Video: Evaluating the Output of an AND Gate Using a Truth Table

The truth table shows the output of an AND gate for various combinations of inputs. What is the value of 𝑝 in the table? What is the value of π‘ž in the table?

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Video Transcript

The truth table shows the output of an AND gate for various combinations of inputs. What is the value of 𝑝 in the table? What is the value of π‘ž in the table? Okay, so in this question, we’ve been given a truth table for an AND gate specifically. But instead of it being completely filled with zeros and ones, we see that in this location we’ve got the letter 𝑝. And in this location, we’ve got the letter π‘ž. Now the question is asking us to work out the values of 𝑝 and π‘ž. So to do this, we need to remember what the behaviour of an AND gate is. We can recall that the AND gate gives an output of one only if input A and input B are set to one. In other words, in any other combination of input such as zero, zero or zero, one or one, zero, the output is still going to be zero. However, if both inputs are set to one, then the output is going to be set to one as well.

So let’s start by looking at letter 𝑝. We can see that letter 𝑝 represents the output of an AND gate in the situation where input A is set to zero and input B is set to one. Well, in this case, both of the inputs aren’t set to one, only one of them is. And so the AND gate will give an output of zero. And hence, we can say that the value of 𝑝 in the table is zero. So let’s move on to looking at letter π‘ž. Now π‘ž represents the output when input A is set to one and input B is set to one. And as we can see from the statement here, when both inputs are set to one, then the output of the AND gate will also be set to one. And hence, we can say that the value of π‘ž in the table is one.

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