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: 167₈ + 765₈ Perform Addition in Octal (Base 8)

167₈ + 765₈

     1  1  (Carry)  
       1 6 7  
   +   7 6 5  
  -----------  
     1 1 5 4  

Explanation:

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=1

      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

---

Example#02: 123)₈+7651)₈

    123)₈  
  + 7651)₈  
  --------  
    7774)₈  

Steps

1. Add column by column, starting from the right:
   • 3 + 1 = 4 (no carry).
   • 2 + 5 = 7 (no carry).
   • 1 + 6 = 7 (no carry).
   • 0 (carry from the next digit) + 7 = 7.
2. In this example after adding each column no sub-sum exceeds to 7. So there is no need of converting equivalent octal value.

Answer: 123)₈ + 7651)₈ = 7774)₈

---

Example:03:246.57)₈+357.1)₈

    246.57₈  
  + 357.10₈  
  ------------  
    625.67₈  

Steps:

1. The columns after octal points don’t need extra calculation.
2. Add fractional part (right of the decimal):
   • 7 + 0 = 7 (no carry).
   • 5 + 1 = 6 (no carry).
3. Add whole numbers (left of the decimal):
   • 6 + 7 = 15₁₀ = 7₈, carry 1.
   • 4 + 5 + 1 (carry) = 10₁₀ = 2₈, carry 1.
   • 2 + 3 + 1 (carry) = 6₈ (no carry).

 Units Column 

 6 + 7 = 13 
 1 ← quotient as carry 
 8⟌13 
     8
    ---
    5 ← remainder as sub-sum 

Tens Column 

4 + 5 + 1 = 10  

1 ← Quotient as carry  
   8 ⟌ 10  
       8  
       2 ← Remainder as sub-sum  

Answer: 246.57)₈ + 357.10)₈ = 625.67)₈

---

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   

For example 23)₈+45)₈

    23)₈  
  + 45)₈  
  --------  
    70)₈  

Steps:

• Look at the table (octal addition table)
• First you have to add 1st column (units 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.

Answer: 23)₈ + 45)₈ = 70)₈

---

Example#01: 167)₈+765)₈

  
    167)₈  
  + 765)₈  
  --------  
   1154)₈  

Steps:

• 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

---

Example#02: 123)₈ + 7651)₈  

       0123₈  
    + 7651₈  
    --------  
      7774₈ 

Steps:

• 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: 123)₈ + 7651)₈ = 7774)₈

---

Example#03: 246.57)₈+357.1)₈

  
    246.57₈  
  + 357.10₈  
  -----------  
    625.67₈  

Steps:

• 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 : 246.57)₈+357.1)₈ = 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.