PRESENTATION ONOR, AND, NOT GATES

Created byMD. NAZMUS SAQIB KHANID 12075768

Contents

FIRST SEGMENT INTRODUCTION TO LOGIC GATES BASIC GATES

SECOND SEGMENT SOME OTHER GATES

THIRD SEGMENT COMBINATIONS OF GATES EXAMPLES OF GATES REAL WORLD PROBLEM

INTRODUCTION TO LOGIC GATES

Boolean algebra is used to model the circuitry of electronic devices. Each input and each output of such a device can be thought as a member of the set {0,1}. A computer, or other electronic device, is made up of a number of circuits. Each circuit can be designed using the rules of Boolean algebra. The basic elements of circuits are called gates. Each type of gate implements a Boolean operation.

BASIC GATES

OR GATE AND GATE NOT GATE

OR GATE

OR GATE: An OR gate is a circuit that has two inputs and one output. The output voltage of an OR gate is high(or 1) if either one or both of the input voltages is high(1), and the output voltage is low(or 0) if both of the input voltages are low(0). Clearly, the output signal of an OR gate corresponds to a proposition which is the disjunction of the propositions corresponding to the input signals. In other words, the output of this gate is the Boolean sum of the inputted variables. This is shown in the following figure.

OR GATE

AND GATE

AND GATE: An AND gate is a circuit that has two inputs and one output. The output voltage of an AND gate is high(1) if both of the input voltages are high(1), and the output voltage is low(0) if either one or both of the input voltages is low(0). Clearly, the output signal of an AND gate corresponds to a proposition which is the conjunction of the propositions corresponding to the input signals. In other words, the output of this gate is the Boolean product of the inputted variables. This is shown in the following figure.

AND GATE

NOT GATE

NOT GATE: A NOT gate, or an inverter, is a circuit that has one input and one output. Its output voltage is high(1) if the input voltage is low(0), and the output voltage is low(0) if the input voltage is high(1). The output signal of a NOT gate corresponds to a proposition which is the negation of the proposition corresponding to the input signal. In other words, the output of this gate is the Boolean complement of the inputted variable. This is shown in the following figure.

NOT GATE

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SECTION??

SOME OTHER GATES

NAND GateNOR GateXOR GateXNOR Gate

NAND GateNAND Gate: A NAND gate is equivalent to an AND gate followed by a NOT gate. The output voltage of an NAND gate is high(1) if one or both of the input voltages are low(0), and the output voltage is low(0) if both of the input voltages are high(1). This is shown in the following figure.

NOR GateNOR Gate: A NOR gate is equivalent to an OR gate followed by a NOT gate. The output voltage of a NOR gate is high(or 1) if both of the input voltages are low(0), and the output voltage is low(or 0) if one or both of the input voltages are high(1). This is shown in the following figure.

XOR Gate

Exclusive-OR Gate: An XOR gate is a circuit that has two inputs and one output. The output voltage of an XOR gate is high(or 1) if one, and only one, of the input voltages is high(1), and the output voltage is low(or 0) if both input voltages are low (0) or both are high(1). An XOR gate is shown in the following figure.

XNOR Gate Exclusive-NOR Gate: An XNOR gate is equivalent to an XOR gate followed by a NOT gate. The output voltage of an XNOR gate is high(or 1) if both of the input voltages are the same, and the output voltage is low(or 0) if one but not both of the input voltages are high(1). An XNOR gate is shown in the following figure.

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COMBINATIONS OF GATES

Combinations of Gates:Combinational circuits can be constructed using a combination of inverters, OR gates, and AND gates. When combinations of circuits are formed, some gates may share inputs. This is shown in one of two ways in depiction of circuits. One method is to use branchings that indicate all the gates that use a given input. The other method is to indicate this input separately to each gate. Fig.(d) illustrates the two ways of showing gates with the same input values. Note also that output from a gate may be used as input by one or more other elements, as shown in Fig.(d). Both drawings in Fig.(d) depict the circuit that produces the output

COMBINATIONS OF GATES

ExampleExample 1 The following Figure shows the outputs: (a) , (b) , and (c)

Example of gates

Real World Problem

Suppose we want to design an electric circuit that will sound a buzzer in a car if the speed of the car exceeds 100 km/h or if the car is in gear and the driver did not have seat-belt buckled. Clearly, we have the relationship

or

where b is the proposition “sound the buzzer”, p is the proposition “the speed of the car exceeds 100 km/h”, q is the proposition “the car is in gear”, and r is the proposition “driver’s seat belt is buckled”.

To build an electronic circuit that will behave as described, we must first decide upon a convention for representing propositions by electronic signals. If the proposition is true, it will be represented by high voltage(or 1), and if the proposition is false, it will be represented by low voltage(or 0). We now see the result in the truth table as well as in the figure.

Real World ProblemTruth Table:

p q r r rq. ).( rqpb 1 1 1 1 0 0 0 0

1 0 1 0 1 0 1 0

1 1 0 0 1 1 0 0

0 0 1 1 0 0 1 1

0 0 1 0 0 0 1 0

1 1 1 1 0 0 1 0

= the speed of the car exceeds 100 km/h = the car is in gear = driver’s seat belt is buckled = sound the buzzer

Real World Problem

REFERENCES

“Discrete Mathematics and its Applications” – Kenneth H. Rosen

“Elements of Discrete Mathematics” – C. L. Liu

WikipediaSome Web Links

THANK YOU ALL!

END OF THE PRESENTATION