About Lesson
Addition of Octal Numbers
The addition of octal numbers is carried out by the same principle as that of decimal or binary numbers.
An addition table for octal numbers is given below:
+ | 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 |
With the help of this table addition of octal numbers is best illustrated by the following examples:
Evaluate:
(i) (162)8 + (537) 8
Solution:
1 1 <—- carry
1 6 2
5 3 7
7 2 1
Therefore, sum = 7218
(ii) (136) 8 + (636) 8
Solution:
1 <—- carry
1 3 6
6 3 6
7 7 4
Therefore, sum = 7748
Subtraction of Octal Numbers
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.
Example 1: 3458 – 1468
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 the hundreds column.
So tens column subtraction is 3 + 8 – 4
Answer: 1778
Method 2: Minuend<Subtrahend
This method is same as binary subtraction. This method is also valid for Minuend>subtrahend the 8’s complement of subtrahend and add it to minuend.
Minuend – Subtrahend = Difference
Or
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: 257 8 – 765 8
8’s complement of subtrahend=013)8.
1
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
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