Math Problem Statement
solve this cs honour question
Two logic gates are the AND gate and the OR gate. Complete the truth tables for these two gates:
Solution
The question is asking to complete the truth tables for the AND gate and the OR gate based on the given input combinations for and .
AND Gate Truth Table:
The AND gate outputs a value of 1 only when both inputs and are 1. Otherwise, it outputs 0.
\hline A & B & X (\text{A AND B}) \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array}$$ ### OR Gate Truth Table: The OR gate outputs a value of **1** when at least one input $$A$$ or $$B$$ is **1**. It only outputs **0** when both inputs are **0**. $$\begin{array}{|c|c|c|} \hline A & B & X (\text{A OR B}) \\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \hline \end{array}$$ ### Completed Answer: - The AND gate truth table: $$X = A \land B$$ - The OR gate truth table: $$X = A \lor B$$ Let me know if you need further clarification or details! --- Here are 5 questions to expand your understanding: 1. What is the difference between the AND and OR gates in terms of logical operations? 2. How would you represent an XOR (exclusive OR) gate in a truth table? 3. Can you explain a real-life example where an AND gate might be used? 4. What would the truth table look like for a NAND gate (NOT AND)? 5. How does Boolean algebra simplify logic circuits using these gates? **Tip**: When working with more complex circuits, combining multiple gates can achieve specific behaviors, and simplifying them through Boolean algebra is often key to designing efficient systems.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Logic Gates
Truth Tables
Boolean Algebra
Formulas
AND Gate: X = A AND B
OR Gate: X = A OR B
Theorems
Boolean Theorem for AND Gate: Outputs 1 when both inputs are 1
Boolean Theorem for OR Gate: Outputs 1 when at least one input is 1
Suitable Grade Level
Grades 9-12