Unit 8 Boolean Algebra

Unit 8 Boolean Algebra

1. T2 - Simplifying Boolean Expressions

   • De Morgan's 1st Law
     • This states that: ¬(A v B) = ¬A ^ ¬B
     • De Morgan's 2nd Law
       • This states that: ¬(A ^ B) = ¬A v ¬B
   • Simplifying expressions
     • There are 9 useful rules for simplifying expressions
       • X ^ 0 = 0
       • X ^ 1 = X
       • X ^ X = X
       • X ^ ¬X = 0
       • X v 0 = X
       • X v 1 = 1
       • X v X = X
       • X v ¬X = 1
       • ¬ ¬X = X
     • Commutative rule
       • X ^ Y = Y ^ X
       • X v Y = Y v X
       • Associative rule
         • X ^ (Y ^ Z) = (X ^ Y) ^ Z
         • X v (Y v Z) = (X v Y) v Z
         • Distributive rule
           • X ^ (Y v Z) = (X ^ Y) v (X ^ Z)
           • (X v Y) ^ (W v Z) = (X ^ W) v (X ^ Z) v (Y ^ W) v (Y ^ Z)
           • Absorption rules
             • X v (X ^ Y) = X
             • X ^ (X v Y) = X