Learning Objectives:

1. To get introduction of Boolean Algebra.
2. To learn basic operations in Boolean Algebra.
3. To be able to relate Boolean operations to associated truth tables.

• A + 0 = A
  

• A * 0 = 0
  

• A + 1 = 1
  

• A * 1 = A
  

• A * \(\overline{A}\) = 0
  

• A + \(\overline{A}\) = 1
  

• A * A = A + A = A
  

Solved Example: 9895-01

Which of the following is a functionally complete set of gates?
(i) NAND
(ii) NOT
(NIMCET 2017)

A. I but not II

B. II but not I

C. Neither I not II

D. Both I and II

Correct Answer: A

Solved Example: 9895-02

A tautology is a Boolean formula that is always true. Which of the following is a tautology? (NIMCET 2013)

A. x

B. (x + x̅)y

C. x + y̅ + x̅

D. (xy) + x̅

Correct Answer: C

Solved Example: 9895-03

Which of the following Boolean rules is correct? (RPSC Lecturer 2011)

A. A + 0 = 0

B. A + 1 = 1

C. $\overline {A + A} = \overline {A.A}$

D. $A + A.B = \overline {A+B}$

Correct Answer: B

Solved Example: 9895-04

Which of the following is not a valid rule of Boolean Algebra? (HTET PGT Computer Science 2018)

A. $A + A' = A$

B. $A . A = A$

C. $A . A' = 0$

D. $A + A' = 1$

Correct Answer: A

Learning Objectives:

1. State and prove De Morgan's theorems with the help of truth tables.
2. Apply De Morgan's theorems to simplify Boolean expressions.

• \(\overline{A * B}\) = \(\overline{A}\) + \(\overline{B}\)

• \(\overline{A + B}\) = \(\overline{A}\) * \(\overline{B}\)

Solved Example: 9896-01

A̅ + B̅ = Q represents: (URSC (ISRO) Tech Asst (Electronics) March 2019)

A. NOR gate

B. NAND gate

C. EX-OR gate

D. AND gate

Correct Answer: B

Solved Example: 9896-02

According to De Morgan's theorem: NAND = ________. (UPRVUNL AE Electronics and Instrumentation 2021)

A. Bubbled AND

B. Bubbled NOR

C. Bubbled XOR

D. Bubbled OR

Correct Answer: D