1.4.3 Boolean Algebra

Question 1

Which logic gate is this truth table representing?

Answer 1

XOR

Only 1 single input can be true

Question 2

Which logic gate is this truth table representing?

Answer 2

AND

Both inputs must be true

Question 3

Which logic gate is this truth table representing?

Answer 3

OR

At least one input needs to be true

Question 4

Which logic gate is this truth table representing?

Answer 4

NAND

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

Question 5

Which logic gate is this truth table representing?

Answer 5

NOR

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

Question 6

Which logic gate is this truth table representing?

Answer 6

NOT

Inverts the input

Question 7

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

Answer 7

Half-Adder

Question 8

What is the circuit for the following expression?

( ¬ A ) V ( B Λ C )

Answer 8

Question 9

What are the Boolean expressions for the following circuit?

Answer 9

S = (A V B) V Cin

COUT = ((A V B) Λ Cin) V (A Λ B)

Full Adder

Question 10

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 10

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 11

What would be the simplified expression for this Karnaugh map?

Answer 11

(NOT A and NOT D)

OR

(A AND B AND C)

OR

(NOT B AND NOT C AND NOT D)

Question 12

What can an adder do that a half-adder cannot?

Answer 12

Half-adder only handles 2 inputs so cannot handle previous carries

Question 13

What are the key facts about D-Type flip flops?

Answer 13

Data Input (D) can be at 1 or 0

Output (Q) can only change at a clocks rising edge (goes high)

When clock is high output(Q) changes to input (D)

Triggered by a clock pulse

Question 14

What are the De Morgan’s Laws?

Answer 14

Each term is complemented, and then the ORs become ANDs, and
the ANDs become ORs

Question 15

What is commutation?

Answer 15

It doesn’t matter which way around expressions go,
they mean the same thing both ways

X ^ Y = Y ^ X

Question 16

What is association?

Answer 16

It doesn’t matter how we group the numbers it will produce the same answer.

X ^ (Y ^ Z) = (X ^ Y) ^ Z

Question 17

What is absorption?

Answer 17

The operators inside and outside must be different and the term outside must also be inside.

X v (X ^ Y) = X

Question 18

What is double negation?

Answer 18

If you invert something twice, you return to the original value.

¬¬X = X

Question 19

What is distribution?

Answer 19

These are similar to the way multiplying out brackets works. 5 x (6 + 2) is the same as (5 x 6) + (5 x 2).

X ^ (Y v Z) = (X ^ Y) v (X ^ Z)