Boolean Variables

In Boolean algebra, boolean variables take on only two possible values: true or false, also represented as 1 or 0.

These variables are pivotal in building boolean expressions, which lay the groundwork for digital logic circuits and programming algorithms.

Operations involving these variables are governed by boolean operators such as AND, OR, and NOT.

Employing boolean variables enables a clear definition of decision rules within simple logical frameworks.

In fields like computer science and digital electronics, boolean variables are crucial for directing program flow, making logical decisions, and denoting straightforward states or conditions. For example, a boolean variable could determine whether a user is logged into a system ("true" for logged in, "false" for not logged in). In digital circuit design, each boolean variable might signify an input or output signal, influencing the circuit's overall behavior. For instance, in a traffic light circuit, a boolean variable could indicate whether the light is green (1) or not green (0).

Example

Consider determining whether an alarm should activate based on the temperature and smoke presence in a building.

The alarm will trigger if the temperature rises above 50 degrees Celsius or if smoke is detected.

Let's define two boolean variables:

• \( T \): Indicates whether the temperature is over 50 degrees Celsius (true if so, false otherwise).
• \( S \): Indicates the detection of smoke (true if detected, false otherwise).

The alarm's control logic can be expressed using the boolean OR operator (\( \vee \)):

$$ A = T \vee S $$

Here, \( A \) denotes whether the alarm should be activated (true) or not (false).

To visualize the interaction of these variables, consider the following truth table:

\( T \) (Temp > 50)	\( S \) (Smoke)	\( A \) (Alarm)
False	False	False
False	True	True
True	False	True
True	True	True