1.4.3 Boolean Algebra

Question 1

Which logic gate is this truth table representing?

Answer 1

AND

Both inputs must be true

Question 2

Which logic gate is this truth table representing?

Answer 2

OR

At least one input needs to be true

Question 3

Which logic gate is this truth table representing?

Answer 3

XOR

Only 1 single input can be true

Question 3

Which logic gate is this truth table representing?

Answer 3

NAND

The flip of the AND gate - both inputs must not be true

Question 4

Which logic gate is this truth table representing?

Answer 4

NOR

The flip of an OR gate - both inputs need to be false

Question 5

Which logic gate is this truth table representing?

Answer 5

NOT

Inverts the input

Question 6

What would the logic circuit look like for this truth table?

Answer 6

Question 7

What is the circuit for the following expression?

( ¬ A ) V ( B Λ C )

Answer 7

Question 8

What are the Boolean expressions for the following circuit?

Answer 8

S = (A XOR B) XOR Cin

COUT = ((A XOR B) AND Cin) OR (A AND B)

Question 9

How big would the expressions be for each of the following group sizes on a Karnaugh map?

• Group of 8
• Group of 4
• Group of 2
• Group of 1

Answer 9

8 = Evaluates to single expression (A)

4 = Evaluates to two expressions (A Λ B)

2 = Evaluates to three expressions (A Λ B Λ C)

1 = Evaluates to four expressions (A Λ B Λ C Λ D)

Question 10

What would be the simplified expression for this Karnaugh map?

Answer 10

(NOT A and NOT D)

OR

(A AND B AND C)

OR

(NOT B AND NOT C AND NOT D)