Boolean-Algebra-from-Bits-to-Logic

• Computers represent information by bit (Binary digit)
• A bit has two possible values, namely 0 and 1.
• A bit can be used to represent a truth value, true and false.
• Therefore bits operations correspond to the logical operations in Boolean Algebra.

Boolean Functions

• A function is a relation that uniquely associates members of one set with members of another set
• A Boolean function has
  • At least one Boolean variable
  • At least one Boolean operator
  • At least one input from the set
• It produces an output that is also a member of the set
• $F=X+Y{Z}^{\prime }$
• Precedence
  • NOT top priority,
  • followed by AND
  • then OR

Canonical Forms

• There are two canonical forms
  • Sum-of-products
  • Product-of-sums

Sum-of-Products

• Also called Disjunctive Normal Form (DNF) 析取范式
• Look at ONE

Product-of-Sums

• Also called Conjunctive Normal Form (CNF) 合取范式
• Look at ZERO