Free ALU 101 Boolean Algebra Questions and Answers — Questions and Answers
Question 1: If 𝐴⋅𝐵=1, what can be concluded about A and B?
- Both A and B are 1 (Correct answer)
- Both A and B are 0
- At least one of A or B is 0
- A is 1 and B is 0
Correct answer: Both A and B are 1
In Boolean algebra, the AND operation (represented by ⋅) yields 1 only if all its inputs are 1. Therefore, for A⋅B to equal 1, both A and B must individually be 1. If either A or B (or both) were 0, the result of the AND operation would be 0.
Question 2: Simplify the Boolean expression 𝐴⋅(B+C)
- A+B+C
- A⋅B+A⋅C (Correct answer)
- A⋅B⋅C
- A⋅(B⋅C)
Correct answer: A⋅B+A⋅C
This is an application of the Distributive Law in Boolean algebra, which is analogous to its counterpart in ordinary algebra. The AND operation (⋅) distributes over the OR operation (+). Thus, A⋅(B+C) expands to (A⋅B) + (A⋅C).
Question 3: If A⋅B=1, what can be concluded about A and B?
- At least one of A or B is 0
- Both A and B are 0
- Both A and B are 1 (Correct answer)
- A is 1 and B is 0
Correct answer: Both A and B are 1
In Boolean algebra, the AND operation (represented by ⋅) results in 1 only when all its inputs are 1. Therefore, for the expression A⋅B to be equal to 1, both Boolean variables A and B must individually hold the value of 1. If either A or B were 0, the product would be 0.
Question 4: What is the result of the Boolean expression A+A⋅B?
- A (Correct answer)
- 1
- 0
- A⋅B
Correct answer: A
This is an example of the Absorption Law in Boolean algebra. The expression A + A⋅B simplifies to A because if A is 1, the entire expression is 1. If A is 0, the expression becomes 0 + 0⋅B, which simplifies to 0 + 0 = 0. In both cases, the result is A.
Question 5: Which Boolean identity represents the expression 𝐴 ⋅¯A?
- ¯A
- 1
- A
- 0 (Correct answer)
Correct answer: 0
This Boolean identity represents the Complement Law for the AND operation. The expression A ⋅ ¯A means A AND NOT A. Since A and ¯A (the complement of A) will always have opposite values (one is 0 and the other is 1), their AND product will always be 0.
Free ALU 101 Boolean Algebra Questions and Answers
If 𝐴⋅𝐵=1, what can be concluded about A and B?