Hello, everyone.
I'm typhoon.
Welcome to today's comprehensive lecture on binary subtraction and handling signed integers using two's
complement.
We will explore important concepts clearly and interactively to help you deeply understand how computers
perform arithmetic with signed numbers.
In binary arithmetic, numbers can be positive or negative.
To represent this in binary, we typically use one bit, known as the sign bit.
This is the sign bit in assigned integers.
In unsigned integers, we don't have a sign bit.
Since we don't have a sign bit, we have more values to store.
But the drawback is in unsigned integers we don't have a negative numbers, so the sign bit indicates
whether a number is positive or negative.
Initially, you might consider simply just that this zero.
If you have zero in assigned integers as a first bit, it is.
What?
Positive, right?
But here if we have one, it means it is negative.
However, this straightforward method known as sign magnitude leads to problems when adding numbers.
Now let's look at a simple example here.
So we have what zero one.
Or let's use another color for this.
We have 0010 which is what.
Positive two.
And 1010.
Which is what.
Negative two.
And if you calculate that what we will get one one.
The result is 1100 which represents what Minus four instead of two.
But the real result should be.
What?
Two.
Zero.
Now, clearly a different method is needed here to overcome this problem.
Most computers use two complement notation.
Before we dive deeper, let's clearly understand complement concepts in mathematics.
Now we have the complement of number a number you add to another to reach a specific base or whole.
Example is the complement of 37.
In base ten which is decimal with two digits are 63.
Because what 37 plus 63 is 100, right?
This is complement and the two's complement in binary.
Now for binary numbers two's complement is simple way to represent negative numbers allowing easy addition
and subtraction operations.
Us now here.
Let's look at how two's complement notation works practically in binary arithmetic.
Here you see plus one is 0000010.
And minus one is 1111110.
So it works like in reverse basically.
So key observations about two's complement is the first bit is often called the sign bit with what zero
for positive and one for negative.
This notation allows arithmetic operations without special instructions and the range from a four bit
integer integer.
So what we have here is four bits, right?
The range for the four bit integer is what is from minus eight to plus seven.
In the unsigned it can from 0 to 16 or 15 or 16, right?
That's how it basically works.
You get negative numbers.
But the drawback is you will get twice less.
Now let's revisit our previous example on adding plus two and minus two.
This time using two's complement.
So we will use again 0010.
And the two is remember 11101110.
And what we will get here is 0000.
The result is zero correctly represents zero.
Demonstrating the advantage of two's complement notation.
Clearly here you can see zero is always 000 doesn't matter in an inside or outside right.
To ensure you understand these concepts well here's a quick exercise using four bits four bit two's
complement at minus three and plus three for the binary result.
Clearly and explain yourself briefly on your own notepad.
Pause the video.
Now try to exercise yourself and resume the solution to see the solution here.
The solution is but 1101 and 1100.
This is minus three plus 311 goes as zero again 000.
The binary result correctly represents zero, confirming our understanding of two's complement addition.
So use complement.
Now two's complement is extensively used in modern computing for arithmetic operations due to its efficiency.
Now this simplicity in arithmetic circuits make it the standard across nearly all computing devices,
from smartphones to supercomputers.
Understanding these two's complement helps you grasp more complex computing principles clearly.
And in today's lecture, we have covered why simple sine magnitude methods aren't practical for arithmetic.
You see, when we try to use the minus one plus two, we got the wrong result here, right?
And we also learned the importance and utility of two's complement notation.
We also learned the practical examples and interactive exercises for adding and subtracting sine integers
using two's complement.
Now by mastering these concepts, you will well be prepared for advanced topics in computer organizations
and computing or low level computing.
Thanks for joining today's lecture.
Feel free to ask any questions and I look forward to seeing you in our next lecture.