Free ALU 101 Boolean Algebra Questions and Answers

Question 1

If 𝐴⋅𝐵=1, what can be concluded about A and B?

Accepted Answer

Both A and B are 1

Answer

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)

Accepted Answer

A⋅B+A⋅C

Answer

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?

Accepted Answer

Both A and B are 1

Answer

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?

Accepted Answer

A

Answer

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?

Accepted Answer

0

Answer

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.

ALU 101 - Arithmetic Logic Unit 101 Exam Practice Test

ALU 101 - Arithmetic Logic Unit 101 Exam Practice Test

Free ALU 101 Boolean Algebra Questions and Answers