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All right. Good morning. Let's get started. So the last lecture we showed you how to go digital. The fact that going digital had some key benefits for us. And what we'll do today is go inside the digital gate.

Let's do a quick review. We began life by observing nature. We said those Maxwell's equations are tough. Let's simplify our lives by discretizing or lumping matter. So we got the lumped circuit abstraction.

Then we had this noise problem here. In order to be able to handle that let's do some more discretization, some more lumping. So we said let's discretize values and deal with two levels, a high and a low.

That's where the binary voltage levels come up, a high level and a low level. And then we said that in discretizing it we have to make some assumptions. We have to impose some constraints on ourselves.

Just as with the lumped matter discipline, we imposed a couple of constraints in going from the continuous matter world to a lumped matter world. Similarly, we have to impose some discipline on ourselves, some constraints on ourselves in going from the continuous value regime to the digital value regime.

And that discipline is called the static discipline. And what the static discipline says is that if you have senders and receivers in a digital system then they all need to adhere to some standard.

If I was a sender I had to adhere to some tough output standards. I had to be sure to shift values that exceeded some high voltage threshold. And if I was sending a low value I had to make sure my values were lower than some output low voltage threshold.

Similarly, if I was the receiver then I had to guarantee to recognize as a one all voltages that where above some input high voltage threshold. And similarly I had to guarantee to recognize as a zero voltages that were below some input low voltage threshold.

So provided senders and receivers in a system adhere to these voltage levels, to this discipline then they would all very comfortably work correctly in a digital system. Then we also said that once you deal with such values, one you deal with digital values we can now postulate a bunch of digital elements that process these values in a manner very reminiscent of our analog circuits where we get analog signals.

And you've already learned how to process analog signals. You've learned about resistor dividers and so on and so forth. You feed in an analog signal and you get an output analog signal as well. Now, here the resistor in the analog domain, elements like resistors and voltage sources were the symbols that you dealt with.

Here, in the digital domain, the primitive elements that we will be using are called gates. As one example, this is called the NAND gate. So we looked at the AND gate in the previous lecture. This is an example of another gate called the NAND gate.

The NAND gate has the following truth table. Our two inputs A and B and this output C. And the NAND gate works as follows. The output — In English I can describe its properties as the output is a high at all times when at least one of these inputs is a low value.

So it's high whenever at least one input is a low. So it's high here. It's high here. Oops, it's high here, high here. And when, oops. And when both inputs are a high the output is a low. This is a NAND gate.

Notice that these are exactly complimentary to the AND gate. The AND gate outputs were 0-0-0-1. And the AND gate symbol looked like this.

Let's do a quick review. We began life by observing nature. We said those Maxwell's equations are tough. Let's simplify our lives by discretizing or lumping matter. So we got the lumped circuit abstraction.

Then we had this noise problem here. In order to be able to handle that let's do some more discretization, some more lumping. So we said let's discretize values and deal with two levels, a high and a low.

That's where the binary voltage levels come up, a high level and a low level. And then we said that in discretizing it we have to make some assumptions. We have to impose some constraints on ourselves.

Just as with the lumped matter discipline, we imposed a couple of constraints in going from the continuous matter world to a lumped matter world. Similarly, we have to impose some discipline on ourselves, some constraints on ourselves in going from the continuous value regime to the digital value regime.

And that discipline is called the static discipline. And what the static discipline says is that if you have senders and receivers in a digital system then they all need to adhere to some standard.

If I was a sender I had to adhere to some tough output standards. I had to be sure to shift values that exceeded some high voltage threshold. And if I was sending a low value I had to make sure my values were lower than some output low voltage threshold.

Similarly, if I was the receiver then I had to guarantee to recognize as a one all voltages that where above some input high voltage threshold. And similarly I had to guarantee to recognize as a zero voltages that were below some input low voltage threshold.

So provided senders and receivers in a system adhere to these voltage levels, to this discipline then they would all very comfortably work correctly in a digital system. Then we also said that once you deal with such values, one you deal with digital values we can now postulate a bunch of digital elements that process these values in a manner very reminiscent of our analog circuits where we get analog signals.

And you've already learned how to process analog signals. You've learned about resistor dividers and so on and so forth. You feed in an analog signal and you get an output analog signal as well. Now, here the resistor in the analog domain, elements like resistors and voltage sources were the symbols that you dealt with.

Here, in the digital domain, the primitive elements that we will be using are called gates. As one example, this is called the NAND gate. So we looked at the AND gate in the previous lecture. This is an example of another gate called the NAND gate.

The NAND gate has the following truth table. Our two inputs A and B and this output C. And the NAND gate works as follows. The output — In English I can describe its properties as the output is a high at all times when at least one of these inputs is a low value.

So it's high whenever at least one input is a low. So it's high here. It's high here. Oops, it's high here, high here. And when, oops. And when both inputs are a high the output is a low. This is a NAND gate.

Notice that these are exactly complimentary to the AND gate. The AND gate outputs were 0-0-0-1. And the AND gate symbol looked like this.

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