So anything that has two states corresponds
to one bit.
Heads or tails, as well as true or false, zero
or one.
If you have four states, that corresponds
to two bits.
But now what corresponds to three bits?
Would it be six states?
No, actually what happens is that you have
eight states.
That corresponds to three bits.
So why is this so?
So if I look at three bits, I can have zero
zero zero, zero zero one, zero one zero,
zero one one, one zero zero, one zero one,
one one zero and one one one.
Three bits, eight states.
All I'm doing is just counting out and here
you see me counting in binary notation.
These are just the numbers zero, one, zero
one zero is two in binary notation, zero one
one is three, one zero zero is four, one zero one
is five, one one zero is six, one one one is seven,
which shows the rationale behind the old joke,
which is that there are ten different kinds of
people in the universe. Those who understand
binary notation and those who don't.
If I go to more bits, so if I have n bits, where
n is equal to one, two, three, et cetera,
what it means is that I have two to the n
different possibilities.
Or sometimes called states.
So I can have 00....0, 00....1, 00....10, 00....11,
you can tell, there's a heck of a lot of possibilities
here, and end up going 11111....1.
So this is zero, this is one, this is two,
this is three and this is two to the n minus one,
because two to the n would be 1000.....0,
which is two to the n.
So when you are counting in binary, when
you have bits, you have for a relatively small
number of bits, you can have a very very very
large number of possible states, possible things
that you could label with these bits.
In fact, it's an interesting question to ask
how many bits are there in the universe?
How many bits in the universe?
Well, this seems kind of a crazy question,
you would think.
There's an infinite number of bits in the
universe.
But actually this is not so, if you look at
it in our universe, which is the part that
we have access to since the Big Bang, which
was, last time I read, 13 * 10^9 years ago.
So the part of the universe that could be
within 13 billion light years in any direction,
this amount is actually finite.
This is a rather surprising result that the
amount of information in the universe is finite.
It comes from the laws of quantum mechanics,
but it turns out that within the universe,
there are 10^90 particles, most of these are
microwave photons from the black body,
radiation that is left over from the Big Bang.
They are all over the place, they are around us
right now.
There are particles of light, wavelength is
roughly about that size.
There are 10^90 of them, so this is a one
followed by 90 zeros, in ordinary digital notation,
and each of these particles carries a few bits
of information with it.
And in fact, if you go to the absolute limits
that are allowed by the Laws of Physics,
the total number of bits that could be
allowed would be 10^120,
which is a one followed by 120 zeros.
These are large numbers of bits, but they're
not infinite.
They're big numbers, but I could think of much
bigger numbers.
For instance, 10 to the 120 plus one is bigger
than 10 to the 120.
Or 10 to the 220, or 10 to the 240.
There are large numbers, but there's a finite
number of bits, and a large number of bits but
it's finite.
Now what does this mean?