Boolean Algebra AQA

De Morgan’s Law

NOT(A AND B) = NOT A OR NOT B

NOT(A OR B) = NOT A AND NOT B

How do you carry out De Morgan’s Law

1. Change the operator in the bracket (OR/AND)

2. NOT the terms on each side of the bracket

3. NOT everything that has changed

4. Get rid of any double negation

X AND 0

0

X AND 1

X

X AND X

X

X AND (NOT X)

0

X OR 0

0

X OR 1

1

X OR X

X

X OR (NOT X)

1

Association

• Allows for brackets to be removed if the operator is the same

  • A OR (B OR C) = (A OR B) OR C = A OR B OR C

Commutation

• The order is not important

  • A OR B = B OR A

Distribution

• Allows you to multiply out brackets

• A AND (B OR C) = (A AND B) OR (A AND C)

• A OR (B AND C) = (A OR B) AND (A OR C)

Absorption

• The second term inside the bracket can be absorbed

• This can only happen when the operator on the outside of the bracket is different to the one inside

  • A OR (A AND B) = A

  • A AND (A OR B) = A

Double Negation

• When 2 negatives cancel out to make a positive

  • NOT (NOT A) = A

Logic Circuit for a half adder

What is the difference between a half and full adder

A full adder has an extra input for a carry bit. This means that carries are included in the next calculation

D-Type Flip Flop

A 1 bit memory device that is enabled/disabled by a clock signal

When can the value of the output change in a D-Type Flip Flop

Rising Edge

Uses of D-Type Flip Flops

• Creating Registers

• Immediate Storage

• Static RAM