Table of contents

Basic Logical Operations

There are only three basic logical operations in logical algebra , namely

" And ", " Or ", " Not ".

AND logical operation

Definition : Only when all the conditions for determining an event are met, the event is established; if one or more conditions are not met, the event is not established. Such a causal relationship is called an " and " logical relationship.

AND logic operation in digital circuit

If the state of the switch is off and the light is off is expressed by the logic quantity " 0 " ; the state of the switch on and the light is on is expressed by the logic quantity " 1 " , then there is a truth table:

AND logic truth table

A	B	$F=A\cdot B$
0 0 1 1	0 1 0 1	0 0 0 1

$F=A\cdot B$

Truth table : the logical relationship between all possible combinations of input variable values and the corresponding output variable values is listed in the form of a table .

The logical function of AND gate is summarized as follows:

1) "0" out of "0";

2) All "1" out "1".

or logical operation

Definition : Among the various conditions that determine an event , as long as one or more conditions are met, this event is established ; only when all the conditions are not met , this event is not established . Such a causal relationship is called " or " logical relationship.

or logic truth table

A	B	$F=A+B$
0 0 1 1	0 1 0 1	0 1 1 1

$F=A+B$

The logical function of the OR gate can be summarized as :

1) "1" out of "1";

2) All "0" out "0".

illogical operation

Definition : Assuming that the establishment of event F is related to the possession of condition A , if A is met , then F is not established ; if A is not met , then F is established . This causal relationship between F and A is called "not" logic relationship .

illogical truth table

A	$F=\overline{A}$
0 1	1 0

$F=\overline{A}$

Note :

Both AND and OR gates can have multiple inputs and one output.
A NOT gate has only one input and one output.

compound logic operation

AND logic

( will be combined with logical and not logical )

NAND logic truth table

A	B	$F=\overline{A\cdot B}$
0 0 1 1	0 1 0 1	1 1 1 0

$F=\overline{A\cdot B}$

The logical function of the NAND gate is summarized as: "There are 0 out of 1, all 1 out of 0" .

OR illogical

( A combination of OR logic and NOT logic )

or illogical truth table

A	B	$F=\overline{A+B}$
0 0 1 1	0 1 0 1	1 0 0 0

$F=\overline{A+B}$

The logical function of the NOR gate is summarized as: "all 0s out 1, 1 out 0".

AND OR NOT logic

( combined with , or , and not logic)

AND OR NOT Logical Functions : $F=\overline{AB+CD}$

Logical symbols for AND-NOR gates:

The logical function of the NOR gate is summarized as: "Every group has 0 out of 1, and a certain group of all 1 out of 0".

Chip type corresponding model

XOR logic

The functional formula of XOR logic is: $F=\overline{A}B+A\overline{B}=A\oplus B$

XOR logic truth table

A	B	$F=A\oplus B$
0 0 1 1	0 1 0 1	0 1 1 0

$F=A\oplus B$

The function of XOR logic is:

1) The same result is "0";

2) The difference is "1".

NOR logic

The same OR logical function is: $F=\overline{A}\cdot \overline{B}+A\cdot B=A\bigodot B$

NOR logic truth table

A	B	$F=A\bigodot B$
0 0 1 1	0 1 0 1	1 0 0 1

$F=A\bigodot B$

The function of exclusive OR logic is:

1) If they are the same, get "1";

2) The difference is "0".

Comparing the XOR and XOR logic truth tables , it can be found that XOR and XOR are inverse functions of each other, namely :

$A\bigoplus B=\overline{A\bigodot B}$

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Digital logic and analog electronic technology - some knowledge points (3) - digital and electrical part - basic logic operations, compound logic operations