Today we're going to revise logic gates first of all AND, OR and NOT Let's take a look to AND, first of all I am going to write out a so called a truth table in my old way which it might be slightly different to the way other people lay it out I like to lay these things out as in a sort of square matrix Let's call here on the left input A into my "AND" gate and up at the top I'm going to talk about input B.
It has two inputs and one output and the output from the gate is represented inside this
square area here. So, the A input we're working in binary as ever can take on values of 0 and 1 so can be
okay - AND is very simple. It says the outcome is true which is
normally denoted by a 1 nowadays in binary, the outcome is true only if both of
the inputs are true of course that's what and means in English that must be true
and that must be true so let's do 1 and 1 first of all, 1 and 1 is like true and true yes the outcome is true but if you take
0 and 0, given that 0 means false then the AND can't be true because you're saying
it's false and it's false so the outcome is false - it's a zero
and equally if one of them is true and one of them is false the outcome still is false because the
outcome of an AND gate, for it to be true, both of them have got to be true.
So you end up with a result matrix here look with three 0s in it and only one 1. Now, just this once I
won't do it for all of the others but just this once I shall say, feel free to
write it down like this with a f and a t, standing for true and false, but it's
still the case that under AND logic for the outcome to be true you must have a couple of true inputs here. So that's exactly the image of that
using fs and ts rather than 1s and 0s. If you're an electronics engineer
and you're building some electronics to do these logic functions, what you would
draw is your AND gate with two inputs A and B one output and yeah the
thing to remember is that the AND is a fairly rounded kind of shape at the
front. But the point here is that the outcome of doing A and B together can be
written in lots of ways you can write it as A AND B. Sometimes if you look in
logic textbooks you'll find that they use a thing looking like a little spike down
on the baseline that is the mathematical logicians favorite way of saying AND
but it's the same thing as writing A N D. Very occasionally you'll also see A dot B.
That dot is like the one that some of you will have been taught at high
school to denote multiplication rather than using the multiplying symbol. It was noted early on that AND is a bit
like doing multiplication. Because if you say, what happens if I just multiply the
two inputs instead of doing this AND nonsense. Well 0
times 0 is 0, 1 times 0 is 0, that 1 multiplied by 1, 1 times 1 is 1! You get the same outcome there as if
you'd be multiplying the 1s and 0s with each other and that is why
AND is sometimes called: logical product. OK now we've got the notation
established, we can go ahead fairly quickly now on the other possibilities
here. Let's take a look at the OR gate.
Well, for this which is the so-called INCLUSIVE OR, if you want to give it it's
full name. The rule is that the outcome is true if
either or both of the inputs are true. 1 INCLUSIVE ORed with 1 - 1 OR 1,
well, they're both true, so the outcome is true. 1 ORed with
0, if either one of them is true the outcome is true so you put a 1 there. Similarly 0 ORed with 1 well, one of them is true so the outcome is
true and only 0 ORed with 0 gives you a 0 or a false. So it's called an inclusive OR because
it includes this situation here where they really are both true to start with
writing it down in... what an electronics engineer likes to see Here you come, fast back go faster tail fin there
and it slips around like this There is your OR gate with the A and a B
inputs here it comes the output and again we can either write it down as A ORed with B
or we could say A notice it's the opposite way around to the AND it
looks like a little V on the baseline so you can write it like that or many
people noted very early on when studying mathematical logic that OR does more or
less behave like addition not quite, I mean look at it 0 plus 0 is 0,
0 plus 1 is 1, 1 plus 0 is 1, 1 plus 1 ah... really referring back to the binary
adder video I did a week or two ago 1 added to 1 should really put down
a 0 and carry a 1 but here it's as if the carried bit's retained and held
inside but as far as logicians are concerned a lot of them like to call this the
logical sum. Whereas AND is the logical product. To complete these three there's a very familiar indeed now,
there is a very special one and that's our good old friend NOT, it's special in that
it doesn't take two operands, it only takes one operand. NOT is a simple
inverter, give it a 0 - it will turn it to a 1, give it a 1 - it'll turn it to a 0. So we've only
got one input let's call it a day. What's the outcome? Well, the outcome is a single
column now. It's not a square. Because what you're saying is, if you apply NOT
to 0 - you get a 1, if you apply NOT to 1 - you get a 0. It just flips it, as simple as that.
And the circuit diagram, electronics type notation which is a triangle with
a little circle at the end and what comes out of here. Well, there's lots of... ways of writing
NOT A, you can write it as NOT A, sometimes you'll see it written as
twiddle A. Sometimes you'll see that some logicians like to use a thing like this
little bent crowbar to denote NOT so that can also be used to call the
output NOT A. Those three taken together are what's called
logically sufficient to do anything you want in logic AND, OR and NOT taken
together. Dr. "Heartbleed" - bless his cotton socks - has done even more advanced stuff
with you now which I just mention. If you want to glue a NOT gate onto the
output of an OR gate say, so you do the INCLUSIVE OR but then the moment you
get it's result you flip its direction you turn it over instead of just taking
that and gluing it onto there you're allowed to abbreviate by putting
the circle on the end of the OR gate it's still got the A and B inputs and
it's still got output but notice the moment you do the OR you turn it the
other way around that's what the circle says so that is a
NOR gate and I know for a fact that Dr. Bagley has done that with you in one of
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our memory of how an or gate works so that's an order and he has two inputs
which were labeled as A and B
