Boolean algebra is the branch of mathematics that includes methods for manipulating logical variables and logical expressions. It performs the logical operations such as AND, OR, NAND, NOR, NOT and X-OR. The Boolean values are represented by using logic values 0 and 1. The basic laws used in Boolean algebra are commutative law, associate law, distributive law, identity law and redundance law. So the Boolean algebra calculator is used to perform the logical operations such as conjunction, disjunction, implication and equality. These operations can be stated in the following ways:
The application of the Boolean algebra is same as an electric switch state that can be either: in, on, or off mode, and these states can be represented by the logic values ‘1’ or ‘0’. The truth table can also be developed with the use of connectives.
Boolean algebra simplification calculator is an advanced calculator that immediately gives the result in the form of a math expression by performing the operations, such as multiplication, addition, etc., and, it also simplifies the fraction. The Boolean calculators are free to use and are the most compatible with any computer compared to a regular calculator.
Boolean Algebra Calculator Circuit
Power Supply Unit: The device that supplies electrical energy to one or more loads is known as power supply, and – in the same way, it converts other forms of energy like mechanical, chemical, solar energy into electrical energy. In this project, the power supply is about 5V, and it is given to the microcontroller, keypad and display.
Micro Controller: Microcontroller reads the data from the keypad and sends it to the display unit. Here, the microcontroller acts as the brain of the project, which is programmed in keil software.
Display and Numeric Keypad: The LED display used here is 3-bi-colors LED that displays the glowing pattern of the desired minimized expression. So, these Bi colors represent the normal and complements of the variables. Like switches, the keypad in this project – which gives the min terms as input, i.e., each digit on the keypad – corresponds to each min term.
This is a low-cost, low-power, portable, reliable and fast performing calculator that is built by the simple available component in the market like resistors, keypad, LEDs and microcontroller as shown in the figure.
The circuit is a simple three-variable minimizer that uses the Quine MC Cluskey algorithm and finds minimum sum of products by implementing Boolean functions. Boolean algebra calculator simplifies the logic functions and Boolean expressions by using the laws and theorems that are implemented on this algorithm. The microcontroller plays a major role in this project which is coded with this algorithm and controls the other components used in the circuit.
When the power is switched on, the LED glows indicating that the microcontroller is ready to take the inputs as min terms provided by the keypad, and these Boolean expressions are given in the SOP (Sum of Products) form.
Here, we are using 9 switches on the keypad, among them, 8 switches correspond to minterms that performs the product operation, and the 9th switch is used as the next button. After entering the expression, the LED gets off, and the microcontroller reduces the minterm expression, based on the algorithm; and then, the input LED glows which means that the expression is minimized, and it gets displayed.
The output is displayed as one min-term at one time, and the next min term is displayed by pressing the next button, so after reaching the last min term, the expression gets reduced, and the input LED switches off which indicates that the output gets ended. After that, the LED automatically switches on indicating the microcontroller is ready to take the next input.
Boolean algebra Simplification Examples
For better understanding of this concept, here, we are giving some Boolean algebra simplification examples.
From the logic diagram, truth table expression is simplified by using De Morgan theorem. Here, this original form that involves the sum of products and common factors is eliminated by using the single variable theorems.
The above diagram comprises two NAND and two OR gates that form the equation as AB + BC (B+C) as shown in the figure. By applying the identity rule and factorization final, the expression gets simplified to a simple form.
Applications of Boolean algebra
Boolean algebra can be applied to any system in which each variable has two states: ‘1’ and ‘0’
1.Two Floor Elevators
This is the application of Boolean algebra that performs the Boolean operations in the circuit for opening and closing a door or moving up or down the elevators. To perform these operations, three inputs are needed in the first floor and the second floors. Therefore, pushing the button represents 1, otherwise zero, and these buttons are placed in the elevator both inside as well as outside. By implementing the Boolean algebra operations in the main controller, the elevator can perform the desired operation.
2. Simple Vending Machine
The Boolean algebra can be applied for implementing simple vending machine wherein the selection of Coffee, Tea and milk options is based on customer choice. The pressing of buttons corresponds to the logic 1 otherwise logic zero. So, based on the given inputs, the logical operations are performed and the output is obtained.