DE Unit 1 — Part B (2 marks each)

1. Simplify: Y=A+AB′+A′B

1. A+AB′=A(1+B′)=A
2. So Y=A+A′B
3. Use consensus / expansion: A+A′B=(A+A′)(A+B)
4. A+A′=1 ⇒ Y=1⋅(A+B)=A+B
5. Y=A+B.

2. State DeMorgan’s Theorems.
(A+B)′=A′⋅B′

(A⋅B)′=A′+B′

3. What are the various number systems used in computer?
Answer: Binary, Octal, Decimal, Hexadecimal.

5. What is the base of the binary number system?
Answer: Base = 2.

8. How many digits are used in the binary number system?
Answer: Two digits: 0 and 1.

9. Write an example of SOP form.
Example:

F=A′B+AB′C

F = A’B + AB’C