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 , octal multiplication, and octal division.
Key Questions
- How to perform subtraction in the octal number system?
- How to perform fractional octal numbers subtraction?
- How to perform octal numbers subtraction using 8’s complement?
Octal Numbers System Subtraction Examples:
Case #1: Minuend > Subtrahend
This is the method we used to do in elementary mathematics. All the rules we follow remain the same as we do in other number systems. Borrow is equal to the base of the 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
1 1
3 4 5
– 1 4 6
---------------
1 7 5Units place:
5 − 6, which is not possible. We borrow 1 from the tens place (which is 8 in octal).
5 + 8 becomes 13 (octal) → 13 − 6 = 5
Tens place: 4 − 4, but we already borrowed 1, so it’s 3 − 4. which is not possible, so we borrow 1 from the hundreds place.
3 + 8 becomes 11 (octal) → 11 − 4 = 7
Hundreds place:
3 − 1, but since we borrowed 1, it’s now 2 − 1 = 1
Answer: 177)8
Example # 02: 757.76)8 – 451.77)8
1 1
7 5 7 . 7 6
– 4 5 1 . 7 7
---------------------
3 0 5 . 7 7Hundredths Column
6 − 7, which is not possible in octal. To proceed, borrow 1 (which is 8 in octal) from the tenths column.
8 + 6 − 7 = 7. So, the result in the hundredths column is 7.
Tenths Column
After borrowing, 7 becomes 6.
Now we have: 6 − 7, which is not possible.
So, we borrow 1 from the units column.
8 + 6 − 7 = 7 So, the result in the tenths column is 7.
Example # 03: 565.67)8 – 234.34)8
5 6 5 . 6 7
– 2 3 4 . 3 4
------------------
3 3 1 . 3 3Answer: 331.33)8
Case # 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
Or
Minuend + [8’s complement of subtrahend] = 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
Octal Complement Calculator
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 the sum (272) = 506)8
Answer: -506)8
Example # 2: 675)8-722)8
8’s complement of subtrahend (that is 722) = 056)8
6 7 5
+ 0 5 6
-------
7 5 38’s complement of the sum= 025)8
Answer: -25)8
Example # 03 : 345)8-146)8
In example 1 and example 2 of case 2 where menuend is less than subtrahend. In this example, menuend is greater than subtrahend. We can solve this example by taking complement of the subtrahend, then add it to menuend. As we did in previous two examples of case 2.
8’s complement of the subtrahend (that is 146) = 632)8
3 4 5
+ 6 3 2
--------
1 1 7 7Diacard carry.
Answer: 177)8
Example # 04: 757.76)8-451.77)8
Again, in this example, there are two ways to solve this example. Using simple subtraction. The other method is to calculate the complement of subtrahend. Then add the resultant number and menuend.
8’s complement of the subtrahend (which is 451.77 here) = 326.01)8
7 5 7 . 7 6
+ 3 2 6 . 0 1
---------------
1 3 0 5 . 7 7Discard carry.
Answer: 305.77)8
Example # 05 : 565.67)8-234.34)8
8’s complement of the subtrahend=543.44)8
5 6 5 . 6 7
+ 5 4 3 . 4 4
---------------
1 3 3 1 . 3 3
Discard carry.
Answer: 331.33)8