Logic Gate Combinations

This is the second in a series of videos introducing

logic

gate

s and covers creating truth tables for

combinations

of simple

logic

gate

s. Logic gate

combinations

manipulate pulses of electricity, and because these pulses represent binary ones and zeros, logic gate combinations can perform useful data operations such as comparing values, performing arithmetic, and even storing data, creating truth tables. for combinations of logic gates is an extremely important aspect of computer circuit design because truth tables can help us see how circuits work, let's start by reviewing the basic components, this is a In the acht gate, the input has been labeled as a and the output has been labeled Zed.

You can see from the truth table that when a is 0, Zed is 1 and when a is 1, Zed is 0, this is a gate and there are two inputs here when both the inputs are 1 the output at Zed is 1 in all the other circumstances the output is 0 by convention the combinations of inputs count up in base 10 this helps ensure that they are all covered and finally this is the door or when all the other input is 1, the output is 1 and also when both inputs are 1 the output is 1 here is a combination of gates, the general combination has two inputs and one output but there are two gates involved to generate a truth table for this. combination of gates it is useful to consider the point C each value of C is the result of passing a and B through a gate or you can see when one or the other of a and B or both are 1, the value in C is 1, so to get the value of Z we pass each value of C through a zero.

You can see that each value of Z is simply the inverse of C, so here is our general truth table and we can discard column C if we are not interested in those values. This combination of gates is sometimes called not all or nor combination for short it is actually very useful as you will see in a later video this combination is an and gate followed by a not gate to get the values ​​in Zed that we can consider . Position C, first of all, each value in C is simply the result of passing combinations of a and B through a gate and you can see in the bottom row when both a and B are 1, the value of C is 1 for get each value of Z. then we pass each value of C through a not gate, so here is our truth table.

We can ignore the values ​​of C if we are not interested. This combination of gates is also extremely useful and is sometimes called knot and merge or simply NAND for In summary, here is an example involving 3 logic gates, the values ​​of a and B are passed through non-gates before being combined through of a door or to produce a truth table for this combination. It is useful to consider points C and D. Each value of C is simply the inverse. of each value of a, each value of D is simply the inverse of each value of B and now that we have values ​​for C and D we can combine them through a gate o to give us each value of Z here is our truth table. ignore C and D now, you may have noticed that this truth table is exactly the same truth table for the not and combination that we saw earlier.

It is not uncommon for different door combinations to produce the same result. Here's another example you might like. Try it yourself, pause the video now if you want to try it and continue in a few minutes. Now I will show you the solution, just as we did before, it is useful to consider points C and D, each value of C is the result. of passing each value of a through a not gate each value of D is the result of passing each value of B through a not gate and now that we have values ​​of C and D we can pass combinations of these through an and gate giving as each value of what was said here is our truth table, did you get the same?

You may have noticed that this is the same truth table as the non-complete join you saw earlier in this example. We have three inputs, A B and C, and only one output, which means our truth table has eight rows, each combination of B and C must count up in base 10 to ensure you have them all covered. To solve this, we need to consider the intermediate point D that each value of D can be reached by passing pairs of values ​​for B and C through a gate or, then we take each value of a along with each value of D and pass them through a gate and here is the result here is another example, maybe you would like to try this Pause the video now if you want to try it and I will show you the solution in a few moments.

When you continue solving this, you will consider the intermediate point D. Each value of D comes from passing pairs of values ​​for B and C through a gate and and then each value of Z comes from passing pairs of values ​​of D and a through a gate or got this result in this example, we have three inputs like we did before, but notice that input a has been split into input a is feeding the top and bottom and the door in this example, you are also asked to include the intermediate points D and D in the truth table; otherwise there's nothing terribly new here to get each value of D we pass combinations of a and B through a and gate so to get each value of e we pass combinations of a and C through a gate and now that we have pairs of values ​​for D and E we can pass them through a gate or to give us values ​​of Z here is a similar example if you would like to try this, pause the video now and I will show the solution in a moment.

This time you will be asked to create the truth table from scratch. Okay, before we address this, notice that entry B has been split. B is feeding the top, the door, and the door hit because we only have two inputs, we're only going to need four rows in the truth table. First, calculate the values ​​of C. Each value of C can be arrived at by passing combinations of a and B through a gate and then we calculate the values ​​of D each value of D is simply the inverse of each value of B and finally to obtain each value of Zed we pass combinations of C and D through the second gate and here is our truth table in this example we have four inputs, which means we are going to need 2 to the power of 4, that is, 16 combinations of inputs and , therefore, 16 rows in the truth table.

You might want to try it yourself. I'll show you. the solution in a moment and here is the solution notice how we are counting from zero to 15 while reading the combinations of input values ​​each value of e is A and B each value of F is C and D and each value of Z is E or F , if you've done yours as I suggested, you should have exactly the same truth table. This final example seems a little more complicated than anything you've seen before, but there's nothing new here. Review it systematically and you will arrive. get a result, why not try it yourself?

Well, before we tackle this one, notice that input A has been split, it's feeding the top gate and the bottom gate and the gate. Also notice that the input B has been split, B is feeding the bottom gate and the top gate to produce a truth table, we need to consider the intermediate points C D E and F, so we will need a truth table with four rows and seven columns starting with C C is simply not a, so D is simply not B now that we have C and D we can consider that e e is B and C F is a and D and finally Z is E or F here is our truth table.

This is actually a very useful combination of logic gates. It is sometimes known as the exclusive whole or X for short. If you look at the truth table you can see that it is almost the same as a gate or when one or the other input is 1 the output is 1, when both inputs are 1 the output is 0 so literally if a or another the input is 1, the output will be 1 exclusively, this combination of doors even has its own symbol