Boolean Algebra

Basics

• You can design any circuit using basic operators
• Functionality can be represented using truth tables

Formal Notation

• Two input operators: $B^2\to B$
  • $\vee$: Disjunction, Or
  • $\wedge$: Conjunction, And
• Single input operator: $B\to B$
  • $\neg$: Negation, Not
• Switching algebra is a boolean algebra with the smallest support $B=\{0,1\}$

Normal Notation

• Basic Operators
  • AND: $\cdot$
  • OR: $+$
  • NOT: $\overline{A}$
• Precedence
  1. Not
  2. And
  3. Or
• Exclusive OR
  • Exclusive OR
    • XOR: $\oplus$
    • $A\oplus B=\overline{A}B+A\overline{B}$
    • Detects if not equal
  • Exclusive NOR
    • XNOR: $\odot$
    • Detects if equal

Boolean Algebra Rules Two Level Logic Boolean Optimization