Hey! In this lesson we’re gonna get negative. No, not that kind of negative! I’m more of a
“the glass is incorrectly sized” kinda guy anyway. We’re going to talk about
negative numbers in how we store negative numbers in Java. If you’re not
sure how computer store negative numbers differently, you’ll definitely wanna keep watching this
video. The goals for this lesson are to
understand how we store negative numbers in binary. This is also how numbers are stored in Java.
We’re gonna use something called two’s complement numbers. Now let’s start with
what we know. We talked about binary numbers in the
last lesson, and how they’re organized to represent positive numbers. Each digit represents a power of two. This
is like the normal power of 10 numbers we already use. So how does it work with negative numbers? Well your first thought might be to sacrifice
the first digit, and use it as a sign bit. Let’s try that! Let’s start with
three bit numbers and add -3 and 2. The first number will be 111. That will be our -3. And then we’ll add 010. That’s our two. Add it and we get 001 or one. Wait -3 plus two. That didn’t work!! We should get 101 as a result. The answer
is -1 Maybe if we add special code for the
sign bit? But how will we know when to do that
programmatically? The problem with this strategy is it induces a bunch of cases. A case for two
positive numbers A case for two negative numbers. A case where the
positive number is larger. Case where negative number is larger. A case where the positive and negative number add to
zero. This completely wrecks our simple adder. It won’t work. Okay time out! Now I’m gonna take an aside. We need to talk
about something else that might help and come back to this problem later. Imagine a clock. On the clock you have the
numbers one to twelve. If it’s three o’clock and you add 12 hours its still three o’clock. We’re not looking
at days here. Just the hour. If we add three hours that makes it six. Add fifteen hours and it’s still six. If we subtract nine hours, yep still six. This works for multiplication too. You
can try that one at home. The reason this works is 3, -9, and 15 are all equivalent numbers for a
clock. It doesn’t matter which one you use. You get the same number in the end. The
math way to say this is that they are all congruent modulo 12. Don’t worry, that’s not
on the quiz. So, back to binary land. How can we use this information for our
computer numbers. We do the same thing for our numbers. Imagine our computer holds 3 bits. We’re only using
3 bits because I want to show you every possible number. On
a computer. the numbers vary from 8 bits to 64 bits.
That’s just too many to display here. Now think of the
numbers as positions on the clock. We’ll map our
numbers this way. The first bit still means negative, but the other bits are not how you’d
represent positive numbers. For example -4 is 100 and -1 is 111. So the positive numbers
look the same and negative numbers look weird. What happens
now? Let’s try adding -3 and 2 again. So we add 101 and 010. That gives us 111 which is -1! It works! No special logic. It works because these are equivalent
numbers in binary. So how do we calculate the special
number when we’re using 16 bits? Well there’s really no magic to it.
To change the sign of a number all the bits are flipped, and you add one.
Earlier we had -3. So three in binary is 011. Step 1, flip the bits to get 100. Then we add one. So the compliment number is 101. Just like on our clock. If this number were
eight bits the number would be 1111 1101. So the number of bits in your mapping matter
to calculate the correct equivalent number. Luckily this is all
handled for us behind-the-scenes. However it is important to understand
what your computer is doing. So this is why we use two’s complement
for all numbers in Java. There are no unsigned numbers in Java.
Every counting number type is doing this for negative numbers.
For some of the larger number types there are ways to use them unsigned,
but we can’t cover that until we get to number classes. That’s a ways away. In the next lesson
we’ll actually look at out first type. The byte. Hey thanks for watching the video! There is a
quick quiz for this on DeegeU.com if you’d like to gauge how much you
learned. If you like the videos you are seeing please
let me know by liking the video and hitting the subscribe button for the DeegeU
channel on YouTube. I’d really appreciate that! If you have
concerns or questions please leave them in the comments below or on DeegeU.com. There’s a poll on the front page of
DeegeU.com, so you can let me know what topic is
covered next. Thanks for watching and see you in the next
video!

How do computers store negative numbers? – 005

### 5 thoughts on “How do computers store negative numbers? – 005”

• January 10, 2016 at 12:23 am

Great Work. I finally understood the concept. Thank you very much

• May 16, 2016 at 9:36 pm

GOOD VIDEOS!!! I subscribed

• June 28, 2016 at 1:06 am

you use colours to show when you have a number and then another colour to show when you subtract from the number, (hope that makes sense)
but how does a computer recognise a colour?
if I have 101, should it not be 5?
How does the computer understand that you want it to be a subtraction?
Sorry if I missed something.

Great vids so far, hope they continue the way you have started 🙂

• December 18, 2017 at 10:56 am
• 