Boolean Algebra From Bits To Logic

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 {0,1}
  • It produces an output that is also a member of the set {0,1}
  • $F = X+YZ’$
  • Precedence
    • NOT top priority,
    • followed by AND
    • then OR CO-Boolean-Identities

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 DNF

Product-of-Sums

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

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