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Experiment of De-Morgan’s Theorem

Boolean Algebra is the mathematical system which defined with the set of the elements, a set of the operation and the number of common postulation. A De-Morgan’s theorem is one of the postulation of Boolean Algebra. By using De-Morgan’s theorem we can solve the many complex problems in Boolean Algebra. The main objective of experiment of De-Morgan’s theorem is to implement the logical expression in practical field and find out the out of the theorem’s functioning in practice and know about the circuit for the theorem. After the complete the experiment from the digital lab we are able to   connect the circuit and we are able to implement in practice of De-Morgan’s theorem

The following targets are should be prepared before do experiment.

  Ø  To find out the Gate functioning

  Ø  To connect the circuit in practice field

  Ø  To see the actual result of the circuit connection

  Ø  For finding of output

  Ø  Theoretical knowledge implementation

Experiment Topics are:

1 

   1. De-Morgan’s First Theorem:The DE-Morgan’s first theorem states that the total Complement of the sum is equal to the product of the individual complement. That is:

According above truth table the following circuit diagram is design. The output of the circuit is depending on the input. For eg: when we provide A=0 and B=0 then the circuit produce 1 output as a result. The output of the circuit is change when change in input. The output of the circuit is shown using lead, lead on or off according to output. The logic circuit as below: 

In the above circuit every gate’s 14 no.pin is connect with the +5v i.e. binary 1, every gate’s 7no.pin is connecting to the grounding line i.e. binary 0, it provide the power for gate to run or functioning properly. And gates function as input provided for the circuit and produce the output according to the inputs. The gates are in the IC form they have special symbols which are representing the gates, these symbols are as follows:

Name of the Gates                    Symbols/ Codes

NOT Gate:                                     7404

OR Gate:                                       7432

AND Gate:                                                                                                                                                               

NOR Gate:                                    7402

NAND Gate:                                 7400

X-OR Gate:                                  7486

2.DE-Morgan’s Second Theorem:

De-Morgan’s second theorem states that the total complement of the product is equal to the sum of individual complement. This can be explain as follows:

In the above figure the output will be change when the input changes. The light is bright or not it depends on the input of the circuit.

Conclusion:

IN conclusion we can say that our experiment was better because of we have opportunities to learn and see the practically result of experiment of De-Moran theorem. So we realize the experiment is necessary to improve knowledge of students practically and clear all confusion if have any.  At now all students are able to connect the any circuit of any expression of problems in lab practically.

1.    

   Experiment of Adder and Sub-tractor

Logic circuit for digital system may be combinational or sequential. A combinational circuit consists of logic gates whose output at any time is determined directly from present combination of inputs. A combinational circuit consists of input variables, logic gates variables, and output variables. The logic gates accept signal from inputs and generate signal to the output. Adder and sub-tractor are the combinational circuit. In today’s lab we are going to experiment of adder and subtractor of combination circuit. The following is the today’s experiment:

1.Half ADDER: It is a combinational circuit having two inputs and two outputs, one is sum and other is Carry. The following figure had shown the truth table and circuit diagram of the half adder.

In the above circuit every gate’s 14 no.pin is connect with the +5v i.e. binary 1, every gate’s 7no.pin is connecting to the grounding line i.e. binary 0, it provide the power for gate to run or functioning properly. And gates function as input provided for the circuit and produce the output according to the inputs.

2.Half Sub-tractor: A half sub-tractor is a combinational circuit that subtracts two bits and produces the difference and borrows. Figure below shows the truth table and logic diagram as follows:

Truth table is as follows:

In the above circuit every gate’s 14 no.pin is connect with the +5v i.e. binary 1, every gate’s 7 no. pin is connecting to the grounding line i.e. binary 0, it provide the power for gate to run or functioning properly. And gates function as input provided for the circuit and produce the output according to the inputs.

Summary: 

IN conclusion we can say that our experiment was better because of we have opportunities to learn and see the practically result of experiment Half Adder and half  Subtractor . So we realize the experiment is necessary to improve knowledge of students practically and clear all confusion if have any.  At now all students are able to connect the any circuit of any expression of problems in lab practically.

                                                                                                       

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