# Tag Info

Accepted

### Why do logic gates behave the way they do?

As stated by user120366, 16 possible 2-input logic gates exist, I've tabulated them for you here: ...
• 690

### Why do logic gates behave the way they do?

It's easiest to think of $1$ representing a true statement and $0$ representing a false statement. The logic gates then act as truth functions. Say you put two statements, $p,q$, together to form a ...
• 351

### Why do logic gates behave the way they do?

I think the questioner has it backwards. If we have a logical function such that ...
• 231
Accepted

### Boolean absorption

Here is one way to prove the first identity: $$A \land (A \lor C) = (A \lor 0) \land (A \lor C) = A \lor (0 \land C) = A \lor 0 = A.$$ The second identity has a similar proof. Alternatively, you ...
• 278k
Accepted

### Representing binary functions with a finite gate set without exponential blow-up?

No. No matter what representation of functions as circuits/formulas you use, there will exist some functions that require exponential size to represent. This was proven by Shannon in 1949. See ...
• 162k

### How to construct XOR gate using only 4 NAND gate?

I think you are asking for this proof: ...
• 216
Accepted

### Absorption Law Proof by Algebra

First of all, this is a math question. I think you are confused on how brackets are used. They indicate precedence of operations, and can be used anywhere, even in places where such indication is not ...
• 30.9k

### Why do logic gates behave the way they do?

The why of it actually comes from the development of logic, which is a philosophical study of what is true and what is not true. Logic was originally a study of human language with the assumption that ...
• 699
Accepted

• 162k