Computer Systems

• Boolean algebra concerns representing values with letters and simplifying expressions
• Boolean values


  TRUE and FALSE, which can be represented as 1 and 0 respectively
• Boolean algebra notation


  • A, B, C, etc. (unknown Boolean values)
  • A (NOT A)
  • A • B (A AND B)
  • AB (alternative notation for A AND B)
  • A + B (A OR B)
• Algebraic operations have an order of precedence, meaning that some operations must be applied before others
• Order of precedence in Boolean algebra

  • Brackets
  • NOT
  • AND
  • OR
• Boolean identities


  • A • 0 = 0
  • B • 1 = B
  • C • C = C
  • D + 0 = D
  • E + 1 = 1
  • F + F = F
  • G = G
• De Morgan's laws


  "Break the bar and change the sign"
• Applying De Morgan's laws


  1. Break the bar

  2. Change the sign
• Distributive rules in Boolean algebra: A • (B + C) = A • B + A • C
• Example 1: Simplify A + B • A

  • A + B • A

  = B + A

  = 1
• Example 2: Simplify C • B + C • B

  • C • B + C • B

  = B • (C + C)

  = B