Explain the significance of De Morgan’s Theorems in Boolean algebra.

De Morgan’s Theorems are important for simplifying and transforming Boolean expressions involving negations. They state:

  • The complement of a product of variables is equal to the sum of the complements: (AB)′=A′+B′
  • The complement of a sum of variables is equal to the product of the complements: (A+B)′=A′B′

These laws allow for the conversion between AND and OR operations when a NOT operation is applied, helping simplify logic circuits and expressions.

Related Questions:

  1. What is a logic gate?
  2. Define truth table.
  3. Define Boolean function.
  4. What is Karnaugh map and why is it used?
  5. Draw three-variable Karnaugh map for variables X, Y, and Z.
  6. Define the XOR gate and write its Boolean expression.
  7. Why is the NAND gate considered a universal gate?
  8. Draw the graphical symbols of AND, OR, NOT, NAND, and NOR gates and write their functions.
  9. Explain how NAND and NOR gates can be created using AND, OR, and NOT gates.
  10. Draw truth tables of the following Boolean functions.
  11. Simplify the Boolean functions of Question 5 using Karnaugh map.
  12. Draw the logic circuits of the following Boolean functions.
  13. What is meant by the complement of a Boolean function?
  14. How can a logic circuit be simplified using Boolean algebra?
  15. Show memory hierarchy with the help of a diagram.
  16. Write four properties of computational thinking.
  17. Model Papers (1-10)
  18. Define computer.
  19. What is an algorithm and what is the role of an algorithm in problem-solving?
  20. What is a flowchart?