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Current time:0:00Total duration:10:00

Video transcript

for as long as human beings have been around we've been counting things and we've been looking for ways to keep track and represent the things that we counted so for example if you if you were an early human and you were trying to keep track of the days since its last rained you might say okay let's see didn't rain today so it's that's it's it's one day has gone by and you know the we now use the word one but they might have not used it back then now another day goes by then another day goes by then another day goes by another day goes by another day goes by another day goes by that it rained and so when his friend comes it says well how long has it been since we last rained well dinner that you would say well this is how many days it's been and your friend would say okay I think I have a general sense of that and at some point they probably realized that it's useful to have names for these so they would call that we call this one two three four five six seven and obviously every language in the world has different names for these and I'm sure there are lost languages that had other names for them but very quickly you start to realize that this is a pretty bulky way of representing numbers one it takes a long time to write down it takes up a lot of space and then later if someone wants to read the number they have to sit here and count and it's hard enough with seven but you could imagine if there were what we call twenty-seven of it or or a thousand of it then it would take up you know possibly a whole page and even when you counted you might make mistakes and to solve this human beings have invented number systems and you it's something that we take for granted you might say well isn't that just the way you've always counted but hopefully over the course of this video you'll start to appreciate the beauty of a number system and to realize that our number system isn't the only number system that is around the number system that most of us are familiar with is the base ten number system often called the decimal the decimal number system and why 10 well probably because we have 10 fingers or most of us have 10 fingers and so it was very natural to think in terms of bundles of in order to have ten symbols so however many bundles you have you can use your maybe your fingers and eventually your symbols to think about how many there are and since we needed ten symbols we came up with 0 1 2 3 4 5 6 7 8 9 these 10 digits these are our 10 symbols that we use in the base 10 system and it just give us a little bit reminder of how we use them imagine the number imagine the number 231 so 230 231 what does this represent well what's neat about number systems is we have place value this place all the way to the right this is the ones place this is the ones place this literally means one one one bundle of one so this is one one right over here this right over here this is in the tens place this is in the tens place this simplice three here literally means three tens so this literally means three tens and this to here this to here is in the hundreds place it's in the hundreds place hundreds place and so this represents two hundreds to hundreds and you add them together and once again I'm still thinking in base ten you'd get 231 this is two hundreds plus 3 tens plus 3 tens plus one and in our base 10 system notice every time we move to the left we're thinking in bundles of ten of the space to the right so this is the ones place you multiply by ten you go to the tens place you want to you want to go to the next place you multiply by 10 again you get the hundreds place if you're familiar with exponents 1 is the same thing as 10 to the 0 power 10 is the same thing 10 is the same thing as 10 to the first power so is the tens place three tens and 100 is a is ten to the second power and obviously we could keep going on and on and on and on that is the power of the base-10 system so you might be curious now well what if this wasn't a ten here what if we did let's just go as simple as we can you can almost view this as a base one system you only have one symbol right over here but what if we went to something slightly more complex a base two system and you'd be you'd be happy to know that not only can we do this but the base two system often called the binary system this is called the decimal system often call it the base two system often called a binary system is the basis of all modern computing its underlying the underlying mathematics and operations that computers perform are based on binary and in binary you have two symbols you have zero and you have one and the reason why this is useful for computation is because all of the hardware that we use to make our modern computers all of the transistors and the logic gates they either result in a on or an off state an on or an off State and so what we do is you know when you when you use your calculator whatever you might be operating in base ten but underlying everything it is doing the operations in binary but you might say well how do we actually think in terms of binary well we can construct similar places here but instead of them being powers of ten they're going to be powers of two so let's set up some places here so all the way on the right two to the zero power is still one so we could still call that the ones place then we can move to the left of that we can move to the left of that that would be two to the first power so we could call that the twos place and I could even write it out if I want to z' place instead of the tens place then I could keep going instead of a instead of this space being the 10 to the second or the hundreds place it'll be the two to the second or the fours the fours place and I can keep going this and I encourage you actually you pause the video and try to build this out for yourself what would this be well this would be two to the third or the eighth place and notice every time we're doing this we're multiplying by two time we go every time we go to the left just like we multiplied by 10 here so notice everywhere you see these these tens we're now dealing with twos let's keep going let's keep going and then we can actually represent this number using binary so let's do that so this right over here I've already used that color this right over here this is two to the fourth we could call that the 16s place and then we could have I'll reuse some of these colors this is two to the fifth we could call this the 32nd the 32 is place then we can go we can go two to the sixth two to the sixth we could call that well we're multiplied by two again or to the sixth is 64 so this is 64 is place it tells us how many 64 is we have a zero or one 64's and we'll see that in a second and then we can go over here this would be two to the seventh that would be the 128 place 128 128 place and we could obviously keep going on and on and on but this should be enough for me to represent this number in future videos I will show you how to do that but let's actually represent the number it turns out that this number in decimal can be represented as 1 1 1 0 0 0 1 1 1 million yellow 1 1 1 in binary and so what does this mean this means you have 1 128 + 1 64 + 1 32 + no 16s + no 8 + no fours I sorry plus 1/4 plus 1 2 + 1 1 and so you can see that these are going to be the same thing notice this is 1 128 so it's 128 plus 64 plus 64 plus 32 plus 32 we don't have we have zero 1608 so we're not going to add those plus four plus four 1/4 plus 1/2 plus 1/2 plus 1 1 plus 1 1 and add these together and once again when we're doing this when I'm writing it this way I'm kind of using the number system that we're most familiar with that we're most used to doing the operations in but when you do it you will see that this is the exact same number is 231 that this is just another representation one isn't better than the other only reason why I converted this is this is what I'm just used to thinking in it's what I'm used to doing operations in so hopefully you find that pretty interesting this to me this was kind of open my mind so the power of even our decimal system in future videos we'll explore other number systems and the most used ones base 10 is obviously most is used very heavily binary and there's also hexadecimal where you don't have two digits or not ten digits but you have 16 digits and we'll explore those in future videos and how to convert between or rewrite the different representations in different bases