Video Transcript
The diagram below shows a logic
circuit consisting of three AND gates. One row of a truth table is shown
below, indicating the output value for one of the possible combinations of input
values. What is the value of 𝑞 in the
table?
This question is asking us to work
out the value of input 𝐴 in this combination of three AND gates. Before we start to tackle this
question, let’s remind ourselves how a single AND gate works.
Recall that an AND gate is a kind
of binary logic gate. It’s called a binary gate because
the inputs and output can each take one of two values, zero or one. An AND gate has two inputs and one
output. It’s called an AND gate because it
only outputs a value of one if both this input and this input have a value of
one. If either or both of the inputs
have a value of zero, then the output of the gate is zero.
In this question, we’ve been given
a combination of three AND gates. The AND gates are connected so that
the inputs to the third gate are the outputs of the first two AND gates. Let’s start by labeling this
diagram with the information given to us in the table. We know that input 𝐴 has an
unknown value labeled as 𝑞. This is the value that the question
is asking us to work out. We also know that inputs 𝐵, 𝐶,
and 𝐷 all have a value of one. Lastly, the output of the third AND
gate has a value of zero.
Since we know both of the input
values for 𝐶 and 𝐷, we can work out the output of this AND gate here. Both of the inputs have a value of
one, so the output of this gate will also have a value of one. The output from this AND gate is
also one of the inputs to this third AND gate here. Looking at this final gate, we know
that this lower input is one, but we don’t know the value of the other input. However, we do know that the output
of this gate is zero.
Now an AND gate outputs a value of
one only if both of its inputs are one. For all other combinations of
inputs, the output of the AND gate will be zero. So, what does that tell us about
the value of this upper input? Well, if this input were also one,
then since both inputs are one, the output of the AND gate would be one. But we know that’s not the case
here. The output of the gate is zero, so
this input must have a value of zero. Then the value of this input is
equal to the output of this AND gate here.
So, looking at this gate, we see
that we have one input value of 𝑞, one input value of one, and an output of
zero. Using the exact same logic as we
did for the last gate that we looked at, we know that since this input is equal to
one, then if 𝑞 were also equal to one, then the output of the gate would be
one. Since we know this output is, in
fact, zero, then 𝑞 must also be equal to zero. So, the answer to this question is
that 𝑞 has a value of zero.
