Question Video: Evaluating the Input of Multiple AND Gates Using Truth Tables | Nagwa Question Video: Evaluating the Input of Multiple AND Gates Using Truth Tables | Nagwa

Question Video: Evaluating the Input of Multiple AND Gates Using Truth Tables Physics • Third Year of Secondary School

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 ๐‘ž in the table?

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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 ๐‘ž in the table?

This question is asking us to work out the value of input ๐ด in this combination of three AND gates. Before we start to tackle this question, letโ€™s remind ourselves how a single AND gate works.

Recall that an AND gate is a kind of binary logic gate. Itโ€™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. Itโ€™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, weโ€™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. Letโ€™s start by labeling this diagram with the information given to us in the table. We know that input ๐ด has an unknown value labeled as ๐‘ž. This is the value that the question is asking us to work out. We also know that inputs ๐ต, ๐ถ, and ๐ท 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 ๐ถ and ๐ท, 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 donโ€™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 thatโ€™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 ๐‘ž, 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 ๐‘ž were also equal to one, then the output of the gate would be one. Since we know this output is, in fact, zero, then ๐‘ž must also be equal to zero. So, the answer to this question is that ๐‘ž has a value of zero.

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