Hey there! Struggling with binary to hex conversions? This video makes it SUPER easy—no math required! Learn to convert between binary and hexadecimal with simple patterns you’ll memorize in no time. Perfect for computer science students, coders, or anyone curious about how computers work. Subscribe for more tutorials, and scan the QR code to visit my site for extra resources. Drop a comment with your questions or video ideas! #Binary #Hex #ComputerScience #Coding
Introduction to Binary and Hex Conversion 00:00:00
Why Convert Between Binary and Hex 00:00:13
Recap of Number Systems 00:00:41
Binary Base Two System 00:01:01
Hexadecimal Base Sixteen System 00:01:24
Benefits of Hexadecimal 00:02:06
Simplifying Binary-Hex Conversion 00:03:04
Four Bits Equal One Hex Digit 00:04:32
Memorizing Binary-Hex Patterns 00:05:13
Creating a Binary-Hex Conversion Table 00:06:26
Converting Hex to Binary Example 00:08:52
Understanding Nibbles and Bytes 00:10:44
Converting Binary to Hex Example 00:13:19
Conclusion and Verification 00:15:38
Call to Subscribe and Engage 00:16:20
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Hi there! Let’s talk about converting back and forth between binary and hexadecimal.
Why would you want to do that? Well, maybe you’re in computer science. Maybe you’ve been presented
with some numbers that you need to convert. Maybe you have like a bunch of ones and zeros.
Maybe you have like an ox and then something that looks really weird. It’s got some letters in it,
but it’s also got some numbers. And you’re trying to figure out what are these? What are we trying
we try to convert back and forth between.
You should have watched my other videos by now,
which will teach you how to convert back and forth
between both of these number bases and decimal.
So you can understand what they are
in just normal human terms.
But as a quick recap, decimal is a base 10 number system
because we have 10 possible characters that we can use.
We can say zero, one, two, three, four,
five, six, seven, eight, nine.
So that’s 10 total characters, zero through nine.
We also have binary, which is what computers use, which is a base two system.
It’s base two because the only characters you have available are just zero and one.
So base two, two characters.
You can represent a number between zero and one in a single digit.
Then we have hexadecimal, which is a way to represent a number in a more compact way.
system there because we have 16 possible characters we have 0 1 2 3 4 5 6 7 8 9
just like decimal but then we add more numbers we had like six numbers we say
a b c d e f and what happens is the a has a strength of 10 whereas the you know
the 9 just to its left had a strength of 9 the a has a strength of 10 the b has a
of 11 the c has a strength of 12 and the d has a strength of 13 and the e has a strength of 14
and the f has a strength of 15 and so you know we just have more characters that we can use in one
single digit which means we can rent we can represent the same number in decimal but just
we can represent it smaller if we use hexadecimal so it’s kind of useful when you’re working with
looking at bits in binary or hex and not necessarily decimal because binary as
you’re going to learn in this video gives you kind of a good idea just by
looking at it after you’ve practiced a little while gives you a good idea of
what hex numbers you would be seeing if you were looking at the same number and
vice versa if you’re looking at hex numbers if you look at them a lot in
your daily life you’ll start to kind of like see through the matrix and you’ll
And if you’re interested in finding what bits are on and off,
it’s convenient to be able to look at a hexadecimal number
and kind of intuitively know,
okay, those bits are probably like on and off.
Those bits are all on, you know, whatever.
So this is the basics of number basis.
Here’s a trick.
In all my other videos,
when we converted back and forth
between decimal and binary and hex and all that stuff,
we used multiplication, we used division,
you know, we messed with the numbers quite a bit.
the great thing about binary and hex conversions is you don’t even really need to do math.
Maybe a little math at first while you’re learning, but eventually when you get used to it,
you start to realize you can memorize short patterns. Let me bring your attention to the
fact that in hexadecimal, you have 16 possible combinations, or you can represent a number
you can do the same thing in four characters if I had four characters right
here in binary very quickly you could do the calculation in your head if you’ve
watched my other videos you can see well that one counts for a one and this one
counts for a two and this one counts for a four and this one counts for an eight
if I want to know what the maximum value is that I could represent with four
digits I just take the the top numbers strength multiply it by two and then
strength multiply it by 2 and then subtract 1. So if we have 1, 2, 4, 8, I’ll just multiply 8 by 2,
that’s 16, and then subtract 1, that’s 15. So I can represent a number between 0 and 15 with 4
binary digits. But I just said you could do that with one hexadecimal digit, right?
So that means one hexadecimal digit is actually four binary digits. And if you just memorize
16 combinations of numbers, which is not like that hard.
And even if you don’t memorize them all,
I don’t have them all memorized.
It’s really easy to convert in your head
a four digit binary number to decimal
and then convert that back to hexadecimal pretty fast,
hexadecimal.
So what’s the equivalent of 1111?
Well, we know it’s the highest possible value
with just one hexadecimal digit.
So that would have to be an F.
So you can memorize already
You can memorize already a couple of really, really easy combinations.
We could say, let me say zero binary, OB to say that we’re looking at binary is equal
to zero X F. So just the letter F in hex.
Remember that we like to prefix different base number systems to give the reader a reminder
of what base they’re looking at.
one i’m going to say that 000 in binary is just zero in hex if i didn’t put that prefix how would
you know if you’re looking at hex or binary or decimal it would be even more confusing if you
had like you know one two zero is that hex one two zero or is that uh decimal one two zero i guess it
can’t be binary one two zero but if we did one one zero now it could be binary or hex or decimal so
i’m just going to put uh zero b for binary and i’m going to say it’s zero so that’s two of the
of the 16 total possible combinations that we would memorize.
So let’s iterate through all the combinations.
Just for the sake of making this table more compact,
actually, let me start a new little notepad page here.
I’m going to omit those prefixes because those are a good idea,
but while we’re doing our lookups, they’re a little irritating.
So I’m going to take them out.
So I’m going to say 0001.
Let me say this.
So I’m just going to count from 0 to 15 in binary.
to 15 in binary.
So this is going to be one, one,
and then zero and then zero, one, zero, one, zero, one,
I don’t know, that’s a lot of copy pasting.
Let me just double check here that I’m doing this right.
I should have 16 lines.
I don’t, so I’ve done something wrong.
Let’s see.
So this is like 0, 1, 2, 3, and this is 4.
This is 5, and then 6, and then 7, and this is 8.
Oh, I have that twice.
Okay, 8.
And then since I copy pasted the bottom part,
I think I can probably assume that’s okay.
One, two, three, four, five, six, seven.
That was kind of spooky.
I guess a lesson learned is that relying on a battery pack
or a light that’s gonna stay on for many hours
is probably a dumb idea.
Anyway, continuing, we have this table here.
We have like 16 possible combinations.
So now I’m gonna map these to hexadecimal digits.
uh you know like 10 are going to be really easy right it’s just going to be zero and then one
and then two you can make a vertical table if you want for yourself I’m just doing it this way
because it’s easier the way that I’m typing in this notepad the way that I’m typing in this
notepad so I’m going to do seven eight nine and then when we get to 10 let me just double check
- So this is eight plus two. So that means this is indeed a 10 and oh, 10 in hex, not a decimal.
So that’s a and then B and then C and then D and then E and then F. Okay. So now that we have this
little table set up, you know, if you want to write it horizontally, that’s fine. It’s actually
binary and hex now imagine we have a gigantic hex number zero x and then i’m just going to do like a
bunch of numbers and then i’m going to do change some of these to like letters just to make things
more interesting a b c d e did i use any d e f e b i didn’t use a b oh there we go and i’ll put like
another aid in there okay so this is huge and this would take like a while to calculate right
to calculate right if you were going to convert it to decimal for hex to binary conversion it’s
actually pretty easy you literally just go b what is b b is that so b is just that you don’t even
have to do any math let me copy paste this down here so i can show you a really easy way to do
D is this right here.
So I’m going to say the D is that.
And then the 6 is that pattern right there.
So move you over.
1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4.
Maybe that’ll line up later, hopefully.
So the 1 is pretty easy.
Probably didn’t even need to copy-paste that.
I could have just looked at it and typed.
looked at it and typed the E is going to be that and the seven is going to be that
and the two is going to be this eight see what I’m doing I’m literally just
copy pasting the bit patterns if you don’t have copy paste when you’re doing your conversion
that’s okay you can at least write down zeros and ones really fast if it’s just
you know four at a time I should also point out that um you know this is pretty important to
good term that people like to use. Four bytes or one hexadecimal digit, it’s called a nibble.
So usually you’re used to seeing eight bytes in a row and you call that, sorry,
usually you’re used to seeing eight bits in a row and you call that a byte or two hex digits in a
row and you call that a byte. If you just see four bits or one hex digit, that’s a nibble.
Two nibbles make a byte. Try to remember that. So we have this giant thing here.
we have literally now successfully converted binary.
I’m going to put, I’m just going to put OB here
and then remove all the spaces.
This is the binary number that we originally had
in hexadecimal.
So again, just to emphasize, these are the two same numbers.
They’re just represented differently.
Differently.
Let me punch this into my personal calculator
to make sure that I gave you the right walkthrough
so I don’t have to correct in a video later.
so expression X result binary oh god I can’t even I can’t even read that okay
so let me let me do it backwards I’m gonna copy paste this one in there okay
so let’s see X okay so it’s telling me that supposed to get to B and then a D6
728fac. Okay, so I did it. And this is also a good reminder that you kind of want to pair off
into groups of one byte at least. So, you know, each two characters, that’s one byte. One character
by itself is a nibble. So you want to pair off into bytes. And notice how this b is all by itself.
So you want to pad to the left with a zero so that you’re just kind of working with bytes.
It’s easier on the eyes and the brain. And you’ll usually see something like this
output from a program or something. In fact, you might see something like this representing,
here’s a word, or you might see something like this showing that this is like a D word or,
you know, like a 32 bit number. And if we wanted to say, oh, this is a 64 bit system. So let’s
look at 64 bits. Let’s look at eight bytes. Then we’ll just like pad it with, let’s see, one, two,
that’s one, two, three, we’ll pad it with a bunch more zeros. One, two, three, four, five, six,
So this is a proper 64-bit number or an 8-byte number that works with modern systems,
whether you have the space in there or not.
And so I’m not going to do another example from hex to binary.
Let’s do a quick example from binary to hex.
It should be just as easy.
So I’m going to start a new tab here and just copy-paste the table that I made.
Let’s make a bunch of random numbers for binary.
And so now we’ve got like a bunch of numbers.
All we have to do is I’m going to copy paste this so I don’t ruin the original thing that
I wrote down.
And I’m just going to break it up into groups of four, starting from the least powerful
digits, you know, like all the way on the right.
So I’m going to go doop, doop.
Okay.
So after breaking it into groups of four, you can see that the, you know, the most powerful
digit there is a one all by its lonesome.
I could put 000 to make sure that they’re all groups of four bits. I don’t really have to because
I could still kind of understand just by looking at the one that it’s going to end up being a one
and then literally just translate it the same way I did before. Okay that’s a 1.
1 0 1 0 that’s an A. What’s a thousand and one? It is a nine. What’s a 0 100?
what’s one oh one oh a what’s a thousand and one didn’t i just do that that’s a nine
what’s a zero zero oh ten that’s going to be a two for sure yeah two i finally got one off the
top of my head one zero one one that’s a b and then uh basically 15 minus eight i don’t really
want to work that out of my head right now so i’m gonna look at the table seven okay i guess i
should have done that easy right like how fast was that so i’m just going to copy paste these
put an ox in front of it and maybe bunch them into groups of two first to see what’s up
okay so they’re not in groups of two that means this one is kind of i should have started grouping
them on the right side kind of messed it up someone just you know rearrange the grouping
Let me punch this into my personal calculator to make sure that I got this right. Actually, let me do this original number here
I must say
This binary number is supposed to be
1 a 9 4 a 9 2 b 7. Okay, we did it
Really easy, right? So every time you have to convert back and forth between binary and hex
It’s your lucky day because that’s like one of the easiest conversions you could do
Thanks for watching this video. I hope you learned a little bit of stuff and had some fun
I’ll see you in the next video.
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