CS355 Sylabus
Boolean Algebra

• Boolean Algebra

• is defined over the set {0, 1}, 0 represents "false" and 1 represents "true"
• contains 2 boolean operations: * and +, * represents "and", and + represents "or"
• Boolean constants are: 0 or 1 (false or true)
• there is also a "negate" operation, but we do not count it as an operator (it's not binary)
• the inverse of 0 is 1 and inverse of 1 is 0.
• Boolean variables can take on the values 0 or 1 (false or true)

• Boolean expression:

• is made up of boolean variables and boolean opeartors (*, + and negate)
• Example of a boolean expression:

• The value z can be expressed as a boolean expression of the input variables a, b and c:

• z = a*b + b*c + a*c

• You can check that you can compute z for any given values of a, b, c.

• For example: a = 1, b = 0, c = 0
• z = 1*0 + 0*0 + 1*0 = 0 + 0 + 0 = 0

• Another example: a = 1, b = 1, c = 0
• z = 1*1 + 1*0 + 1*0 = 1 + 0 + 0 = 1

• Some Boolean equations involving * (and):

• 0 * x = 0
• 1 * x = x
• x * x = x
• x * x = 0    (x = not x)

If you look carefully at "0 * x = 0" and "1 * x = x" and a little imagination, you will realise why the and function can be use as a switch !

I will demonstrate the switching effect of the and gate in class: click here

• Some Boolean equations involving + (and):

• 0 + x = x
• 1 + x = 1
• x + x = x
• x + x = 1    (x = not x)

The OR-circuit is used as a "collector circuit". We will see how it is used very soon in circuit design.