📚 Seth MB


Search IconIcon to open search

Boolean Logic

Last updated May 26, 2023 Edit

# Set representation

# Order

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

# Associative Laws

# Simplifying boolean expressions

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

  1. A
  2. B
  3. A.B
  4. D.F+G+A.(-)B


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

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

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

# 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.

# DeMorgan’s 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

Binary Logic