Video: Evaluating the Input of AND Gates

The diagram shows an AND gate. If input A is 1 and the output is 0, what must input B be?

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Video Transcript

The diagram shows an AND gate. If input A is one and the output is zero, what must input B be?

Okay, so in this question, we can see that we’ve got an AND gate. And we’ve been told that the input A is one and the output is zero. Based on this information, we need to work out what input B is. Now to answer this question, we can recall the truth table for an AND gate. So here’s the truth table for an AND gate. Now, one way to memorize this truth table really easily is to remember that the reason this gate is called an AND gate is because the output can only be one if input A is one and input B is one. In other words, we need input A to be one and input B to be one for the output to be one.

In every other situation, regardless of what other combination of inputs we have, the output will always be zero. So in this question, we’ve been told that input A is one and the output is zero. And hence, we need to find the row in this truth table that corresponds to that. In the very first row, input A is zero. So we’re not looking at this row. In the second row, input A is also zero. So we’re not looking at this one either. The third row shows input A to be one. So we could be looking at this row. And the same is true for the fourth row. Input A is one.

Now, let’s look at the values of the output, specifically for the two rows that we haven’t yet cancelled out. In other words, we need to look at these two rows. And out of these two rows, we see the one that has an output of zero is the third row. In other words, because the fourth row has an output of one, we’re not looking at this row either.

So now, we see from the third row that input A is one and output is zero. And this means that input B must be zero. And so we can write a zero next to input B. So at this point, we found the answer to our question. If input A is one and the output is zero, then input B must be zero.

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