Tool to generate logical truth tables. In Boolean algebra or electronics, logical truth tables allow defining a function / gate / element / component according to its inputs and outputs.
Truth Table - dCode
Tag(s) : Symbolic Computation, Electronics
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A truth table is a table representing the output boolean values of a logical expression based on their entries. The table thus displays all the possible combinations of the $ n $ input logical variables (generally 0 / FALSE and 1 / TRUE over $ n $ columns) and the result of the equation as output (last column).
Example: The table of the logical NOT function with 1 input A (1st column) and the output value NOT A (last column):
Every electronic circuit is associated with a truth table which describes it.
Usually the array starts with input values at $ 0 $ and ends with input values at $ 1 $ but sometimes it's reversed.
dCode truth table generator interprets the Boolean logical expression and calculates (using Boolean algebra) all the possible combinations of 0 and 1 for each variable (among the Boolean variables requested) in order to make the truth table.
dCode also makes it possible to find the Boolean logic function/expression from a truth table.
The only important column of the truth table is the last one, which describes the output values (the first columns are always identical for a given number of inputs) and which allows to convert into the Boolean expression.
Example: The output values are 0,1,1,0, (and the table is ordered from 00 to 11), so the truth table is:
Here are the different calculations (which give the same result for the given example)
Calculation from the output values 1 of the truth table (Minterms): for each 1, write the corresponding input values separated by logical AND, then group these results with a logical OR.
Example: Rows 2 and 3 are equal to 1, row 2 is written as A AND NOT(B) (because A is 1 and B is 0), row 3 is written as NOT(A) AND B and therefore the equation is (A AND NOT(B)) OR (NOT(A) AND B) which possibly simplifies to A XOR B
Calculation from the output values 0 of the truth table (Maxterms): for each 0, write the corresponding input values separated by logical OR, then group these results with a logical AND.
Example: Rows 1 and 4 are equal to 0, row 1 is written as A OR B, row 4 is written as NOT(A) OR NOT(B) and therefore the equation is (A OR B) AND (NOT(A) OR NOT(B)) which possibly simplifies to A XOR B
The truth table for the AND function is:
|A||B||A AND B|
The truth table for the OR function is:
|A||B||A OR B|
The truth table for the NAND function is:
|A||B||A NAND B|
The truth table for the NOR function is:
|A||B||A NOR B|
The truth table for the TRUE (=1) function is:
The truth table for the FALSE (=0) function is:
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Cite as source (bibliography):
Truth Table on dCode.fr [online website], retrieved on 2023-12-06,