Basic Logic

• I am using Carpinelli as a reference.
  • Chapter 2 for the basics of logic
  • Chapter 3 for the basics of digital Logic
• Boolean algebra forms the basis for most modern computation.
  • This system was proposed by George Boole (1815 -1864)
• If you take a logic class, you will get a completely
  • Most likely this will be discussed in finite math.
  • Or a logic class.
  • They may use different symbols.
  • I don't care
    • For other classes use their symbols and methods.
    • For this class, use the ones I present.
      • These represent the use in cs.
    • They are all equivalent, but use the proper symbols in the proper context.
• An algebra is a set of objects combined with operations on that set.
  • For example the integers with addition and subtraction.
• For the boolean algebra we will study
  • The objects are the set {0,1}, or possibly {false, true}
  • The operations include: not, and, or
  • Other Operations: nand, nor, xor
• Boolean variables and operations can be combined to form boolean expressions.
  • f(x,y) = operations on x and y.
• Boolean expressions, truth tables and circuits.
  • These three things are just different ways to present a boolean expression.
  • We will work with all three
  • In the end, we probably want a circuit.
  • But we may use truth tables to design these circuits.
  • And boolean expressions to simplify or validate these circuits.
  • In the end you will need all three.