When will the output in each of the following logic gates be zero?
So, firstly, in this question, we’ve got a NOT gate and secondly, we’ve got an AND gate. And we’ve been asked to state the situations in which each one of these outputs is going to be zero. So let’s start with the NOT gate first. Now, a NOT gate is fairly simple. For this gate, whatever the input is, the output is not that. In other words, if we make a truth table for the NOT gate, which is a table that shows the possible values of the input 𝐴 and the resulting output values, then we can say that if the input value is zero, then the output value is not zero. Or in other words, it’s one. And similarly, if the input value is one, then the output value is not one which is zero. This is why it’s called a NOT gate.
And so, if we want to answer the question when will the output in each of the following logic gates be zero, then for the NOT gate, the output is zero when the input is one. And hence, we can say that the answer to our question for the NOT gate is that when 𝐴 is equal to one, the output is zero. Moving on to the AND gate then. Now, a truth table for an AND gate looks slightly different because we can notice that an AND gate has two inputs 𝐴 and 𝐵 in this case. And so, our AND gate truth table will have a column for the input 𝐴, the input 𝐵, and the output.
Now, an AND gate is called an AND gate because the only way for the output value to be one is if both input 𝐴 and input 𝐵 are set to one. In other words, if input 𝐴 is zero and input 𝐵 is zero, then the output has to be zero. Also if we set input 𝐴 to zero once again but this time set input 𝐵 to one, then the output is still zero. Similarly, if we switch input 𝐴 to one but set input 𝐵 to zero, then the output is zero once again. However, if we set both input 𝐴 and input 𝐵 to one, then the output is one. This final row tells us why it’s known as an AND gate because both the first and the second input need to be one in order for the output to be one. But anyway, so this is the truth table for the AND gate.
Now, let’s go back working out when the output for the AND gate will be zero. Well, the output of the AND gate is zero for three different configurations of the inputs: firstly, when both inputs are zero; secondly, when input 𝐴 is zero and input 𝐵 is one; and thirdly, when input 𝐴 is one but input 𝐵 is zero. So we can say that for the AND gate, the output is zero when firstly 𝐴 is equal to 𝐵 is equal to zero; that’s this row here saying both inputs are zero, secondly, when 𝐴 is equal to zero but 𝐵 is equal to one; that’s this row over here, and thirdly, when 𝐴 is equal to one and 𝐵 is equal zero; that’s this row here.
And hence, at this point, we’ve arrived at our final answer. The NOT gate’s output is zero when the input is set to one. And for the AND gate, the output is zero when either both inputs are set to zero or one of the input is set to zero and the other is set to one.