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9.4 Logic Gate

Common terminology of logic gates

Logic gate : An electronic circuit with a single output and one or more inputs .

Truth table : A table that summarises all the possible input and output of a logic gate.

Boolean algebraic: A form of symbolic logic which provides a mathematical procedure for manipulating logical relationships in symbolic form.

Number of possibilities inputs and outputs..

N = 2n

N = number of outputs

n = number of inputs

Types of logic gates

There are seven types of logic gates:

(a) NOT gate

(b) AND gate

(c) OR gate

(d) NAND gate

(e) NOR gate

NOT gate

The symbol of for a NOT gate is:

clip_image002

The Boolean algebraic is:

clip_image004

The truth table is:

Input

Output

A

X

0

1

1

0

An equivalent circuit to a NOT gate:

clip_image006

 

Input

Output

A

X

Switch off

Lights up

Switch on

Goes off

AND gate

The symbol of for an AND gate is:

clip_image008

The Boolean algebraic is:

clip_image010

The truth table is:

clip_image012

An equivalent circuit to an AND gate:

clip_image014

 

clip_image016

OR gate

The symbol of for an OR gate is:

clip_image018

The Boolean algebraic is:

clip_image020

The truth table is:

clip_image022

An equivalent circuit to an OR gate:

clip_image024

clip_image026

NAND gate

The symbol of for an NAND gate is:

clip_image028

The Boolean algebraic is:

clip_image030

The truth table is:

clip_image032

NOR gate

The symbol of for an NOR gate is:

clip_image034

The Boolean algebraic is:

clip_image036

The truth table is:

clip_image038

Example 1

The figure shows a logic gate with inputs P and Q.

clip_image040

If the input P = 0011010 and the input S = 1100011 , what is the output X?

Solution

Example 2

The diagram shows two signals are connected to the inputs A and B of an OR gate.

clip_image042

Draw the output signal X.

Solution

clip_image044

Example 3

Work out the truth for the combination of logic gates in figure below.

clip_image046

Solution

Applications of Logic Gates in Control Systems

(1) Automatic Fan for cooling system

clip_image048

clip_image050

(2) Fire Alarm system

clip_image052

clip_image054

(3) Fire Control system

clip_image056

clip_image058

(4) Automatic Heater

clip_image060

clip_image062

(5) Control system for street lights

clip_image064

clip_image066

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