Logic and Bit Operations

• Translating English Statements into Logical Expressions

  • Removes ambiguity
  • Easy manipulation
  • Able to solve puzzles
• If the sun is shining


  I shall play tennis this afternoon
• Finishing the writing of my computer program before lunch


  Is necessary for my playing tennis this afternoon
• Low humidity and sunshine


  Are sufficient for me to play tennis this afternoon
• Translating English statements into logical expressions

  1. Step 1: Find the connectives which are connecting the two propositions together

  2. Step 2: Rename the propositions
• You are not allowed to watch adult movies

  • If your age is less than 18 years
  • Or you have no age proof
• Truth Value


  T = 1, F = 0
• Bit Operators


  • OR
  • AND
  • XOR
• Finding bitwise OR, bitwise AND, and bitwise XOR


  Take the OR, AND, and XOR of the corresponding bits, respectively
• Logical Equivalence


  If two logical expressions have the same truth values
• Logical Equivalence Laws


  • Identity Laws
  • Domination Laws
  • Idempotent Laws
  • Double Negation Laws
  • Commutative Laws
  • Associative Laws
  • Distributive Laws
  • De Morgan's Laws
  • Absorption Laws
  • Negation Laws