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# 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.