to evaluate equivalent octal value.
• The remainder is going to be the part of the answer (sub-sum) while the quotient is going to become carry

Example#01: 167)8+765)8

    1  1                                    

    1 6 7

  +7 6 5

1 1 5  4

 

Remember the first step. Think each number as a decimal number and add them as a decimal numbers.

1st column (units column) addition 7+5=12

    1 ← quotient as carry

8  ⟌12  

        8

        4 ← remainder as sub-sum

2nd column (tens column) addition 1+6+6=13

   1← quotient as carry

8⟌13

      8

      5 ← remainder as sub-sum

3rd column (hundreds column) addition 1+1+7=9

   1← quotient as carry

8⟌9

      8

      1 ← remainder as sub-sum

Answer: 1154)8

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Example#02: 123)8+7651)8

          1 2 3

 +7 6 5 1

  7  7  7 4

In this example after adding each column no sub-sum exceeds to 7. So there is no need of converting equivalent octal value.

Answer: 7774)8

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Example:03:246.57)8+357.1)8

     1   1

  2 4 6 . 5 7

+3 5 7 . 1

  6 2 5 . 6 7

The columns after octal points don't need extra calculation.

1st column (units column) addition 6+7=13

 1 ← quotient as carry

8⟌13

       8

       5 ← remainder as sub-sum

2nd column (tens column) addition 4+5+1=9

 1 ← quotient as carry

8⟌10

      8

      2 ← remainder as sub-sum

3rd column (hundreds column) addition don't exceeds to 7. No need of extra calculation.

Answer:625.67)8

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Method#2:

In this method octal addition table is given. How this table is helpful in addition of octal numbers. Let's understand.

• Look at first row (red colored row), you can call it as X
• Look at first column (blue colored column) , you can call it as Y
• The rest of the table is black. This is the sum of X and Y

+	0	1	2	3	4	5	6	7
0	0	1	2	3	4	5	6	7
1	1	2	3	4	5	6	7	10
2	2	3	4	5	6	7	10	11
3	3	4	5	6	7	10	11	12
4	4	5	6	7	10	11	12	13
5	5	6	7	10	11	12	13	14
6	6	7	10	11	12	13	14	15
7	7	10	11	12	13	14	15	16

For example 23)8+45)8

   1

   2 3

 +4 5

  7  0

First you have to add 1st column numbers. Assign X=3, Y=5. Search in table you will get your result. The intersection of column 3 and row 5 is your answer.

For 2nd column again assign X=2+1 Y=4

The intersection of column 3 and row 4 is your answer.

Example#01: 167)8+765)8

   1  1                                    

    1 6 7

  +7 6 5

1 1 5  4

1st column addition X=7 Y=5

2nd column addition X=6+1 Y=6

3rd column addition X=1+1 Y=7

Answer: 1154)8

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Example#02: 123)8+7651)8

          1 2 3

 +7 6 5 1

  7  7  7 4

1st column addition X=3 Y=1

2nd column addition X=2 Y=5

3rd column addition X=1 Y=6

4th column addition X=0 Y=7

Answer 7774)8

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Example:03:246.57)8+357.1)8

     1   1

  2 4 6 . 5 7

+3 5 7 . 1

  6 2 5 . 6 7

Consider columns after octal point.

Hundredth column addition X=7 Y=0

Tenth column addition X=5 Y=1

Units column addition X=6 Y=7

Tens column addition X=4+1 Y=5

Hundreds column addition X= 2+1 Y=3

Answer :625.67)8

Conclusion:

So this is all about octal addition. I used both methods for calculation. This is simple and easy task. I rechecked and verified all the answers in this post. If you still find any mistake, please inform me. If you have suggestions I will be grateful to you.