• 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)

• 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

• 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:

Use 1 of the signal as control signal Use the other signal as a data signal When the control signal = ZERO, the output is always equal to ZERO (switch is off) When the control signal = ONE, the output is always equal to the input value (switch is on)

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

/home/cs355001/bin/cs355sim /home/cs355001/demo/circuits/and-switch

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

The OR-circuit can also be used as a "switching circuit":

If all inputs except one are equal to ZERO: The output of an OR-gate is equal to the value of the one input that was excluded

I will show this in class:

/home/cs355001/bin/cs355sim /home/cs355001/demo/circuits/or-switch

We will see how it is used very soon in circuit design