The diagram shows two OR gates where the output of the first OR gate is one of the inputs to the second. If input 𝐴 is zero, input 𝐵 is zero, and input 𝐶 is one, what is the output?
The question is asking us to work out the output from this logic circuit containing two OR gates. We’ve got this OR gate over here on the left, which has got two inputs labeled as 𝐵 and 𝐶. The output from this left-hand gate then becomes one of the two inputs for this OR gate over here on the right. The other input to this right-hand OR gate is labeled as input 𝐴. We’re told that input 𝐴 has a value of zero, input 𝐵 has a value of zero, and input 𝐶 has a value of one. In order to work out what happens to these input values, 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 two inputs are equal to zero, then the output is zero. We can use this description of how an OR gate works to write out a truth table for it. This truth table tells us what the output of an OR gate will be for each combination of the two input values. We know that this output will be one if either of the two inputs or both of them have a value of one, and the output will be zero if both inputs are zero.
So then in our truth table, we can say that a first input of zero and a second input of zero gives an output of zero. If the first input is zero but the second input is one, then the OR gate’s output will be one. Likewise, if the first input is one and the second input is zero, the output will also be one. Finally, both inputs to an OR gate equal to one again gives an output value of one.
Now that we’ve got this truth table, we can use it to help us work out what happens to these input values in our logic circuit. We’ll begin by looking at this left-hand OR gate. The first input to this gate is input 𝐵, which has a value of zero, and the second input is input 𝐶, which has a value of one. We can see that a first input of zero and a second input of one corresponds to the second row in our truth table. The table then tells us that in this case the output of the OR gate must have a value of one. So let’s add this output value to our diagram.
Now we need to consider the second OR gate over on the right. Its first input is input 𝐴, while its second input comes from the output of the left-hand OR gate. We know that input 𝐴 is zero, and we just found that the left-hand OR gate had an output value of one. This means that for the right-hand OR gate, the first input is zero and the second input is one. Just like before with the left-hand OR gate, a first input of zero and a second input of one corresponds to the second row in our truth table. This means that the output from this OR gate has a value of one. This output of one is then the output from the circuit as a whole. That output is exactly what we were asked to find.
So our answer to the question is that for these three input values, the output is equal to one.