THE LOGICAL GATES AND OR NOT
A logic gate , in digital electronics and information technology, is a digital circuit capable of implementing (that is, of realizing, simulating its “mathematical logic” by means of suitable controls on electrical signals) a particular logical operation of one or more Boolean variables. This definition will be clearer when we talk about Boolean algebra. In this post we will introduce logic gates. Let’s start with the fundamental logic gates (to then see all the others) capable of performing the operations of addition, product and negation indicated, respectively, with OR (logical sum), AND (logical product) and NOT (negation or complementation).
INPUT AND OUTPUT VARIABLES
Each logic gate has one or more input variables and only one output variable. The input and output variables are of the digital type, therefore it is possible to insert in a table all the possible combinations that can occur between the input variables. The output assumes the value 0 or the value 1 in correspondence with each combination of the input variables according to the assigned definition.
THE LOGICAL GATES NOT
The purpose of the NOT gate is to invert the logic level at the input. The entrances are indicated with capital letters, the exit is indicated with Y. The dot placed at the end of the gate highlights precisely the negation. Each logic gate has its own truth table which indicates the output logic level as the input state(s) vary.
NOTICE PORT TRUTH TABLE
| A | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
LOGIC GATE AND
This is the first logic gate that we examine having two inputs A and B. To have a state of 1 at the output both inputs must be at 1 (logical product).
AND PORT TRUTH TABLE
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
LOGIC GATE OR
To have a state of 1 at the output, at least one of the two inputs must be in the high logic state.
LOGIC GATE TRUTH TABLE OR
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
THE NAND LOGIC GATE
the NAND gate returns the negation of an AND gate, so it returns 1 when 0 is present at the inputs, and 0 only when all input values are 1. The outgoing value can be found using the formula Y=1-(A*B) where Y is the output, with three inputs Y=1-(A*B*C) and so on. The truth table follows:
TRUTH TABLE
|
INPUTS |
OUTPUT |
|
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
NAND GATE SYMBOL
THE LOGICAL GATE NOR
Conversely, the NOR gate returns the negation of an OR gate and therefore returns 1 only when all input values are 0.
The truth table follows:
TRUTH TABLE
|
INPUTS |
OUTPUT |
|
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
NOR GATE SYMBOL
THE EXOR LOGIC GATE
EXOR (or XOR)-(EXclusive OR) is a logic gate which receives “n” values as input and returns “1” as output if, and only if, there is at least one input that differs from the others. Here is the truth table of an XOR gate with “n=2” inputs:
TRUTH TABLE
|
INPUTS |
OUTPUT |
|
|
A |
B |
Y |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
XOR GATE SYMBOL
THE EXNOR LOGIC GATE
EXNOR (EXclusive NOR) is a logic gate which receives “n” values as input and returns “1” as output if, and only if, all the inputs have the same logic value. In short, it is equivalent to negating the EXOR gate (EXclusive OR).
The truth table of an EXNOR gate with “n=2” inputs follows:
TRUTH TABLE
|
INPUTS |
OUTPUT |
|
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
EXNOR GATE SYMBOL
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