1.4.3 Boolean Algebra

Question 1

What are the AND (∧) identities?

Answer 1

A ∧ 0 ⇒ 0
A ∧ 1 ⇒ A

Question 2

What are the OR (∨) identities?

Answer 2

A ∨ 0 ⇒ A
A ∨ 1 ⇒ 1

Question 3

What are the negation identities?

Answer 3

A ∧ ￢A ⇒ 0
A ∨ ￢A ⇒ 1

Question 4

what is the absorption law?

Answer 4

A ∧ (A ∨ B) ⇒ A
A ∨ (A ∧ B) ⇒ A

Question 5

What is the distribution law?

Answer 5

A ∧ (B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C)
(like multiplying out brackets)

Question 6

what are De Morgan’s laws?

Answer 6

￢(A ∨ B) ⇒ ￢A ∧ ￢B
￢(A ∧ B) ⇒ ￢A ∨ ￢B

Question 7

What is a half adder?

Answer 7

A circuit which adds two single bit binary numbers together

Question 8

what are the input and outputs of a half adder?

Answer 8

Inputs:
- two single bit binary numbers (eg, A and B)
Outputs:
- S - the sum of the two numbers
- C - the carry bit

Question 9

what is the logic diagram for a half adder composed of?

Answer 9

S = A XOR B
C = A AND B

Question 10

How can you tell if a circuit is a half adder?

Answer 10

it has 2 inputs

Question 11

what is a full adder?

Answer 11

a circuit used to add larger binary numbers together.

Question 12

What are the inputs and outputs of a full adder?

Answer 12

Inputs:
- two single bit binary numbers (eg, A and B)
- the carry input bit (Cin)
Outputs:
- the Sum - S
- the carry output bit (Cout)

Question 13

how can you tell a circuit is a full adder?

Answer 13

it has 3 inputs

Question 14

what is a full adder made up of?

Answer 14

two half adders connected by an OR gate

Question 15

what is a D-Type flip flop?

Answer 15

A circuit which stores one bit of data

Question 16

what are the inputs and outputs of a D-type flip flop?

Answer 16

• data input
• clock input
• output of Q and NOT Q
• Q is set to the data input on the rising edge of the clock and stays that value for one clock cycle

Question 17

How do you use a Karnaugh map to simplify Boolean expressions?

Answer 17

• split expressions by the ORs and add 1s where each section is true
• draw boxes that are powers of 2 (eg, 1, 2, 4 etc 1s in them)
• look at each box and see which variables stay the same
• put each expression from each box together with ORs

Question 18

what is important to remember for Boolean simplification?

Answer 18

AND takes precedence over OR
so:
A ∧ B ∨ C ⇒ (A ∧ B) ∨ C