Logic gates

Basic logic gates

This digital electronics course will focus on the easiest logic gates. There are in all 4 gates to know because it is essential to be able to then understand the most sophisticated gates.

  • YES gate
  • NAND
  • AND gate
  • OR gate

YES gate

This is the most basic gate that is, and also the simplest to understand. Indeed, the output of this gate is equal to the input.
If the input is equal to a logical 1, then the output is 1. As if the input is a logic 0 then the output is 0.

Scheme (European standard)

porte-logique-oui

Boolean formula

S = E

Truth table

Here is the truth table of the logic gate. As we can see, the input level is equal to the output level.

Entrance Exit
E S
0 0
1 1

NAND logic gate

This gate is strictly the inverse of a YES gate. Indeed, the output will complement what is input. I.e. that the logic level output is the inverse of the logical input level.
Thus, if the input is a logic 0, then the output is a 1 and vice versa if there is a logic level 0 input.

Scheme (European standard)

porte-logique-non

Boolean formula

S = Ē

Truth table

Here is the truth table of the logic gate. We clearly see that the output level is actually complemented the level of entry.

Entrance Exit
E S
0 1
1 0

AND gate

Here, at last, is an interesting gate to study. This time, there are two inputs on the logic gate. This time, the condition to be met for the output is logic 1 is that it must be the 2 inputs to 1. Otherwise, the output is 0.

Scheme (European standard)

porte-logique-et

Boolean formula

It should be noted that this formula points to say “and.”

S = AB

Truth table

Here is the truth table of the logic gate. As I have said previously, the output is the NL 1 only if both inputs are 1 also.

Entrance Exit
AT B S
0 0 0
0 1 0
1 0 0
1 1 1

OR gate

This latter basic gate is somewhat similar AND gate. This time out is the NL 1 if at least one of the two inputs is 1.

Scheme (European standard)

porte-logique-ou

Boolean formula

Attention on the form the plus sign to say “or”.

S = A + B

Truth table

On this truth table, we can clearly see that the output is 1 if at least one of the two inputs is 1 NL. Seen from another angle, we can also say that the output is 0 to NL if 2 inputs are 0.

Entrance Exit
AT B S
0 0 0
0 1 1
1 0 1
1 1 1

advanced logic gates

To follow this course on advanced logic gates you must have understood the basic logic gates . If it does not, will revise slightly the previous course to better understand what will follow.

All gates will be studied here are all derived from basic gates AND, OR and NOT.

  • NAND gate
  • NOR gate
  • Exclusive or gate
  • Non-exclusive or gate

NAND logic gate

The first thing I will tell you that’s the name of this gate in English. Indeed, this gate can also be called NAND.

The NAND gate is simply an AND gate followed by a NOT gate (hence its name).
There is thus the output of the AND gate which is connected to the input of the NAND gate, which complements all the results of the initial AND gate.

Scheme (European standard)

porte-logique-non-et

Boolean formula

             
S = AB 

Truth table

To understand this Veritee table to remember the Veritee table of an AND gate, and do not forget to complement the result.

Entrance Exit
AT B S
0 0 1
0 1 1
1 0 1
1 1 0

NOR logic gate

Again this brings to an English name, which is: NOR.

Like the NAND gate, the gate is simply an OR gate followed by a NOT gate.

Scheme (European standard)

porte-logique-non-ou

Boolean formula

                 
S = A + B

Truth table

Again, if you want to understand the advantage consulted courses on basic and gates complement the result of an OR gate to understand this truth table.

Entrance Exit
AT B S
0 0 1
0 1 0
1 0 0
1 1 0

 

Exclusive OR Logic gate

Here is a more complicated to understand gate. This is one of the last gates to know. This logic gate also called XOR in English, the NL is 1 when only one of its input is at 1. Thus, if the two inputs are 0 or 1 at the same time, then the output is a 0 .

Scheme (European standard)

porte-logique-ou-exclusif

Boolean formula

S = A signe-ou-exclusif B

                                 
S = (A.B) + (A.B)

Truth table

Entrance Exit
AT B S
0 0 0
0 1 1
1 0 1
1 1 0

 

 


 

 

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