- 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
Bidmas for logic gates
Order for gates:
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 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
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 not—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.
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.
# DeMorgan’s Laws
- Two most important laws.
# DeMorgan’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 Morgan’s Second Law
Essentially the inverse of the first law.
Therefore, NOT A AND B is the same as NOT A OR NOT B