Simplifying Boolean Algebra

Simplifying Boolean Algebra

1. De Morgans law's

   • FIrst Law= ¬(AvB) = ¬A^¬B
   • Second Law= ¬(A^B) = ¬Av¬B

2. Other Laws

   • Commutative law: A v B = B v A A^B=B^A
   • Distributive Laws: A(B v C) – AB v AC / A v BC= (A v B)( Av C)
   • Associative Law: (A v b) v C = A v (B v C) = A v B v C (AB)C = A(BC) =ABC

3. Karnaugh map.

   • what is a Karnaugh map?
     • A Karnaugh Map is a grid-like representation of a truth table
     • Karnaugh Map is designed to present the information in a way that allows easy grouping of terms that can be combined.
       • You can group terms in groups of 2, 4, 8, 16, etc. And then are able to simplify when common terms are found.
   • Is it a better way to simplify Boolean Algebra than the laws?
     • No, it has its pros and cons.
       • Pro: it makes it easier for your brain to understand the simplifying processes
       • Con: it takes longer to draw out and work out the final answer.

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