The diagram shows a NAND gate. If input 𝐴 is one and the output is one, what is input 𝐵?
Okay, so in this question, we can see that we’ve got a NAND gate in our diagram. And along with this, we’ve been told that input 𝐴’s value is one and the output is one as well. We need to use this information to find what input 𝐵 is. So to work this out, we need to recall the truth table of a NAND gate. So here is the truth table of the NAND gate. Now, an easy way to memorize this truth table is to actually think of a NAND gate as a NOT-AND gate. And the reason we say this is because, starting with an AND gate, we can recall that an AND only produces an output of one when both the inputs 𝐴 and 𝐵 are one.
In other words, this is the truth table of an AND gate. Only if both of input 𝐴 and input 𝐵 are one, then the output is one. And in every other scenario, the output is zero. And then in order to take this AND gate and turn it into a NAND gate, we take all of the output values of the AND gate and flip them, just like how a NOT gate takes its input values and flips the output values. In other words, all the zeros become ones and all the ones become zeros. And that’s how we arrive at this truth table. We can see that it looks similar to the truth table of the AND gate except that where there are zeros in the AND gate, we have ones. And when there’re ones in the AND gate, we have zeros.
So that’s how to memorize the truth table of a NAND gate. Coming back to the question at hand then, we need to find the row in this truth table that corresponds to input 𝐴 being one and the output being one as well. So if we want input 𝐴 to be one, then we need to look at one of these two rows. And if we want the output to be one as well, then we specifically need to look at the third row of the table because only in this row is input 𝐴 one. And the output is one as well. And this row tells us that the value of input 𝐵 must be zero. Therefore, that’s the answer to our question. If for a NAND gate input 𝐴 is one and the output is one, then input 𝐵 must be zero.