classical computing, a Boolean circuit is a mathematical mode

 In classical computing, a Boolean circuit is a mathematical model used to describe logical operations. It consists of gates, inputs, and outputs, all of which can have the value of 0 or 1 (true or false). Let's explore some common gates and their meanings in a classical Boolean circuit:
1. **AND Gate** (Symbol: ∧):
   - Description: Outputs true (1) if and only if both inputs are true.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   0
     0 | 1 |   0
     1 | 0 |   0
     1 | 1 |   1
     ```
2. **OR Gate** (Symbol: ∨):
   - Description: Outputs true (1) if at least one of the inputs is true.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   0
     0 | 1 |   1
     1 | 0 |   1
     1 | 1 |   1
     ```
3. **NOT Gate** (Symbol: ¬):
   - Description: Outputs the opposite value of the input (inverts the input).
   - Truth Table:
     ```
     A | Output
     0 |   1
     1 |   0
     ```
4. **NAND Gate** (Symbol: ⊼):
   - Description: Outputs false (0) if and only if both inputs are true; otherwise, it outputs true.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   1
     0 | 1 |   1
     1 | 0 |   1
     1 | 1 |   0
     ```
5. **NOR Gate** (Symbol: ⊽):
   - Description: Outputs true (0) if and only if both inputs are false.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   1
     0 | 1 |   0
     1 | 0 |   0
     1 | 1 |   0
     ```
6. **XOR Gate** (Exclusive OR) (Symbol: ⊕):
   - Description: Outputs true (1) if the inputs are different, false (0) if they are the same.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   0
     0 | 1 |   1
     1 | 0 |   1
     1 | 1 |   0
     ```
7. **XNOR Gate** (Exclusive NOR) (Symbol: ⊙):
   - Description: Outputs true (1) if the inputs are the same, false (0) if they are different.
   - Truth Table:
     ```
     A | B | Output
     0 | 0 |   1
     0 | 1 |   0
     1 | 0 |   0
     1 | 1 |   1
     ```
These gates form the building blocks of classical Boolean circuits and can be combined in various ways to perform complex logical operations. They provide a foundational understanding of how digital logic and classical computation operate.