CODEWITHSUNDEEP
iobinarylogicboolean-logic
Tgwizman
Tgwizman

Reputation: 1538

Complete Truth Tables Based On Binary

I am trying to figure out names for every combination with truth tables.

In the first table, I have each truth table for a two input and one output system. The inputs are read by row. The outputs are in a binary counted format. Each Output is read by column and is labeled with a hex number 0 to F. The input by row is related to the outputs within the specified output column.

In the second table, I have listed by row how each output column on the first chart works. In each row I have listed the binary logic gate name, if statement in javascript, and a description for how each would work. I have a hyphen for spaces that are not complete.

Are there names for the blank spaces in the gate names in the second table?

Complete Truth Tables

Inputs | Outputs
 1  2  | 0 1 2 3 4 5 6 7 8 9 A B C D E F
-----------------------------------------
 0  0  | 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
 0  1  | 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
 1  0  | 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
 1  1  | 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

Num | Gate  | Javascript | Return True If
--- | ----- | ---------- | --------------
 0  | -     | 0          | FALSE
 1  | AND   | I1&&I2     | I1 AND I2
 2  | -     | I1&&!I2    | I1 AND NOT I2
 3  | -     | I1         | I1
 4  | -     | !I1&&I2    | I2 AND NOT I1
 5  | -     | I2         | I2
 6  | XOR   | I1!==I2    | I1 NOT EQUALS I2
 7  | OR    | I1||I2     | I1 OR I2
 8  | NOR   | !I1||!I2   | NOT I1 OR NOT I2
 9  | XNOR  | I1==I2     | I1 EQUALS I2
 A  | -     | !I2        | NOT I2
 B  | -     | !(!I1&&I2) | NOT ( I2 AND NOT I1 )
 C  | -     | !I1        | NOT I1
 D  | -     | !(I1&&!I2) | NOT ( I1 AND NOT I2 )
 E  | NAND  | !I1&&!I2   | NOT I1 AND NOT I2
 F  | -     | 1          | TRUE

Upvotes: 1

Views: 155

Answers (1)

sifferman
sifferman

Reputation: 3112

Some of the other combinations have gate names, but not all do.

The A and C cases are each an example of a NOT gate, and the 3 and 5 cases are each an example of a BUFFER.

The D case is known as an IMPLY gate, but this is not as commonly known as the others.

For the rest, there are no commonly used gate names because to implement their boolean function would require either no gates (as in TRUE and FALSE), or they would require a combination of two or more of the conventional gates that you have already identified. There may be specific implementations of tools or systems that have created names for these "quasi-gates", but they are not in common use.

See Also

Logic Gate (Wikipedia)
Imply Gate (Wikipedia)

Upvotes: 2

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