Octal Numbers Subtraction Solved Examples

Octal Subtraction Examples

This is my second article on octal number system arithmetic. In this post I will explain octal numbers subtraction. You can check my article on octal addition.

Key Questions

How to perform subtraction in octal number system?
How to perform fractional octal subtraction?
How to perform octal subtraction using 8's complement?

Octal Number System Subtraction Examples:

Method#1: Minuend>Subtrahend

This is the method we used to do in elementary mathematics. All the rules we follow remains same as we do in other number systems. Borrow is equal to the base of number system. If you are working with base 2 you borrow 2. If you are working with base 8 you borrow 8. You can verify your results by using this online calculator.

Example#01: 345)8-146)8

2 3 8

3 4 5

-1 4 6

1 7 7

1st column (units column) subtraction. 5-6

This is not possible. You have to borrow from tens column. The number you borrow is 8. So units column subtraction is 5+8-6

2nd column (tens column) subtraction. 4 becomes 3 after borrow. 3-4. To proceed this subtraction you have to borrow from hundreds column. So tens column subtraction is 3+8-4

Answer:177)8

Example#02:757.76)8-451.77)8

6 6 8

7 5 7 . 7 6

-4 5 1 . 7 7

3 0 5 . 7 7

Start from hundredths column subtraction.

6-7. To proceed this calculation borrow from tenths column. 8+6-7=7

Tenths column subtraction. After borrow 7 becomes 6. 6-7 not possible. To proceed this calculation borrow from units column. 8+6-7=7

Answer: 305.77)8

Example#03:565.67)8-234.34)8

5 6 5 . 6 7

-2 3 4 . 3 4

3 3 1 . 3 3

Answer: 331.33)8

Method#2: Minuend<Subtrahend

This method is same as I discussed in binary subtraction. This method is also valid for Minuend>subtrahend the 8’s complement of subtrahend and add it to minuend.

Minuend-subtrahend=difference

Minuend+[8’s complement]=difference

There are three steps to follow

Take 8’s complement of the subtrahend
Add minuend and subtrahend
If carry is produced in the addition discard it. Otherwise 8’s complement of the answer and assign negative sign

Example#1:257)8-765)8

8’s complement of subtrahend=013)8.

2 5 7

+0 1 3

2 7 2

Take 8’s complement of the sum and assign negative sign

8’s complement of sum= 506)8

Answer: -506)8

Example#2:675)8-722)8

8’s complement of subtrahend=056)8

1 1

6 7 5

+0 5 6

7 5 3

8’s complement of the sum= 025)8

Answer: -25)8

Example#01: 345)8-146)8

8’s complement of the subtrahend=632)8

3 4 5

+6 3 2

1 1 7 7

Diacard carry.

Answer: 177)8

Example#04:757.76)8-451.77)8

8’s complement of the subtrahend=326.01)8

1 1

7 5 7 . 7 6

+3 2 6 . 0 1

1 3 0 5 . 7 7

Discard carry.

Answer: 305.77)8

Example#03:565.67)8-234.34)8

8’s complement of the subtrahend=543.44)8

1 1 1 1

5 6 5 . 6 7

+5 4 3 . 4 4

1 3 3 1 . 3 3

Discard carry.

Answer: 331.33)8

Octal Addition Solved Examples

Octal Numbers Addition 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

4 ← remainder as sub-sum

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

1← quotient as carry

8⟌13

5 ← remainder as sub-sum

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

1← quotient as carry

8⟌9

1 ← remainder as sub-sum

Answer: 1154)8

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

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

5 ← remainder as sub-sum

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

1 ← quotient as carry

8⟌10

2 ← remainder as sub-sum

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

Answer: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

+	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

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

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

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.