1.4.3

Question 1

De Morgan’s Law

Answer 1

Either logical function AND or OR may be replaced by the other, given certain changes to the equation.

¬ (A ^ B) (¬ A) v (¬ B)
NOT (A AND B) is the same as (NOT A) OR (NOT B)

Question 2

Distribution

Answer 2

This law allows for the multiplying or factoring out of an expression

OR Distributive law
A AND (B OR C) is the same as (A AND B) OR (A AND C)

AND Distributive law
A OR (B AND C) is the same as (A OR B) AND (A OR C)

Question 3

Association

Answer 3

This law allows for the removal of brackets from an expression and the regrouping of the variables.

This is the OR Association Law
A OR (B OR C) is the same as (A OR B) OR C is the same as A OR B OR C

This is the AND Association Law
A AND (B AND C) is the same as (A AND B) AND C is the same as A AND B AND C

Question 4

Commutation

Answer 4

The order of application of two separate terms is not important.

The order in which two variables are AND’ed makes no difference

The order in which two variables are OR’ed makes no difference

Question 5

Double negation

Answer 5

NOT NOT A
(double negative) = “A”

Question 6

Absorption

Answer 6

Where the rule applies the second term inside the bracket can always be eliminated and “absorbed” by the term outside the bracket.

X OR (X AND Y) is the same as X

X AND (X OR Y) is the same as X

Question 7

D-Type Flip Flops

Answer 7

• Stores the value of one bit.
• Has a clock, two inputs and a control signal.
• The clock is a regular pulse from the CPU.
• The clock is used to coordinate the computer’s components.
• A clock pulse has edges which either rise or fall.
• The output can only change at a rising edge.
• Used four NAND gates.
• Updates the value in Q to the value in D whenever the clock
  rises.
• Q is the stored value

Question 8

Adders

Answer 8

• Adds together the number of TRUE inputs.
• Outputs this number in binary.

Question 9

Half Adder

Answer 9

• Has two inputs, A and B.
• Has two outputs, SUM and CARRY.
• Has two logic gates, AND and XOR.
• When A and B are FALSE both outputs are
  FALSE.
• When one of A or B is true, SUM is TRUE.
• When both inputs are TRUE, CARRY is TRUE.

Question 10

Full Adder

Answer 10

• Like a half adder but with a third input, CARRY IN.
• Formed from two XOR gates, two AND gates and an OR gate.
• May be chained together to produce a Ripple Adder with many inputs.