Hello there! Ever wondered what number bases are all about? In this video, we?re diving into decimal (base 10 – the one you already know), binary (base 2 – just 1s and 0s, how your computer thinks), and hexadecimal (base 16 – the compact cool kid). I?ll show you how the same number looks totally different across these systems – binary gets LONG, hex keeps it short and sweet. Plus, why do we even use hex? Spoiler: it?s a game-changer for reading computer memory. Stick around to learn handy prefixes like 0x and 0b to avoid mix-ups. Want to be as cool as those binary-converting pros? Hit subscribe, scan the QR code for more, and let?s geek out together in the next video – conversions are coming up! Drop a comment with your thoughts or just say hi – it might wake me up in the middle of the night with joy!

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Hello there. Let’s talk about number bases. So what are number bases? You’ve probably at some

point heard someone say, hey, I can convert between decimal and binary or between decimal

and hexadecimal or hexadecimal and binary. And you thought that that person was way cooler than you

were. Well, they are way cooler than you. But if you watch my videos, maybe you can be just as cool

Anyway, so what do we mean by number basis exactly?

We’ll start with decimal,

which is the number system that everybody already understands, I hope.

So in decimal, you have 10 characters, right?

So we’ll say like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

It’s like 9, or sorry, 10 possible characters.

So decimal is actually base 10.

I’m going to write base 10 here.

Decimal is base 10.

base 10 because it has 10 available characters. The next thing is binary. You’ve probably heard

of that before. Even a lot of non-computer scientists understand binary at least a little

bit because it’s just ones and zeros, right? This is how your computer represents information.

All characters, all numbers, all floats, all everything. They really just come down to zeros

and ones inside of the computer. And it’s not like there’s an actual zero or an actual one anywhere.

It’s more like there’s a certain voltage that represents a one or there’s a different voltage

represents a 1 or there’s a different voltage that represents a 0.

You can think of it as just like voltage or no voltage, but that’s not always the case.

But you know, long story short, it’s just 1s and 0s.

So in binary, we can just represent a 0 or we can represent a 1 and that’s it.

Because there’s only two characters that we can use to represent numbers, we call this

base 2.

So that’s binary.

Now not a lot of people have heard of hexadecimal outside of computer science, but hexadecimal

outside of computer science but hexadecimal is a number is another

number system that we can use which uses base 16 the reason we use hexadecimal is

it because it kind of it kind of compacts a number I’ll show you in a

second how it can represent the same number but with less characters you can

imagine in binary if we have base 2 there’s only two characters that means

the same number in decimal versus binary it’s probably going to be a lot longer

imagine that, right?

Because it’s not like the actual numbers change

that we’re trying to represent.

It’s just that the representation changes.

So hex or hexadecimal,

we have 16 different characters.

Did I say 15 a moment ago?

Sorry if I did.

So we start with the normal ones that base 10 has,

decimal has.

So we go three, four, five, six, seven, eight, nine.

So that’s 10.

the extra five, we do A, B, C, D, E, F. Sorry, extra six. I knew I was going to say five at some

point. So in hexadecimal, we have the characters zero, one, two, three, four, five, six, seven,

eight, nine, and then A, B, C, D, E, F. For a total of 16 characters, or one digit can represent

here. So this is the basics of the differences between the number systems. Let me show you a

quick example. Let me see if I got my calculator here. Hopefully it’ll work. Okay. I’m going to do,

let’s see, variables. So how do you get into this one? Mode. Oh, number base. So I’m going to do,

let’s just pick a random number in decimal. So I’m going to say like, you know, just hit the

So you can see that if I type a number in decimal and show it in decimal, then well,

it’s the exact same size as you probably have suspected.

But if I represent this exact same number in binary, you should probably expect that

the representation is going to be way longer because again, binary only has two characters

to work with.

So it’s harder for it to represent the same information.

So I’m going to change the expression base here to binary.

Oh no, what’s happening?

What’s going on here?

Expression base.

Oh, I did the wrong thing.

Decimal is the expression base.

Binary is the result base.

Okay.

So that same number that we had before, 871, 876, 42,

look at how huge it is in binary.

Takes up a lot of your screen, right?

So we use binary because it’s the closest representation

to what the actual machine has.

So that’s good.

Especially if you want to start manipulating individual bits

manipulating individual bits for one reason or another. It’s good to know how to, it’s good to

understand binary. But hexadecimal is useful, like I said before, to compact the same number. So

again, because the base of the original number is 10, you know, we had the original number in decimal.

If we show a hexadecimal version of it, it should be shorter because there’s 16 characters to work

with. It’s easier for it to represent the same information. So the result base, I’m just going

hexadecimal here and look at how short that number is the original number is one two three four five

six seven eight it’s eight characters long but the hexadecimal number is two four six seven

characters long and that savings in characters will go up and up and up the more you know the

longer the original or the bigger the original number is let me see if I can just add some more

numbers here okay let’s see if we get more savings here one two three four five six seven eight nine

Okay, so the original number is 15 long and here we have 2, 4, 6, 8, 10, 12, 13.

So that’s a savings.

Now think about it this way.

This is a huge savings compared to binary.

Let’s go back to binary real fast.

Same number, which is currently in hex.

As soon as I start showing it in binary, the number explodes.

So there are a lot of numbers, especially if you have a 64-bit number, which you work

if you were to just take you know one of those 64-bit numbers and try to express it in binary

it’s just kind of like it’s really really long and if you want to represent anything even a little

bit bigger like 128-bit numbers or even the contents of memory from you know one memory

location to another binaries just can explode and fly off the screen so this is why I mean this is

one of the biggest reasons why we use hexadecimal because it’s just it’s easier to see what’s inside

of the computer it’s easier than decimal and it’s easier than binary at least once you understand

hexadecimal one other thing that i want to uh show you real fast let me see like let me change

that back to decimal so i don’t screw myself later okay um suppose that you wanted to represent a

number in binary sorry let’s say decimal well you know we’ll say like one two three four right and

well actually let’s not do one two three four let’s say like a thousand and one and then you

want to represent a number in binary and you write one zero zero one and then you want to

represent a number in hexadecimal you could also have one zero zero one right the problem is that

each of these numbers are actually different numbers they only look the same because the

character representation is the same but not the actual number so how do you uh how do you sort of

How do you sort of like differentiate and make sure that the person reading the numbers that you’ve written down knows what base they’re in?

Because if you know if you’re a computer scientist or you’re doing some kind of crazy math, then

well, it might not be obvious and

you want to be careful that the person doesn’t misinterpret your results.

Okay, so let me do that thing again real fast

just to prove to you. What am I doing here? Units? No.

Mode.

Okay, so I’m going to say if I write 1001, I’m going to display it as decimal,

but the input is first going to be decimal.

So in decimal, 1001 is 1001.

Okay, that’s fine.

But if this 1001 was actually a binary number,

I’m going to say that the expression base is binary here.

Notice how the real number is actually 9 if you represented it in decimal.

expression like the original number was you know the characters were hexadecimal then the real

decimal version of 1001 would be 4097 that’s three totally different numbers so you got to be careful

that you know what you’re reading and you got to be careful that you help the person reading what

you’re writing down if you’re trying to transmit this information so with hexadecimal a really

really common prefix that everyone should use is ox ox and then any number after that usually just

reading this is a hexadecimal number so there’s no ambiguity same thing for binary you’ll just say

like ob and then for decimal you just just leave it alone i think there’s a another prefix you can

use but i usually don’t use anything but at least uh ob says this is binary and ox means this is

hexadecimal and then nothing just means okay just default to human reading just decimal

okay this was the basics of number bases in other videos i’m going to talk about how to actually

between these three bases maybe in the future at some other point in some other

video far off in YouTube land I might talk about octal or some other base but

in the immediate future it’s going to be decimal binary and hexadecimal so I

hope you’ve enjoyed this video I’ll see you in the next

hey everybody thanks for watching this video again from the bottom of my heart

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Thank you.

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