Combinational Logic


Combinational Logic

Video Lectures created by Tim Feiegenbaum at North Seattle Community College.

We're in section 15-2 and we're sorting out looking at a subject Combinational Logic. A combinational logic circuit can have any number of inputs and any number of outputs. Here we have a combinational logic circuit depicted and we noticed here we have our inputs to the left - A, B going on up to a number of inputs and the same - we have any number of outputs.

The logic states of the inputs at any given instance determine the state of the output. With combinational logic, the inputs will immediately determine what is in the output and these are the circuits we'll be looking at in 15-2. Sequential circuits, which we will look at later, will feature circuits in which outputs are not determined solely by the inputs at the same time.


Logic Gates

Here we have some logic gates. All digital circuits are based upon the interconnection of the various logic gates described. Complex logic circuits are based upon OR, AND and NOT functions along with their derivatives. To the right are typical packages containing multiple gates and they're typically packaged this way, for example, here's one package and it's got six inverters in it. Here's another cheap package and this has four NAND gates. They have just done this simply to make it possible to put more gates on a given circuit board.


Logic Symbols

The standard and the IEC logic symbols for the various logic gates are shown below. The IEC is for the International Electrotechnical Commission. The first ones here to your left and then this group to your left are the standard symbols and then the IEC are the newer symbols and they're kind of self-explanatory. Here we have an inverter and you can see we have a little slash here, it means that inversion. The OR gate - this simply means that the IEC has a greater than or equal to one which is basically what an OR gate does. If you have one input then you get an output.

Here we have a NOR function - the same thing except that you have the slash for the inversion - then this is obviously an AND gate. This is AND with inversion which makes it a NAND. Then equals one here would be the exclusive OR because with exclusive OR you must have a zero and a one to get an output.

Both of them are used in the industry, so if you come up on a schematic and it uses the IEC symbols just use those. If you come upon a schematic and it used the standard use it, but they're both out there. They're both being introduced. A this time though, throughout this text we will use the standard symbols.


Gate Conversions 

Two or more logic gates can be combined to provide the same function as a different type of logic gate. This is often done to reduce the total number of IC packages used in products. Rather than having a whole bunch of different IC packages you can just build a digital circuit with just one type of package and you just use inverters to change it to the device that you need.

We'll look at a couple of these. Here we've got NAND and AND and OR and NOR. What you'll see in this diagram is if we just add inverters we can change the output. Notice here, if we have a NAND gate and we want to change this AND gate to a NAND it's quite easy. Just add an inverter to the output and that's quite obvious. If you add an inverter here then it would be a NAND gate and if we wanted to change from AND to a NAND we could just add another inverter. Now, there would be two inverters here but actually, two inverters would put it right back to the what it was before. Anyway, you can go both ways. The same would be true with these two.

You can also go this way and this way we would add inverters to the inputs. If we have a NAND gate and an OR gate and we need NAND gate, so what we could do - we could come down here - if we added an inverter here and an inverter here let's see what would happen. Remember with a NAND gate, if it had a one and a one then the AND gate would give us a one but since it's inverted we would get a zero. Why don't we check this out and see if that would happen here? If we had a one and a one then we would come in here. Those would be both inverted to zero, so we would have a zero out.

Let's try one more. If we had a one and a zero going in here then the AND gate would produce a zero but it would be inverted and we would get a one. Let's try that and this one as well. If we had a one and a zero going in here, then we would get a one out so that would satisfy that one. Those two could be interchangeable and the same thing would happen with these two.

Let's jump to the next page and we'll look at going across. In this case, we have an OR gate and it says to convert an AND gate to an OR we would have to add inverters to both inputs and outputs. Let's put an inverter here and an inverter here and an inverter here.

In this case with the OR gate if we had a zero and a one we would get a one out. Let's see what happens here. If we had a zero and a one then it would go into the AND gate. AND gate would produce a zero but it would re-invert it so it would get a one.

Let's see if we had a zero and a zero. We'd get a zero out. In this case, if we had a zero and a zero those are both pointing to be inverted to a one, this will output a one but it gets inverted and then it's a zero and it would work this way as well.

The idea here is that you can transform one gate into just about any other gate. ^hen if you are building a given circuit you do not have to have a whole bunch of different gates. You can just use one gate and fulfill all of your needs.

In this section, we looked at gate conversions and we looked at the logic symbols, the standard, and the IEC. We looked at the actual appearance of some of these typical packages and we talked about combinational logic and talked about how it was different from sequential logic.

Video Lectures created by Tim Fiegenbaum at North Seattle Community College.