 Logic gates are combined to form transistors
 Transistors combine to form integrated circuits
 The integrated circuit is a silicon wafer that consists of various microelectronic components
 An integrated circuit is usually made of a single type of gate only
Set representation
Order
Bidmas for logic gates
Order for gates:
 Brackets
 NOT
 XOR
 AND
 OR
Big Noonoo Xtreme Apetite Orange Bring Now, eXtremely Angry Otters Behold Newly eX Assistant Orthodontists
If you want to prioritise OR over AND then brackets are required.
Commutive Laws
 The order of the operands does not matter
Associative Laws
 When all the operators are the same, it does not matter what order they are applied in.
Simplifying boolean expressions
 Simplifying means rewriting the expression in a way that uses fewer logic gates but keeping the exact same functionality.
A+()A=1  A OR NOT A IS TRUE A+A=A A.0 = 0 A.1 = A A.A = A A.()A=0 ()()A=A
 A
 B
 A.B
 D.F+G+A.()B
Starter
A AND NOT A IS FALSE
This is correct because A is TRUE and NOT A is FALSE. So an AND operation on a TRUE and FALSE will result in FALSE due to one of the inputs being FALSE.
Boolean Laws (continued)
Absorption Laws
 If a term is ANDed or ORed to itself, then it is equivalent.
A + A.B = A A.(A+B) =A
Practice
C + C.D = C D + C.D.B = D A.(C+A) = A D.F + D.1 = D. E.F.(E.F+D) = E.F A.A+A.1+B.B = A
Distributive Laws

Like mathematical algebra, you should expand brackets where needed.

It is also possible to expand brackets in Boolean algebra expressions when an expression is ANDed with an expression enclosed in brackets.

This can often help to simplify an expression (though sometimes it might notâ€”just because you can expand brackets does not mean it is always right to do so.)
A.(B+C) = (A.B) + (A.C) (A+B).(C+D) = (A.C) + (A.D) + (B.C) + (B.D)
Inverse Distributive Laws
Also known as: factoring
 In algebraic expressions you will have seen that sometimes an expression can be simplified by adding brackets, the same is true for boolean algebra.
Practice
C.(D+B) = (C.D) + (C+B) C.D.(B+A.E) = (C.D.B) + (C.D.A) + (C.D.E) A.(B+C+D)+A.
DeMorganâ€™s Laws
 Two most important laws.
DeMorganâ€™s First Law
Law 1 and Law 2 in a Venn diagram
Therefore, N T A OR B is the same as NOT A AND NOT B
De Morganâ€™s Second Law
Essentially the inverse of the first law.
Therefore, NOT A AND B is the same as NOT A OR NOT B