1.4.3 Boolean Algebra

Question 1

De Morgans Laws

Answer 1

De Morgans Laws : Break negation and change operator between literals

NOT (a AND b) –> NOT b OR NOT a

NOT (a OR b) –> NOT b AND NOT a

Question 2

Distribution

Answer 2

Distribution :

a AND (b OR c) –> (a AND b) OR (a AND c)

a OR (b AND c) –> (a OR b) AND (a OR c)

(a U b) ^ (c U d) = (a ^ c) U (a ^ d) U (b ^ c) U (b ^ d)

Question 3

Absorption

Answer 3

Absorption :

a U (a ^ b) = a

a ^ (a U b) = a

Question 4

Association

Answer 4

Association : involve removal or addition of brackets

c AND (a AND b) = a AND (b AND c) = a AND b AND c

Question 5

Commutation

Answer 5

Commutation : order of literals doesn’t matter

a AND b = b AND a

a OR b = b OR a

Question 6

Double Negation

Answer 6

Double negation : 2 negation arguments cancel out

NOT NOT c = c

Question 7

D-Type Flip Flops

Answer 7

D-Type Flip Flops : Stores the value of one bit when a signal is given.
- Logic circuit that changes value stored (Q) to data value (D) on rising edge of clock to input, value cannot be changed otherwise and is stored.

D-Type Flip Flops combined to form registers - static RAM which is a faster and more expensive memory unit - used in cache.

Question 8

Adders

Answer 8

Half Adder : Add two bits together producing sum and carry out

Full adder : Add two bits and carry in producing sum and carry out

Ripple adders : Chains multiple full adders together to add numbers with multiple bits together.