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Logic gates (1)

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Page 1: Logic gates (1)
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ALLAH, IN WHOSE NAME I BEGIN, THE MOST AFFECTIONATE, THE MOST MERCIFUL.

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Objective:To understand the function of

Logic Gates.

•APPARATUS: Breadboard Diode

Transistor Connecting Wires

Resistor LED

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A digital system deals with quantities or variables which have only

two discrete values or states.

Following are the examples of such quantities:

• a switch can be either closed or open.

• the answer of a question can be either yes or no.

• a certain statement can be either true or false.

• a bulb can be either off or on.

Digital Systems

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•We have mostly two inputs A, B & one output C.

• There are many different ways that C could depend upon A and B.

• The output C is a function, - a logic function - of the inputs A and B.

Operations on logic signals

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• DEFINITION:• A logic gate is an elementary building block of a digital circuit. Most logic

gates have two inputs and one output. At any given moment, every terminal is in one of the two binary conditions low (0) or high (1), represented by different voltage levels. The logic state of a terminal can, and generally does, change often, as the circuit processes data. In most

logic gates, the low state is approximately zero volts (0 V), while the high

state is approximately five volts positive (+5 V).

Logic Gates

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Types of Basic logic gates

AND

OR

NOT

NAND

NOR

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Symbols of Logic Gates

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Inputs & Outputs

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• Some gate symbols have a circle on their output which means that their function

includes inverting of the output. It is equivalent to feeding the output through a not

gate.

The inverting circle (o):

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•A DIAGRAM OF THE OUTPUTS FROM ALL POSSIBLE COMBINATIONS

OF INPUT

Truth Table

Input A Input B Output Q

0 0 0

0 1 0

1 0 0

1 1 1

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Definition

The AND gate implements the Boolean AND function where the output only is logical 1 when all inputs are logical 1.

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SymbolLogical

Expression

The Boolean expression for the

AND gate is C=A.B

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Boolen Expression for AND

Inputs Output

A B C

0 0 0

0 1 0

1 0 0

1 1 1

Truth Table

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Circuit Diagram

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Mode Of Action

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1. When A is at 0V, diode D1 conducts. So the

point C is driven to 0V.

2. The same mechanism is repeated if B is at 0v,

then D2 conducts which switches the point like

0v.

3. When both A & B are at 0V, both the diodes

conduct and point C is at 0V.

4. When both the inputs A & B are at +5V, no

current will flow. The point C will be at 5V and

we get the logic answer 1.

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Application

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Person Sensor

Alarm SwitchBurglar Alarm

ON/OFF

ON/OFFON/OFF

If both the Person Sensor AND the

Alarm Switch are on then the

Burglar Alarm is activated.

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1. ELECTRONIC DOOR WILL ONLY OPEN IF IT DETECTS A PERSON AND THE SWITCH IS SET

TO UNLOCKED.

2. MICROWAVE WILL ONLY START IF THE START BUTTON IS PRESSED AND THE DOOR

CLOSE SWITCH IS CLOSED.

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General Application

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Definition

The OR gate implements the Boolean OR function where the output is logical 1 when

just input is logical 1.

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. SymbolLogical

Expression

The Boolean expression for the

OR gate is C=A+B

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Boolen Expression for OR

Inputs Output

A B C

0 0 0

0 1 1

1 0 1

1 1 1

Truth Table

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Circuit Diagram

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Mode Of Action

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1. When A is at +5V, D1 is forward biased and

hence conduct. We get +5V at point C.

2. Same mechanism happens if B is at +5V, D2

Conducts, switching the point C at 5V.

3. When both A & B are at 5V, both the diode D1

and D2 conduct and the point C is again at

5V.

4. The point C will be at 0V if and only both A &

B are at 0V.

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Application

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Front Doorbell Switch

Back Doorbell SwitchDoorbell

ON/OFF

ON/OFFON/OFF

If either the Front Doorbell Switch

OR the Back Doorbell Switch is

pressed then the Doorbell rings.

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Definition

The NOT gate implements the Boolean NOT function where the output is the inverse of

the input.

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SymbolLogical

Expression

The Boolean expression for the

NOT gate is

A=C’Or

A= 𝑪

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Boolen Expression for NOT

Truth Table

Input Output

A C’ or 𝑪

0 1

1 0

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Circuit Diagram

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Mode Of Action

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1. When A is at 5V, the emitter based junction is

forward biased and the transistor is on and

maximum current flows through the emitter lead.

So point C will be at 0V.

2. When we connect A with 0V, the transistor stops

working and we get the point C at +5V.

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Application

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Temperature Detector

(Above 20°C)Central Heating

ON/OFF ON/OFF

If the temperature is above 20°C

then the Central Heating is switched

off.

If the temperature is below 20°C

then the Central Heating is switched

on.

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1. MICROWAVE WILL STOP IF THE DOOR IS NOT CLOSED.

2. TRAFFIC LIGHT WILL OPERATE NORMALLY IF IT'S NOT IN MAINTENANCE

MODE.

3. STREET LIGHTS ARE TURNED ON WHEN THERE IS NO SUNLIGHT OR JUST

WITH TWILIGHT.

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General Application

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Definition

The NOR is a combination of an OR followed by a NOT gate. The output is logical 1 when non of the

inputs are logical 0NOR gates are so-called "universal gates" that can be

combined to form any other kind of logic gate.

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SymbolLogical

Expression

The Boolean expression for the

NOR gate is

C = 𝑨 + 𝑩

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Boolen Expression for NOR

Truth Table

Inputs Output

A B C D

0 0 0 1

0 1 1 0

1 0 1 0

1 1 1 0

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Circuit Diagram

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• NOR GATE CAN BE USED TO REALIZE THE BASIC LOGIC FUNCTION OF OR GATE, AND GATE

1. AS OR GATE:

THE OUTPUT FROM NOR GATE IS 𝑨 + 𝑩 BY USING ANOTHER INVERTER IN THE OUTPUT, THE OUTPUT IS INVERTED AND IS GIVEN BY , C=A+B, WHICH IS LOGIC FUNCTION OF A SIMPLE OR GATE.

2.AS AND GATE:

TWO INVERTERS WILL BE USED, ONE FOR EACH INPUT. THE INPUTS HAVE BEEN INVERTED BEFORE THEY HAVE BEEN APPLIED TO THE NOR GATE. THE OUTPUT IS

𝑨 + 𝑩 = 𝑨.𝑩

WHICH IS DEMORGAN’S THEOREM.

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NOR gate as Universal Gate

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Mode Of Action

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1. The function of NOR gate is just the reverse

of OR gate function.

2. NOR gate will have an output 1 only when

both inputs A & B are at logic 0V

3. If any of the input is 1V, the output is 0V.

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Application

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Definition

The NAND gate is an AND gate followed by a NOT gate. The output is logical 1 when one of

the inputs are logical 0

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SymbolLogical

Expression

The Boolean expression for the

NAND gate is

C = 𝑨.𝑩

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Boolen Expression for NAND

Truth Table

Inputs Output

A B C D

0 0 0 1

0 1 0 1

1 0 0 1

1 1 1 0

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Circuit Diagram

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• NAND GATE CAN BE USED TO REALIZE THE BASIC LOGIC FUNCTION OF OR GATE, AND GATE

1. AS AND GATE:

THE OUTPUT FROM NAND GATE IS 𝑨.𝑩 BY USING ANOTHER INVERTER IN THE OUTPUT, THE OUTPUT IS INVERTED AND IS GIVEN BY , C=A.B , WHICH IS LOGIC FUNCTION OF A SIMPLE AND GATE.

2.AS OR GATE:

TWO INVERTERS WILL BE USED, ONE FOR EACH INPUT. THE INPUTS HAVE BEENINVERTED BEFORE THEY HAVE BEEN APPLIED TO THE NANDGATE. THE OUTPUT IS

𝑨. 𝑩 = 𝑨 + 𝑩

WHICH IS DEMORGAN’S THEOREM.

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NAND gate as Universal Gate

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Mode Of Action

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1. The function of NAND gate is just the reverse of

AND gate function.

2. NAND gate will have an output 1 only when both

inputs A & B are at logic 0V or any of the inputs is

0V.

3. If both the inputs are 1, the output will be 0V.

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Application

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A door closing system of an automobile

A car needs to be so designed that the driver gets a visual indication if any of the doors of the car is open so that it helps to avoid accident and injury to the passengers. Assuming there are two doors where this system is fitted, the circuit can be designed using a NAND gate as followsYou can see from the figure that when any of the switches is open due to the door position, the NAND gate energies the lamp inside the car, hence warning the driver.

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