Question Video: Finding the Inputs to a Circuit Consisting of OR Gates | Nagwa Question Video: Finding the Inputs to a Circuit Consisting of OR Gates | Nagwa

# Question Video: Finding the Inputs to a Circuit Consisting of OR Gates Physics • Third Year of Secondary School

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The diagram shows a logic circuit consisting of three OR gates. How many of the inputs must have a value of 0 in order for the output to have a value of 0?

04:08

### Video Transcript

The diagram shows a logic circuit consisting of three OR gates. How many of the inputs must have a value of zero in order for the output to have a value of zero?

We’ve got a diagram here that shows a logic circuit with three OR gates in it. The circuit has four inputs, which are labeled as 𝐴, 𝐵, 𝐶, and 𝐷. Inputs 𝐴 and 𝐵 are the two inputs to this upper OR gate on the left, while inputs 𝐶 and 𝐷 go into this lower OR gate. The output from each of these left-hand OR gates then becomes one of the two inputs for this OR gate over here on the right. Then, the output from this right-hand OR gate is the overall output of this logic circuit as a whole.

We’re being asked to consider the case where this output has a value of zero. Our job is to work out how many of these four inputs need to have a value of zero in order to get this output value of zero. In order to do this, since these inputs and this output are connected by this circuit consisting of OR gates, then we’re going to need to recall how an OR gate works.

An OR gate is a type of logic gate that gives an output of one if either of the two input values or both of them have a value of one. Otherwise, so if both of the inputs are equal to zero, then the output of an OR gate is zero. We can use this information in order to draw a truth table for an OR gate. This truth table is a table which lists all of the different possible combinations of the two inputs to the OR gate, along with the output value that will be produced by each such pair of inputs.

If both of the two inputs to an OR gate are equal to zero, then it’s not true that either or both inputs are one. And so, we’re looking at the second bullet point here, which tells us that the output will be zero. If the first input is zero, but the second input is one, then now this first bullet point is true because we do have one of the inputs equal to one. And so, the output from the OR gate will be one. Likewise, if the first input is one and the second input is zero, then again we’ll have an output of one because this first bullet point doesn’t distinguish between the two inputs. It’s just that to get an output of one, at least either one of the two inputs has to be equal to one.

The final case to consider is when both of the two inputs have a value of one. Again, this first condition is met because it says that either or both of the inputs must be equal to one in order to get an output of one. And so when both inputs are equal to one, we know that the OR gate will give an output of one. Now that we’ve written out this truth table, we can use it to help us work out what’s going on in this logic circuit.

We’ll start by considering this OR gate on the right-hand side of the circuit. We know that this gate has to have an output with a value of zero. If we look at our truth table, we can see that the only way to get an output of zero from an OR gate is if both of the two inputs have a value of zero. So then both of the inputs to this right-hand OR gate must be equal to zero. We know that the top input is the output from the upper left-hand OR gate, while the bottom input is the output from the lower left-hand OR gate. What this means is that both of these left-hand OR gates must have an output value of zero.

Now, as we’ve already seen, we know from our truth table that the only way to get an output of zero from an OR gate is if both of the two inputs are equal to zero. So, for this upper left-hand OR gate with an output value of zero, both of its inputs, so that’s input 𝐴 and input 𝐵, must be equal to zero. Similarly, since the lower left-hand OR gate also has an output value of zero, then its inputs, input 𝐶 and input 𝐷, must also be equal to zero.

What we found is that in order to get this output value of zero, all four of these inputs must have a value of zero. So, our answer is that in order for the output to have a value of zero, the number of inputs which must have a value of zero is equal to four.

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