Binary got you baffled? Let’s break it down! In this fun crash course, I’ll show you how to convert binary to decimal step-by-step—super easy, no stress. We’ll go from 765,432 in decimal to 10101111 in binary (that’s 335, btw), with tricks to eyeball it fast. Perfect for beginners or anyone who loves a good tech challenge. Hit subscribe—I wake up in a cold sweat when you do, and it means the world! More vids coming your way!
Introduction to Binary and Decimal 00:00:00
Understanding Decimal System 00:00:44
Decimal Position Strengths 00:01:39
Decimal Formula Explanation 00:03:48
Transition to Binary System 00:06:31
Binary Position Strengths 00:07:19
Binary Formula Breakdown 00:10:46
Calculating Binary Example (335) 00:12:55
Quick Binary Conversion Trick 00:15:24
Memorizing Binary Positions 00:13:52
Small Binary Example (19) 00:15:43
Closing and Subscription Request 00:16:48
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Hello there. Let’s talk about converting binary to decimal.
Just a quick recap for those of you who don’t know. Watch my other videos if you’re not sure
about number bases, but basically, you know, decimal is a number system that has 10 characters
to represent a number. So 0, 1, 2, 4, 5, 6, 7, 8, 9. That’s 10 characters in decimal.
In binary, we just have two characters.
So it’s base two, whereas decimal is base 10.
How can we convert between the two?
Well, first, before we can try to convert between the two,
we should try to understand what’s really going on with normal decimal representations.
So if I have a decimal number here, and I say, I don’t know,
let’s just type a couple of random numbers.
How do we really know what this value is?
How do we kind of understand what is the meaning?
Okay, so you know that, you know,
if you just kind of look at this for a second,
you’ll realize this is 765,000, right?
765,432.
How do we know that this is 700,000?
Because it’s in a certain position.
It’s like, you know, several digits to the left.
How do we know that the next one represents 65,000?
Well, it’s one less to the left.
uh it’s a tenth of the like power of the seven digit same thing for the five how do we know
that’s a thousand same thing for the four and the three and the two what we really do is we end up
deciding okay you know what the uh the first digit here on the right side that two uh the strength of
of one. So like, you know, two times one is just two. So whatever, whatever that digit is, if it
was a five, it would just be a five, five times one is five, right? So the strength of the very
first digit on the right side is just one. Every time we move one digit to the left, we multiply
the strength by 10. The reason we multiply the strength by 10 is because there are 10 possible
digits, or 10 possible characters that we can use in decimal. Makes sense, right? So that means the
Makes sense, right?
So that means the three, we know that represents, you know, an addition of 30 because that’s
the 10th strength place.
Same thing for the four.
We multiply 10 by 10 again to get 100 in that position.
So this one has a strength of 100.
I’m writing this vertically.
Hopefully this is not too messy, but I’m hoping you’ll understand.
Well, I don’t know.
Maybe if I space this out, does that make it better or worse?
maybe it makes it slightly better i don’t know i’m going to roll with it
what can i say i’m a rebel okay so i live dangerously the five we know that’s worth
five thousand because again the four position over here you know that third digit it had a
strength of 100 so we multiply that strength by 10 going to the left to to end up with a thousand
to end up with a thousand.
So same thing with the six.
I’m not going to explain that any further.
You know, it’s got a strength of, you know, 10,000.
Okay.
And then the seven, it’s got a strength of 100,000.
And it just keeps going and going and going to millions and billions and trillions
and however far you actually want to go.
That’s how we understand the decimal numbers
that we’re looking at.
How could you imagine this in terms of a formula?
Well, we’re really raising something to the 10th power.
If you think about this, the one,
we could imagine that the value one
is actually 10 to the zero power
because anything raised to the zero power is just a one.
Let me pull up this calculator real fast.
I got to stick that on my desktop in the future.
If we say 10 to the zero power, it’s just one.
Any number to the zero power is just one.
Okay, so then we would multiply that strength
by the actual digit that we see,
the character that we see.
It’s a two.
Okay, so that’s going to be two times 10 to the zero power.
I’m going to put that in parentheses
to keep it a little bit clean or somewhat cleaner.
So now when we go one to the left
to look at that three digit,
to look at that three digit, we end up with three times something.
Let me get a space here for my brain.
Times 10 to the something power.
Well, every time we go to the left, we just really have to increase the power by one.
It’s 10 to the first power because we’re looking for actually just the number 10.
So if we say 10 to the first power on that calculator, it’s 10.
So then, you know, just keep repeating the process.
10 to the second power. And that should be 100. So if I say 10 to the second power, it’s 100.
All right. And, you know, we’re adding all the positions together, even though we’re multiplying
the digit by its strength. So I’m going to say five times 10 to the third power. And then again,
just to double check here, 10 to the third power is 1000. So you can see the five was supposed to
and then again we’ll say six times ten to the fourth power and then just double check here
the fourth power should be a thousand sorry ten thousand and then we’ll do it one last time we’ll
say seven times ten to the fifth power which should be a hundred thousand all right so now
that we’ve written this all out you know this is kind of madness right what you can do now
do now is you can put this into the calculator and it should give you the exact same number that
we started with. We should see 765432, unless there’s a typo. 765432. Nice. Okay, that might
have seemed like it was a little bit of a waste of time, but it’s not because now we kind of
understand the breakdown of the different positions of the digits in decimal, which means
now we can do the same thing in binary, basically the exact same thing, except just use a power of,
use a two to some power rather than a 10 to some power because the only reason we use 10 down here
it says we were in decimal that has a base of 10 now let’s go into binary
which is um a base of two so i’m going to just i guess maybe what did i do wrong
i hit something and it like did a space i don’t even want to know i don’t even want to know
okay so let’s do a binary number i’m just going to type a few random digits
a few random digits. I don’t know what number this is yet, but let’s work it out slowly
in the same way. You know what, maybe instead of doing the formula first and only, let’s do
both parts like we did with decimal. So what’s the position, what’s the strength of the position
for that first character? Well, I said before the first character is always just going to be,
sorry, the first digit is always just going to be a one, right? That’s going to be true
So I’m going to say this has a strength of 1.
How do we know it’s a strength of 1?
Because we’ll take 2 to the something power.
We start at 0 for that first position, and it’s going to give us a 1.
Okay.
So the strength of this one, I already know binary.
So I just know off the top of my head that to go to the left,
the strength just multiplies by 2.
And that’s pretty easy after you start memorizing it.
I haven’t quite memorized hexadecimal yet, but maybe you will in another video.
So I’m going to multiply one by two and I’m going to end up with two.
Double check over here in the calculator.
Two to the first power is two.
So then the strength of this next digit should be four.
Two times two is four, right?
So let’s do two to the second power.
That’s four.
Multiply by two again.
It’s going to be eight.
Double check over here.
Two to the third power is eight.
The next digit is going to be 16 of its strength.
So I’m going to write this vertically again.
So it’s going to be 16.
Double check over here with the calculator.
Double check over here with the calculator, 2 to the 4th power is 16.
Next digit is going to be 32.
Double check with the calculator, 2 to the 5th power.
And things are starting to get messy, so I think I’m going to like space everything out probably.
Just to make it easier to read.
Tell me if you think this makes it actually easier to read or if I’m making it way harder.
I think I’m making it easier.
Okay, so we got 32.
two. Next one up is going to be 64. Just multiply it by two. Double check two to the sixth power.
That’s going to be 64. And then the biggest one that we’ve written down is going to be 128.
Double check it. Six to the seventh power is 128. We could go on and on and on, but I’m just going
to leave it here because we, I hope we have a pretty good idea of, you know, what this means.
delineation or like a delimiter showing us that these are just representing the strengths and
this is the actual number. Okay, so how can we write this out in a formula?
Whoa, what did I do wrong? Did you see that? Oh no. Hang on a second.
I think I missed it. How many digits are there? If there are eight digits, then I definitely forgot
something. No, no. Okay. There are nine digits, so the last one should be 256. Okay.
- Okay. So I got it all lined up. At some point I must have not lined it up. My apologies,
but hey, maybe I’m making these mistakes on purpose to make sure that you’re paying attention.
You never know. I want you to think. So 256 is going to be the next number. Double check it with
the calculator. Two to the eighth power, 256. Cool. By the way, a quick trick in binary that
the actual highest number that you can represent in an unsigned binary integer is basically the
strength of the highest digit, you know, this 256 here, multiplied by two and then subtract one
from it. So 256 multiplied by two is going to be 512. So it’s going to be 511. So I could
represent a number between zero and 511 or 512 possible combinations. Okay, so now let’s work
let’s work out the formula.
See 16, 30, 16, 40, okay, I did it okay.
I probably should have rehearsed this.
So let’s do each position.
So it’s either always gonna be one times something
or zero times something, right?
Because binary, these characters can only be one or a zero.
So let’s do on the, starting from the right,
we’ll say one times two to the something power.
It’s gonna be two to the zero power
You know, just going to be a one.
Working our way over to the left, it’s going to be one times two to the something power
to the first power because it just increases every time the power increases.
We have four ones in a row here.
I got to try to remember that.
This is where I’m going to start making lots and lots of typos.
Two to the second power.
And then we have another one.
One, two, three, four, one times two to the third power.
And then again, we are going to hit a zero.
So it’s going to be zero times two to the something power.
You might be tempted to omit the zeros.
You can if you want to.
But for me personally, it helps me quickly visually see that I’m getting the powers in
the right order.
I can see two to the zero power, first power, second power, third power, fourth power.
Sometimes when I omit the zeros, I end up kind of like messing up the order of the powers
and or the order of the exponents.
of the exponents and I have to redo everything all over again.
So I just keep it this way.
Okay, so it’s one, one, one, one, one, one, one, one, zero.
So there’s another zero that we need
times two to the fifth power.
So we got both of those zeros now.
And then we need another one times two to the sixth power.
And then we need
0 times 2 to the 7th power.
Okay.
And then we have another 1 times 2 to the 8th power.
And I know we’re supposed to be done on 8
because that’s what we were doing before.
The 256 strength.
So unless I made some mistakes here,
this is probably the number that we can punch up into the calculator
to see what this binary number is.
So I’m going to punch it up.
Huge.
It says that it’s the number 335.
Let’s see if that’s actually right.
I’m going to punch this up in my personal calculator real fast.
I’m going to say 10101111.
And the expression is decimal 335.
Yep.
So that’s it.
We know how to convert from binary to decimal.
And just again, like as a quick shorthand,
it’s probably a good idea if you’re involved in computer science,
to memorize these positions up to maybe
6, 5, 5, 3, 6.
That might sound a little extreme sometimes,
but I don’t know.
Personally, I’m not like the most advanced
binary reader at all times,
but I can remember up to that much.
And what do I mean when I’m saying that?
I’m saying, you know, start with a 1, 2, 4, 8,
8, 2, 56, 5, 12, 1, 2, 4, 2, 0, 4, 8, 4, 0, 9, 6, 8, 1, 9, 2, 1, 6, 3, 8, 4.
Took me a while to remember that one.
3, 2, 7, 6, 8, 6, 5, 5, 3, 6.
So if you think about it, how many bits is this?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
Right here, 16.
That’ll give you two bytes worth of memorization or a word on many systems.
on many systems. For me personally, I just, I like to go up to 6, 5, 5, 3, 5 because
remember I was saying, you know, what is the highest number that you can go up to
with a certain number of bits? It’s always the power or the strength of the highest bit
multiplied by two and then subtract one. So when I remember 6, 5, 5, 3, 6, that tells me that if I
- This is very, very useful if you’re going to be working with binary numbers a lot,
or if you’re taking exams or whatever it is that you’re doing, I would recommend everyone do this.
Okay. What do you say? What do you say we do another binary number, but we’ll just do something
a little bit smaller to make it easy. Okay. So by the way, when you start to memorize these positions,
start to eyeball it, which is really, really fast and a good idea. Like I can see those two
numbers right there. I know the first one is a one and the second one is a two. So that means the
one and the one are just going to be a value of three. Then I just quickly go, all right, one,
two, four, eight, one, two, four, eight, 16. So it’s going to be 16 plus three. So it’s going to
be 19. I guarantee it. Let’s, let’s double check this real fast. We’ll say one times two to the
and then we’ll say 1 times 2 to the first power
and then we’ll say 0 times 2 to the second power
and then we’ll say 0 times 2 to the third power
and then we’ll say 1 times 2 to the fourth power
and if I didn’t go too fast and make a bunch of typos
it should be the number 19
So there is a lot of benefit in memorizing the strength of these different positions.
I personally never remember very much beyond 256 when I’m actually trying to work out a number
conversion, but when I’m just thinking of how to compute things, it’s faster if I can go up to
- Okay, I hope you enjoyed this video. I hope you learned a little bit of stuff. I hope
you had a little bit of fun. I’ll see you in the next one.
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