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modern-day computers use electricity to work and inside of a microchip

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electricity is turned either on or off which is represented by the symbols 1

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and 0. this is called binary you've

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probably heard of binary already and that that's how computers work but do

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you know how binary works well you're about to find out but first we need to

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understand exactly how our numerical base system known as decimal or base 10

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works the way it does so there are 10 count em 10 symbols that we use for all

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of our numbers starting from 0 we can count all the way up to 9 before we run

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out of symbols to use now we could just keep adding symbols at this point but

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that would get out of hand very quickly i mean can you imagine having to

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memorize a specific symbol for every single number that's ridiculous and

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that's why we reuse the same symbols over and over again in a very clever

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system called positional notation so in

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the base 10 system as soon as we get to 10 or an exponent of 10 we need to add

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another digit to the left of our current digit because there are 10 symbols each

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new digit has to have a value 10 times greater than the digit to its right so

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that's using 10 symbols but what if you had only two symbols to work with well

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then everything that i said still applies with just two symbols each new

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digit needs to have a value two times greater than the digit to its right

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so a sequence like this would equal 1 times 128 plus 1 times 16 plus 1 times 8

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plus 1 times 2 plus 1 which is

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155 and that's how you count in binary it's

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actually really simple it's just multiplication and addition now it gets

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a lot more complicated from here with bits and bytes and boolean logic and

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ascii and the list just goes on and on so let's return to base systems there

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are a lot of ways to write numbers other than decimal and binary you've got base

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two base three base four base five i could go on they all work with the same

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principles of positional notation so you might be wondering with all these

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numbering systems to choose from why do we use base 10 that's a good question

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this goes all the way back to roman numerals and egyptian hieroglyphs it's

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likely that we use base 10 simply because we have 10 fingers also known as digits other

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base systems like base 8 and base 12 are actually superior for simple everyday

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math since 8 and 12 are much more easily

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divisible than 10 but it's definitely too late to change our minds about using

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base 10 we'll probably be stuck with it forever switching away from it now would

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be even harder than trying to convince america to drop the imperial system and

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finally switch to metric you know like the rest of the civilized world like

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yeah the metric system is superior but who's going to tell america what to do

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now if you're going to be using base 12 or any other base system with more than

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10 digits it's standard to use letters to represent numerals higher than 9. so

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10 is a 11 is b 12 is c and so on this

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is called alphanumeric you know those url shorteners that you see on twitter

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and elsewhere have you ever wondered how they work all those jumbled characters

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really just represent a very large number by using numerals and every

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letter of the alphabet you can get all the way up to base 36 using lowercase

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and uppercase letters gives you base 62

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and with that you can get all the way up to 14 million with only four digits with

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just 10 digits you can get up to 839 quadrillion possible values that's a

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lot of shortened urls so you just learned about positional notation binary

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numbers numeral based systems alphanumeric characters and url

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shorteners i hope you enjoyed it and if you're in the mood for more learning

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