Computers fundamentally use binary (base-2) to represent data, but the way we measure storage capacity can be confusing due to the difference between decimal (base-10) prefixes (like kilo, mega) and binary prefixes (like kibi, mebi).
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we're going to be looking at the first
section of the syllabus which is
information representation and the
subsection data representation the focus
for us today is going to be how and why
computers use binary to represent all
forms of data
now this is probably going to be a
rehash of some of the information that
you covered in igcse however
there are going to be some unique
aspects which obviously you need to know about
about
so let's start with the first difference
at igcse level you probably worked with
kilobytes megabytes gigabytes and
terabytes however at as level you'll
probably find that in industry there are
two terms that are used the first aspect
is the standard
international units which are kilo mega
giga and terra and then you have the
binary units
kibi maybe gb and tevi
the standard international units kilo
mega giga and tera
are normally based on base 10 so you go
up with 1000
you go to million you go to a billion
and trillion and when we look at kiwi we
go up in base two so this will be about
2 to the power of 10 which should be 1024
1024
and then similarly maybe will go up and
you end up with just a bit more
data than a million and a bit more than
a billion and then obviously a trillion
it is vital for you as a computer
scientist to know the difference between
both units and how
the everyday common person will probably
be using kilobytes and megabytes however
what the difference is with the actual
units and it makes a big difference when
you're dealing with memory for example
kiwibyte means you get a bit more
storage space a bit more space required
in the memory compared to kilobytes
so let's look at how two people will
deal with it so on the left hand side
we've got our amateur and on the right
hand side we've got our professional
their interactions together
based on what kibi is and what killer is
and how
confusing it all gets will give you an
idea of what challenges people face when
they're talking about
memory and storage capacity in kiwi and
kilobytes etc
so our amateur goes that okay i know
that computers work with electricity and
the expert as well computers actually
use binary and electricity can be turned
on or off so that is equivalent to base
two when the electricity is on we have
the digit one if the electricity is off
it's zero so the amateur is like okay well
well
i think that a thousand is a kilo and
that's a kilobyte
and the expert goes well in base two we
use something called geometric
sequencing so we go up in 2 4 8 16 32 64
128 256 and so on until we reach one or
two four and that is known as the kibi 2
to the power of 10.
so our amateur goes well
i still think mega is 1 million bytes
and the expert then goes well actually
it's 148
576 bytes which is also known as a maybe
byte so they're slightly different
even though for
small amounts
it's not a big difference but when you
create all these megabytes into bigger
numbers it can add up to a sizeable sum
our amateur goes well why the two
different approaches
and the expert goes
because of the si which is the systems
international units and to make it easy
for non-experts to remember all of these
these are called decimal prefixes or
base 10 prefixes so
prefixes are basically words which you
add in front of a number in this
particular case kilo is a prefix to
bytes and mega is a prefix to the bytes
so these are called dna prefixes because
they operate in base 10. the amateur
goes well now i am confused
gb is still gigabyte right
and the expert goes well yes that's right
right
however gib is
is
gibby byte
and a 1 gb hard drive will be smaller
than a 1 gib
hard drive because obviously there's a
lot more space in the gibby byte hard
drive version of things which is based
on base 2 and is a binary prefix because
it operates to 2 to the power of
something rather than 10 to the power of
something our amateur goes okay so one
tib is more than one tb or terabyte is
that correct and expert goes yeah you
got it one tabi byte is equivalent to
more than a trillion bytes or
1 trillion 99 million 511
627 776 bytes to be exact
so hopefully you've got a
good idea about what decimal prefixes
and binary prefixes are like and decimal
prefixes remember the term prefix means
adding something in front of a number so
in this particular case when we use the
standard metric system for prefixes they
tend to be kilo mega and giga
and the decimal system increases in
orders of thousands so 1000 gram is
equal to 1 kilogram and we use something
similar which most people are familiar
with in their day to day life
now why did this happen well it's
because consumer is king and this was
all great when storage capacities were
very tiny so in the old days we never
used to worry about like
megabytes and gigabytes
people used to work with bits and bytes
and storage capacities were so tiny that
decimal prefixes seemed normal
but as storage increased in size
unfortunately that caused a bit of a problem
problem
however still 1024 bytes was close
enough to a thousand bytes that we could
get away with things
but as memory capacity and storage
capacities increase things started to
become difficult for both software
developers and manufacturers themselves
so here's an example of this this is an
ad for a 10 megabyte hard disk in the
old days how do we know how big this is
is it 10 million bytes is it 10 485 760
bytes who knows
and that caused the problem for
consumers themselves as well because
they didn't know what they were paying for
for
or what did they get it was pot luck
and of course these days you probably
won't pay three thousand four hundred
ninety five dollars for a ten megabyte
hard drive these were expensive items
and it made sense to be exact
so what was the solution well the
solution of course was binary prefixes
the industry decided to get their heads
together and come up with a new prefix
system that uses binary units to avoid
all of this confusion and back in 2005
the ieee which if you came up on the
internet the institute of electrical and
electronics engineers and they came up
with this new standard so they said well
we're going to be using killer binary
mega binary giga binary and tera binary
which in short form become kibi maybe kb
and tevi the symbols are as what they
are so the bytes become instead of
kilobytes they become kiwi buys and so
on in an exam you might be asked to
equate between both of these units or
you might need to work out something in
megabytes or maybe bytes so when you're
working with megabytes and if that's
what the answer requires you do four
times a thousand times a thousand which
gives you four million and if you're
working with maybe bytes you go with
four times one thousand and twenty four
times one thousand twenty four
you've gotta be careful and you need to
check the required unit to work out what
the answer is
so are people actually using binary
prefixes well change is always very very
slow and if you look at operating
systems like microsoft windows you'll
probably see that microsoft is still using
using
bytes even though they're equating the
answers using binary prefixes they're
still referring to the end result as
deanery prefixes and this change is
prevalent throughout the industry
however people are trying to change step
by step things will change
at this particular point in time you
should try your hand at this particular
worksheet see if you understand the
difference between both decimal and
binary prefixes
and you should try to work this out
physically instead of using a calculator
perhaps use 2 to the power of 2 or 10 to
the power of something to to get those
longer calculations shorter
there's a few questions on screen which
should take you about 10 to 15 minutes
to do so have a go pause the video
and perhaps
see if you can apply
apply
what you've learned so far by solving
these questions
some of the key terms that we've used so
far are binary which is a base two
number system zero and one only
bits which are obviously short form for
binary digits
and obviously the terms binary prefixes
and dna prefixes which are a set of
letters that proceed a unit of measure
such as a byte and
and
the binary one
indicates multiplication by a power of
two and d
indicates multiplication by a power of ten
ten
and another word that is quite common is
what the magnitude of a number is and
that's the actual value of the number
okay we'll stop the lesson here for today
today
hopefully by now you're familiar with
the syllabus itself and if you're not i
would probably suggest download it and
have a look through that
you've completed a worksheet if you
haven't please go back and do that it's
very useful to practice these i'll try
to put these type of questions in future
videos as well so so you can just
practice what you're learning and of
course have you signed up to ripple.it
and if you have fantastic the other
thing i want to add here is that you
might want to start an exercise book for
note keeping and perhaps use the cornell
note-taking system it's fantastic it's
proven to be one of the best ways to
summarize knowledge look it up
it's just fantastic that's all i'll say
okay that's all for now and we'll catch
up in the next session which will be
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