Video Transcript
In this video, we will be looking
at a type of logic gate known as an OR gate.
Now a logic gate is a component
with one or more inputs and one output, each of which can take on two values: zero
or one. In other words then, each one of
these inputs and outputs is known as a binary input or output. Bi- meaning two because it can take
on one of two values, zero or one. Now, based on the values of the
input or inputs as well as the behaviour of that particular logic gate, the value of
the output is decided. Now before we discuss specific
properties of OR gates, let’s just consider a generic logic gate, in this case one
which has one input, and discuss some terminology first.
Now, as we’ve already said, the
input or inputs as well as the output on a logic gate can take one of two
values. For example, the value of the input
could be zero or one and the same is true for the output, zero or one. However, sometimes, we use slightly
different terminology. For example, instead of saying that
the input or output in question is set to zero, we may say that it’s set to
false. And conversely, if either one of
them is set to one, we can instead say that it’s set to true. In other words, instead of saying
that an input or an output is set to zero or one, we can instead say that it’s set
to false or true. Or we could also say that instead
of zero or one or false or ture that the input or output in question is set to off
or on.
Now, these are just different
terminologies. It doesn’t matter which set of
terminology we use as long as we know what we’re talking about. Zero corresponds to false or to off
and one corresponds to true or to on. It’s worth noting by the way that
we most commonly use the off or on terminology when talking about logic gates in
electrical circuits. We can say that an input to a logic
gate is set to on if there is a current flowing through that input and it’s set to
off if there is no current flowing through that input. And of course, the same applies to
the output of the logic gate. In other words, based on whether or
not there is a current flowing to the inputs of a logic gate, the gate will dictate
whether there is a current flowing out of it as well.
So the way that we’ve drawn the
diagram here, we can see that the top input is set to one, whereas the bottom input
is set to zero. But then, the output of the logic
gate that we’ve drawn here is set to one. Or conversely, we could say that
the top input is set to on, but the bottom input is set to off and the output is set
to on. Or we could use the true, false
notation as well if we wanted to. But anyway, so the diagram that
we’ve drawn here happens to be that of an OR gate. So let’s look at OR gates in more
detail now.
The first thing to consider is that
this is the symbol that we use to represent an OR gate. As we can see, it’s got two inputs
which are traditionally represented on the left-hand side of any logic gate and one
output which is traditionally represented on the right. As well as this, we can see that
the gate itself is represented almost as a D shape, but the left-hand edge is curved
rather than being a straight line. Now the whole point of a logic gate
is that depending on the values of these inputs, a specific output would be
produced. And each logic gate behaves in a
slightly different way. So to truly understand the
behaviour of an OR logic gate, let’s set up something known as a truth table.
Now, a truth table is just a table
that shows us what the output value of an end gate will be for every possible
combination of input values. And the reason it’s called a truth
table is because it shows the particular combination of inputs that will result in a
true output or an output of one or on. So to start building a truth table,
we need to set up a column for each one of the inputs as well as a column for the
output. So let’s say that the first input
to our logic gate we will call input A and the second input we will call input
B. And of course, the output we will
call the output since there’s only one of them.
So here’s the skeleton of our truth
table. We’ve got a column for input A,
another one for input B, and one more for the output. So let’s start filling in this
truth table by saying that the first instance involves both input A and input B,
being set to zero. So we can put on our truth table
that input A is set to zero and input B is set to zero. Well, in this situation, the
behaviour of the OR gate is such that the output is also zero.
Now second scenario: let’s say we
keep input A at zero, but we change input B to one. Well, in this situation, the output
of the OR gate also becomes one. And so, we can put on our truth
table that input A was set to zero, but input B was set to one, resulting in an
output of one. Moving on to the third scenario
then. Let’s now set input A to one but
put input B back to zero. Well, in this case, the OR gate
still returns an output of one. And so on our truth table, we can
say that input A was set to one and input B was set to zero, resulting in an output
of one.
And then, there’s one more
combination of inputs that we can put on our truth table. This time, both input A and input B
are set to one and the output is still one. And so in our truth table, we can
say that input A is one, input B is one, and the output is one as well. Now, why is this? Why is it that an OR gate behaves
in this particular way for these combinations of inputs? Well, the reason for this links
back to why an OR gate is called an OR gate in the first place. The name of the OR gate comes about
because an OR gate gives an output of one or true or on if either input A or input B
is set to one or true or on. And we can see that that’s true
from the truth table that we’ve set up.
In the first instance, both into A
and input B are zero and so the output is zero. However, in the second instance, we
switch one of the inputs to one. In this case, it’s input B. And immediately, the output of the
OR gate becomes one as well. In the third instance, input A is
set to one resulting in an output of one. And in the fourth instance, both
inputs are set to one. And so, we have an output of
one. In other words, if either input A
or input B is set to one, then the output becomes one as well. And in the final instance, both are
set to one and the output is still one.
Now in order to clarify our
understanding a little bit more about how OR gates work, let’s think about a very
simple situation in which an OR gate can be used. Let’s say that we have an OR gate
here connected in an electrical circuit. And the output of this OR gate is
connected to a lamp. Now, recalling the truth table for
an OR gate from earlier, we can see that if both inputs to the OR gate are set to
zero, then the output is set to zero as well. In other words, if there’s no
current in either of the inputs, then there’s no current in the output. However, as soon as we pass a
current through one of the inputs, let’s say input A, then immediately there’s a
current flowing through the output of the OR gate. And so, the lamp switches on. And this would also be true if
input B was set to one but input A was set to zero or of course if both inputs are
set to one.
Now this is quite a useful thing to
have because it could act like a double switch. Specifically, both input A and
input B could be different switches in different parts of a room to this lamp over
here. So if you wanted to switch on the
lamp, you could turn on any one of the two switches. So that might seem quite
useful. But the annoying thing is that if
you want to turn off the lamp at any point, it will not do to simply turn off one of
the switches. You will have to turn off the
current into both inputs. So a slightly flawed double switch,
but you can see how this might be useful in a circuit.
Now in real life, OR gates combine
with other logic gates, form a very important part of the circuitry that we can find
inside computers. But anyway, so now that we’ve had a
fairly detailed look at OR gates, let’s have a look at an example question.
The diagram shows the circuit
symbols for four logic gates. Which symbol represents an OR
gate?
Okay, so we need to find the
diagram for an OR gate. So let’s go through each one of the
options one by one. Now the first option looks almost
like the diagram for an OR gate. However, this little circle at the
right-hand end of the gate just before the output means that this cannot be an OR
gate because the circle means that the gate beforehand gets inverted. In other words, whatever the
behaviour of this gate before the circle, the circle will take the output value in
each case and then flip it. So if we were going to have an
output of one, the circle will take it and turn it into zero and vice versa. And so, in reality, option a) is
actually the diagram of a NOR gate, where it’s almost like an OR gate, but with a
NOT gate after it. So this cannot be the answer to our
question.
Option b) then, we see first of all
that it’s got a very nice D shape to it. And secondly, it’s got that little
circle at the right-hand end as well. Now, D-shaped gates are actually
AND gates. And the way to remember that is the
word AND has a D at the end. And hence, the AND gate is a
D-shaped gate. However, remember what we said
about the little circle earlier. It flips the output of the AND
gate. And so, the whole gate including
the circle is now a NAND gate, in other words a NOT AND gate or an inverted AND
gate. And hence, this cannot be our
answer either.
Moving on to option c) then, we can
see that it’s a D-shaped gate without anything on the right-hand end. And so, this is a traditional AND
gate. Hence, this is not the option we’re
looking for. And then finally for option d), we
can see that this is the shape of an OR gate. It’s almost a D-shaped gate but
with a curved left-hand edge. And so at this point, we found the
answer to our question. The symbol that represents an OR
gate is option d) in this case.
Okay, so now that we’ve had a look
at this question, let’s take a quick look at another one.
The truth table shows the output of
an OR gate for various combinations of inputs. What is the value of 𝑝 in the
table? What is the value of 𝑞 in the
table?
Okay, so in this question, we’ve
been given a truth table, specifically for an OR gate. But instead of it being completely
filled with zeros and ones, we can see that in this position we’ve got the letter 𝑝
and in this position we’ve got the letter 𝑞. And in this question, we need to
try and work out the values of 𝑝 and 𝑞. So to do this, we need to remember
what the behaviour of an OR gate is. We can recall that for an OR gate,
the output is one if either input A or input B is set to one.
So we can see that on the first row
of the table, both input A and input B are set to zero and therefore the output is
zero. However, in the second row of the
table, input A is set to zero, but input B is set to one. And so, this condition is
fulfilled: either input A or input B is one. In this case, input B is one. Therefore, the value of 𝑝, the
value of the output in this case, is going to be one. And hence, that’s our answer to the
first part of the question.
Now moving on to the third row, we
can see that the value of input A is one, but input B is zero. However, because at least one of
the inputs is one, the condition is fulfilled yet again. And so, we see that the output is
one. And then, finally, moving on to the
final row, both inputs are set to one. And so this condition is actually
fulfilled. Now, note when we say that either
input A or input B is one, that does not mean that only one of them can be one. In fact, if either of these inputs
is one or both of them is one, then the output is still going to be one. And that is the behaviour of an OR
gate. If we instead said that the output
can only be one, if either input A or input B exclusively were one, in other words
only one of the inputs could be one, then that is the behaviour of an XOR gate or an
Exclusive OR gate, which is a different logic gate entirely.
And so, as an answer to this
question, we can see the value of 𝑞 in this case for a normal OR gate is going to
be one. And that is our answer to the
second part of the question.
Okay, so now that we’ve had a look
at a couple of example questions, let’s summarize what we’ve talked about in this
lesson.
Firstly, we saw that an OR gate is
a logic gate with two binary inputs and one binary output, where the word binary
means that it can take on one of two values: zero or one or if we like false or true
or off or on. We saw that specifically for an OR
gate, the output is one if either input A or input B or both is set to one. And finally, we saw that OR gates
along with other logic gates are very useful in electrical circuits and they’re
commonly used in the circuitry found in computers.
