modern-day computers use electricity to work and inside of a microchip
electricity is turned either on or off which is represented by the symbols 1
and 0. this is called binary you've
probably heard of binary already and that that's how computers work but do
you know how binary works well you're about to find out but first we need to
understand exactly how our numerical base system known as decimal or base 10
works the way it does so there are 10 count em 10 symbols that we use for all
of our numbers starting from 0 we can count all the way up to 9 before we run
out of symbols to use now we could just keep adding symbols at this point but
that would get out of hand very quickly i mean can you imagine having to
memorize a specific symbol for every single number that's ridiculous and
that's why we reuse the same symbols over and over again in a very clever
system called positional notation so in
the base 10 system as soon as we get to 10 or an exponent of 10 we need to add
another digit to the left of our current digit because there are 10 symbols each
new digit has to have a value 10 times greater than the digit to its right so
that's using 10 symbols but what if you had only two symbols to work with well
then everything that i said still applies with just two symbols each new
digit needs to have a value two times greater than the digit to its right
so a sequence like this would equal 1 times 128 plus 1 times 16 plus 1 times 8
plus 1 times 2 plus 1 which is
155 and that's how you count in binary it's
actually really simple it's just multiplication and addition now it gets
a lot more complicated from here with bits and bytes and boolean logic and
ascii and the list just goes on and on so let's return to base systems there
are a lot of ways to write numbers other than decimal and binary you've got base
two base three base four base five i could go on they all work with the same
principles of positional notation so you might be wondering with all these
numbering systems to choose from why do we use base 10 that's a good question
this goes all the way back to roman numerals and egyptian hieroglyphs it's
likely that we use base 10 simply because we have 10 fingers also known as digits other
base systems like base 8 and base 12 are actually superior for simple everyday
math since 8 and 12 are much more easily
divisible than 10 but it's definitely too late to change our minds about using
base 10 we'll probably be stuck with it forever switching away from it now would
be even harder than trying to convince america to drop the imperial system and
finally switch to metric you know like the rest of the civilized world like
yeah the metric system is superior but who's going to tell america what to do
now if you're going to be using base 12 or any other base system with more than
10 digits it's standard to use letters to represent numerals higher than 9. so
10 is a 11 is b 12 is c and so on this
is called alphanumeric you know those url shorteners that you see on twitter
and elsewhere have you ever wondered how they work all those jumbled characters
really just represent a very large number by using numerals and every
letter of the alphabet you can get all the way up to base 36 using lowercase
and uppercase letters gives you base 62
and with that you can get all the way up to 14 million with only four digits with
just 10 digits you can get up to 839 quadrillion possible values that's a
lot of shortened urls so you just learned about positional notation binary
numbers numeral based systems alphanumeric characters and url
shorteners i hope you enjoyed it and if you're in the mood for more learning
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