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 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 𝑟 in the table?

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Video Transcript

The diagram 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 𝑟 in the table?

This question is asking us to work out the value of input C 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 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 gates. Let’s begin by labeling the diagram with the information given to us in the table. We know that inputs A, B, and D all have a value of one and that the final output has a value of zero. Input C has a currently unknown value of 𝑟. To answer this question, we need to work out whether 𝑟 has a value of zero or one.

Let’s start by looking at this AND gate here with inputs A and B, since we know the values of both of these inputs. Both these two inputs are equal to one, which means that the output of this gate will also be one. Then, the output of this AND gate is connected to the upper input of the final AND gate, so we know that this input has a value of one.

So, what does that tell us about this input here? Well, let’s recall that an AND gate only outputs a value of one if both of its inputs are one. If both this upper input and this lower input were equal to one, then the gate would output a value of one. Since this upper input is one, but the gate still outputs a value of zero, we know that this lower input must have a value of zero. This input is equal to the output of this AND gate here, with inputs C and D.

If we look at this gate, we see that we have one input with a value of one and an output with a value of zero. We need to work out the value, 𝑟, of input C. We can apply the exact same logic that we used with the previous gate. Since this lower input is a one, but the gate still outputs a zero, we know that 𝑟 must have a value of zero. If the input were one, then the gate would instead output a one. So we have worked out that 𝑟 must have a value of zero. This is the final answer to this question.

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