1. **Problem Statement:** Explain the logic gate AND and the negation (NOT) operation, including a drawing. 2. **AND Gate Definition:** The AND gate outputs true (1) only if both inputs are true (1). The formula is: $$\text{AND}(A,B) = A \land B$$ where $A$ and $B$ are inputs. 3. **NOT Gate Definition:** The NOT gate outputs the opposite of the input. If input is true (1), output is false (0), and vice versa. The formula is: $$\text{NOT}(A) = \neg A$$ 4. **Truth Tables:** - AND gate: | A | B | A AND B | |---|---|---------| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | - NOT gate: | A | NOT A | |---|-------| | 0 | 1 | | 1 | 0 | 5. **Explanation:** - The AND gate requires both inputs to be 1 to output 1. - The NOT gate flips the input value. 6. **Combined Operation Example:** If we take inputs $A=1$ and $B=0$, then: $$A \land B = 1 \land 0 = 0$$ Applying NOT to the output: $$\neg (A \land B) = \neg 0 = 1$$ This is the NAND operation (NOT AND).