An application of the
exclusive-OR gate |
Integrated
circuit NAND to replace other types of circuits |
3 NOR-circuits to replace a
circuit AND |
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Created it, 06/10/19
Update it, 06/10/24
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5. - THIRD EXPERIMENT : EXAMINATION OF AN EXCLUSIVE-OR GATE
You will use now the integrated circuit MM 74C86 including/understanding 4 exclusive-OR gates as you can note it in the electric diagram of figure 12.
Since the two entries and the exit of the first exclusive-OR gate to test do not correspond at the boundaries of the NOR-circuit examined previously, you must carry out new connections in the following way :
a) Disconnect the food and remove the connections relating to the preceding experiment.
b) Remove the integrated circuit MM 74C02 of support ICX and introduce into this one the integrated circuit MM 74C86.
c) Connect the points indicated below :
stitch 1 of the integrated circuit MM 74C86 and contact SW0,
stitch 2 of the integrated circuit MM 74C86 and contact SW1,
stitch 3 of the integrated circuit MM 74C86 and the L0 contact.
d) Put two switches SW0 and SW1 on the position corresponding to symbol 0, thus the two entries of the exclusive-OR gate are both on the level L.
e) Feed the circuit again,
Now you can check the operation of the circuit in question, while proceeding as for the preceding experiments. Check for each of the four possible combinations of the levels of the two entries, the corresponding level of exit. Write the table of operation thus then the truth table in positive logic of the exclusive-OR gate. Compare then the results obtained with those indicated in the two tables of figure 13.
By examining the table of operation of the figure 13-a, you will note that the principal characteristic of the exclusive-OR gate is to give an exit to the level H when the two entries are on different levels. When the entries are both on the same level L or the level H, the exit is on the level L.
Because of this operating feature, the exclusive-OR gate is sometimes used like detector of difference.
5. 1. - AN APPLICATION OF THE EXCLUSIVE-OR GATE
You will now carry out a exercise how an exclusive-OR gate can find applications as a ordered reverser.
In other words, you will check how in practice, by using one of the two entries like entry of order, at exit of the exclusive-OR gate you obtain the signal present on the other entry, reversed or not according to the level which is on the entry of order.
Let us suppose that you use the entry connected to pin 1 like entry of order :
Leave unchanged the connections made during the
preceding experiment and put two switches SW0
and SW1 on the position corresponding to
symbol 0 ; thus, entry 1
as well as entry 2 are on the level L.
By observing the LED L0, you note that it is extinct what wants to say that the exit of the circuit is on the level of tension L.
Bring now entry 2
of the circuit to the level H by commutating
SW1 on position 1.
You note this time that the LED L0 ignites what indicates that the exit is on the level H. You can thus observe that with the entry of order on the level L, the exit is on the same level as entry 2.
Bring then entry 1
of order to the level H, by commutating SW0
on the position located by symbol 1.
Alternatively put switch SW1
on position 1 and position 0,
applying thus successively to entry 2 a
level H or a level L.
By observing the indicator of the LED L0, you note that when entry 2 is on the level H, the exit is on the level L and vice versa. The demonstration is thus made that under this condition, i.e. with the entry of order on the level H, the exclusive-OR gate provides in exit a signal reversed compared to that present at entry 2.
In short the exclusive-OR gate can function out of reverser ordered by using one of its two entries like entry of order. If entry 1 is used as entry of order, this one is on the level L, the exclusive-OR gate the signal applied to entry 2 does not reverse ; whereas with entry 1 on the level H, the circuit provides in exit a signal reversed compared to that applied to entry 2.
A similar operation is obtained by using entry 2 like entry of order. In this case, if the entry of order 2 is with the state L, the exit is on the same level as that present on entry 1; while if the entry of order 2 is with the state H, the exit is always on a contrary level of that of entry 1.
6. - FOURTH EXPERIMENT : USE
OF AN INTEGRATED CIRCUIT
“NAND” TO REPLACE OTHER TYPES OF CIRCUITS
Often in the same assembly circuits of the different type are : OR, NAND, Reversers, etc…
In certain cases, it would be expensive to use an integrated circuit different for each type of function to realize.
If for example, an assembly envisages the use of a single reverser and of only one door NAND, it would be anti-economic to use a MM 74C04 like reverser and a MM 74C00 for circuit NAND.
Indeed, a sixth of the integrated circuit MM 74C04 (which contains 6 reversers and a quarter of the integrated circuit MM 74C00 containing 4 NAND) would be used. It is thus useful to be able to substitute certain circuits by others providing the same function.
Equivalences between the various circuits were already studied in Digital the Électronique theory of the 3rd lesson. In the experiment which will follow, you will check how it is possible to in practice fulfill some switching functions while being used to you as circuits of the type NAND with the place of the specific integrated circuits.
a) Disconnect the food and remove all the connections relating to the preceding experiment.
b) Remove the integrated circuit MM 74C86 of support ICX and introduce into this last the integrated circuit MM 74C00.
As you already learned in practice preceding, the integrated circuit MM 74C00 includes/understands 4 circuits NAND, each one of them having two entries and an exit.
c) While serving to you as the already prepared pieces of wire of which you lay out, carry out the connections indicated figure 14-a.
In this way, entry 1 is connected to SW0 while entry 2 is connected to the positive tension (level H). The exit of circuit NAND as usual is connected to the L0 indicator.
First test
a) Place SW0 on position 0, you thus carry out the circuit represented figure 14-b.
b) Connect the food, observe the LED L0 : you note that it is lit.
c) Put then SW0 on position 1. Note that the LED L0 dies out.
You can thus conclude from it that : if entry 1 is on the level L, the exit of circuit NAND is on the level H (lit LED) while if entry 1 is on the level H, the exit is on the level L (extinct LED). Circuit NAND connected as indicated in the figure 14-b thus behaves like a reverser.
Since the two entries of circuit NAND are interchangeable, the same result is obtained by maintaining entry 1 permanently on the level H. In this case, the circuit behaves like a reverser, i.e. the exit is on an opposite level of that applied to entry 2.
The operation of a circuit NAND out of reverser can also be obtained by connecting the two entries as indicated figure 15.
In practice, this solution was not adopted solely by convenience of connection, but you will be able to keep it in memory and to resort to it in the event of needs.
Second test (For wiring, to see the figures 16-a and 16-b).
By this test, you will check that it is possible to fulfill the function OR by using only doors NAND.
a) Disconnect the food of the circuit,
b) Remove the connection between pin 3 of the integrated circuit MM 74C00 and the L0 contact, leave the connections of pins 1 and 2 corresponding to the two entries of first circuit NAND.
c) Connect with a piece of wire of approximately 5 cm, an entry of second circuit NAND (stitches 4) to contact SW1 and with a piece of wire of approximately 15 cm, the other entry (stitches 5) same circuit with the second contact +. By these connections, the first and second circuit NAND provide the function of reversers.
d) Using two pieces of wire of approximately 5 cm, connect the exit of first circuit NAND (stitches 3) to the one of the entries of third circuit NAND (stitches 10) then the exit of the second circuit (stitches 6) at the other entry of the third circuit (stitches 9).
e) With a piece of wire of approximately 10 cm, connect the exit of the third circuit (stitches 8) to the LED L0.
f) Put SW0 and SW1 on the position corresponding to symbol 0.
With the connections carried out, you come to carry out the circuit represented figure 16-b.
Notice in this circuit the absence of the symbol of the pile of food represented up to now in the diagrams. Connection on the level H is indicated by the sign “+” in order to simplify the drawing. This simplification is usually practiced for the development of the electric diagrams of the logical circuits.
Now you can replug the food and check yourself the operation of the circuit carried out while proceeding exactly as for the preceding experiments.
Thus carry out all the possible combinations of the levels of entry of the circuit while acting on SW0 and SW1 and check for each one of them the indication of the state of the exit concretized by the LED L0.
You note that the operation of the circuit corresponds to the tables of figure 17.
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By comparing these two tables with those established during preceding experiments carried out on various types of circuits, you notice that they are completely identical to those of the circuit OR.
Each time you have to carry out a circuit providing the function OR, i.e. the logical sum of numerical signals, remember the circuit that you have just tested.
This circuit can be carried out with 3 circuits NAND as you have just seen it, but it can be it also with two genuine reversers connected to the entries of a circuit NAND as represented figure 18.
While indicating by the letters a and b the two logical variables applied to the entry and by S the variable of exit, the switching function carried out by the circuit can be written in the form :
S = a + b
7. - FIFTH EXPERIMENT : USE OF THREE “NOR” CIRCUITS TO
REPLACE A CIRCUIT “AND”
In the preceding experiment, you noted how a circuit OR can be carried out with three circuits NAND or with two reversers and a circuit NAND. You now will check in experiments how a circuit AND can be replaced by three NOR-circuits or by two reversers followed by a NOR-circuit.
a) Disconnect the food, remove the integrated circuit MM 74C00 of support ICX and remove the connections relating to the preceding experiment.
b) Take the integrated circuit MM 74C02 and introduce it into support ICX. As you could note it previously, this integrated circuit contains 4 NOR-circuits internally.
c) Carry out the new connections indicated figure 19-a.
d) Place SW0 and SW1 on position 0. You thus have just carried out the circuit represented figure 19-b.
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e) Feed the circuit and observe the LED L0.
Knowing that the extinct LED L0 indicates at exit of the circuit a bottom grade (L) and the lit LED a high level (H), constitute yourself the table of operation of the circuit in question while realizing by means of SW0 and SW1 the four possible combinations of the levels of tension H and L applied to the entries.
From the table of operation, determine then the truth table in positive logic (remember that the level H is associated at the logical level 1 and the level L at the logical level 0).
Lastly, compare the tables obtained with those of the circuits AND, you will note that they are identical. In the contrary case, re-examine since the beginning the connections carried out and remade the experiment with a greater attention.
The possibility of carrying out a circuit AND by using three NOR-circuits can prove to be useful in the case or having NOR-circuits, you would not intend to add in particular an integrated circuit to carry out only one circuit AND.
Using three NOR-circuits, it is thus possible to carry out a circuit AND to replace an integrated circuit MM 74C08.
Note that in the circuit carried out (figure 19-b), the two NOR-circuits having one of their two entries connected permanently to the mass (level L) provide the function of reverser.
Indeed, if you observe the table of operation of a NOR-circuit, you note that when one of the two entries is on the level L, the exit is always at the opposite level of that of the other entry.
Ultimately, like a circuit AND can fulfill the function of reverser when one of the two entries is permanently on the level H (first test of the fourth experiment) in the same way a NOR-circuit can fulfill the function of reverser in the case or one of its entries is permanently on the level L as indicated figure 20-a. The same result is obtained by connecting the two entries between them as you can see it in the figure 20-b.
By holding account by what precedes, the result of the fifth experiment can be obtained not only with the circuit represented figure 19-b, but also with the circuit of the figure 21-a or by replacing the first two NOR-circuits functioning out of reversers by two truths reversers as represented figure 21-b.
With this practice, we finished the examination of the fundamental logical integrated circuits.
You could raise their characteristics in practice and carry out interesting experiments showing how it is possible to obtain equivalent switching functions by using integrated circuits of different types.
In the next practice, you will widen your knowledge on these circuits as well as rockers R.S. for example and well of others.
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