Using Boolean algebra, simplify the Boolean function F = X’Y + XY’ + XY. Draw the logic circuit for the simplified function.

Let’s simplify the given Boolean function:

F=X′Y+XY′+X

First, group terms to factorize:

F=(X′Y+XY′)+XY

The term X′Y+XY′ is the Boolean expression for XOR, so we have:

F=(X⊕Y)+XY

Now, we simplify further by noting that the expression (X⊕Y)+XY is just an OR operation between the XOR of X and Y and the AND of X and Y. This expression cannot be simplified further directly. Thus, the simplified Boolean function is:

F=(X⊕Y)+XY

The corresponding logic circuit can be drawn using an XOR gate for X⊕Y, and an AND gate for XY, followed by an OR gate combining the two results.

Related Questions:

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