02.2 Variables and functions

Switches

A switch has two values:

• Open (off) $x=0$
• Closed (on) $x=1$

In practice, those are transistors (we will see that in another lecture) The symbol for a switch:

$$-\boxed{S}-$$

Example

Suppose we have a light controlled by a switch. The output of the light can be labeled as $L$

• If the light is on, we will say that $L=1$
• Else, $L=0$ We can describe the state of the light with a logical expression: $L(x)=x$

Two Variable Logic Functions

If we have two switches inline $\boxed{S}-\boxed{S}$, it behaves as an AND:

• Both switches have to be closed for the light to be on
• It is written as "$\cdot$"
  • $x_1\cdot x_2$

If we have two switches in parallel, it behaves as an OR:

• Either switch can be closed to turn on the light
• It is written as "$+$"
  • $x_1+x_2$

We can have a switch bypass a light, by going around it, we call this a Complement (NOT):

• It is written as a bar over the variable: "$\bar{x}$"

02.3 Truth Tables