Boolean algebra: Boolean functions, representation and simplification. - One Line Questions

1. The expression A . (B . C) is equivalent to: — (A . B) . C
2. The expression A + (B . C) is equivalent to: — (A + B) . (A + C)
3. In a K-map, adjacent cells (horizontally or vertically) differ by how many bits? — 1
4. The expression A + 0 equals which of the following? — A
5. What is the result of A . 1 in Boolean algebra? — A
6. The Boolean expression A . A simplifies to: — A
7. According to the Complement Law, A + A' equals: — 1
8. What is the result of A . A' in Boolean algebra? — 0
9. When simplifying a Boolean expression using a K-map, groups of 1s are formed. The size of each group must be a power of: — 2
10. How many variables are needed to represent a Boolean function with 8 minterms? — 3
11. If a Boolean function has 3 variables, how many maxterms are possible? — 8
12. The expression F = AB + A'B simplifies to: — B
13. Simplify the Boolean expression: F = A(A+B). — A
14. If F = (A+B)(A'+B), what is the simplified expression? — B
15. The expression F = (A+B)(A'+B') simplifies to: — B
16. What is the dual of the Boolean expression A + (B . C)? — A . (B + C)
17. The expression A . (A' + B) simplifies to: — A . B
18. The dual of A . (B + C)' is: — A + (B . C)'
19. What is the Boolean expression for the NOR gate? — (A + B)'
20. A Boolean function can be represented in Sum of Products (SOP) form. Which of the following is an example of a minterm? — A' . B
21. The expression F = (A' + B)(A + B') simplifies to: — A XOR B
22. The Boolean expression (AB)' + (A+B)' simplifies to: — A'
23. De Morgan's theorem states that (A + B)' is equivalent to: — A' . B'
24. According to De Morgan's theorem, (A . B)' is equivalent to: — A' + B'
25. The expression F = A + A'B simplifies to: — A+B
26. Which law in Boolean algebra states that A + (A . B) = A? — Absorption Law
27. Which of the following is a canonical form of Boolean algebra? — Sum of Products (SOP)
28. The canonical SOP form of a Boolean function is a sum of: — selected minterms corresponding to output 1
29. The canonical POS form of a Boolean function is a product of: — selected maxterms corresponding to output 0
30. In a Sum of Products (SOP) expression, each product term contains: — all variables in complemented or uncomplemented form
31. Consider the expression F = AB' + A'B. This is the definition of: — XOR operation
32. What does the Boolean expression A + B + C represent? — OR operation
33. Which method is used to systematically derive a minimal sum-of-products expression from a truth table? — All of the above
34. What is the Quine-McCluskey method primarily used for? — Both B and C
35. Which simplification rule is applied to (A+B) + (A+B)' = 1? — Complement Law
36. Which of the following is NOT a standard Boolean algebra postulate? — Transitive Law
37. Which law states that A + A = A? — Idempotent Law
38. Which law states that A + (B + C) = (A + B) + C? — Associative Law
39. Which law states that A . (B + C) = (A . B) + (A . C)? — Distributive Law
40. What is the fundamental property of Boolean algebra that states that an expression remains unchanged when its variables are swapped? — Commutative Law
41. A Karnaugh map (K-map) is a graphical method used for: — simplifying Boolean expressions
42. What is a product term containing all variables in their true or complemented form called? — Minterm
43. What is a sum term containing all variables in their true or complemented form called? — Maxterm
44. A Boolean function in Product of Sums (POS) form is a product of: — Maxterms
45. For a Boolean function with 'n' variables, a K-map typically has how many cells? — 2^n
46. What is the primary goal of using Boolean algebra in digital logic design? — To reduce the complexity of the circuit
47. What is the result of applying the consensus theorem: XY + X'Z + YZ = XY + X'Z? — True
48. Which representation is often used for Boolean functions in computer science, especially in logic programming? — Boolean Expression
49. The expression F = AB + A'B' represents: — XNOR
50. What is the Boolean function for a 2-input multiplexer's output Y, given inputs A, B, and Select S? — Y = A S' + B S
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