Physics Final 2

7/25/2019 Physics Final 2

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In electronics, a logic gateis an idealized or physical device

implementing a Boolean function; that is, it performs a logical

operationon one or more logical inputs, and produces a single logicaloutput. Depending on the context, the term may refer to an ideal logic

gate, one that has for instance zero rise timeand unlimited fan-out, orit may refer to a non-ideal physical device.

Logic gates are primarily implemented

using diodesor transistorsacting as electronic switches, ut can also e

constructed using vacuum tues, electromagnetic relays, fluidic logic,

pneumatic logic, optics, molecules, or even mechanicalelements.!ith amplification, logic gates can e cascaded in the same way that

Boolean functions can e composed, allowing the construction of a

physical model of all of Boolean logic, and therefore, all of the

algorithms and mathematicsthat can e descried with Boolean logic.

Logic circuits include such devices

as multiplexers, registers, arithmetic logic units"#L$s%, and computer

memory, all the way up through complete microprocessors, which maycontain more than &'' million gates. In modern practice, most gates are

made from field-effect transistors"()*s%,

particularly +()*s"metaloxidesemiconductor field-effect

transistors%.

/ompound logic gates #0D-1-Invert"#I% and 1-#0D-Invert

"#I% are often employed in circuit design ecause their construction

using +()*s is simpler and more efficient than the sum of theindividual gates.

In reversile logic, *offoli gatesare used.

ELECTRONIC GATES :

*o uild a functionally completelogic system, relays, valves"vacuumtues%, or transistorscan e used. *he simplest family of logic gates

usingipolar transistorsis called resistor-transistor logic"1*L%. $nli2esimple diode logic gates "which do not have a gain element%, 1*L gates

can e cascaded indefinitely to produce more complex logic functions.
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1*L gates were used in early integrated circuits. (or higher speed and

etter density, the resistors used in 1*L were replaced y diodes resulting

in diode-transistor logic"D*L%. *ransistor-transistor logic"**L% then

supplanted D*L. #s integrated circuits ecame more complex, ipolar

transistors were replaced with smaller field-effecttransistors"+()*s%; see 3+and0+. *o reduce power

consumption still further, most contemporary chip implementations of

digital systems now use /+logic. /+ uses complementary "oth

n-channel and p-channel% +()* devices to achieve a high speed with

low power dissipation.

(or small-scale logic, designers now use prefaricated logic gates from

families of devices such as the **L45'' seriesy *exas Instruments,

the /+5''' seriesy 1/#, and their more recent descendants.

Increasingly, these fixed-function logic gates are eing replacedyprogrammale logic devices, which allow designers to pac2 a large

numer of mixed logic gates into a single integrated circuit. *he field-

programmale nature ofprogrammale logic devicessuch as (36#shas

removed the 7hard7 property of hardware; it is now possile to change the

logic design of a hardware system y reprogramming some of its

components, thus allowing the features or function of a hardwareimplementation of a logic system to e changed.

)lectronic logic gates differ significantly from their relay-and-switch

e8uivalents. *hey are much faster, consume much less power, and are

much smaller "all y a factor of a million or more in most cases%. #lso,

there is a fundamental structural difference. *he switch circuit creates acontinuous metallic path for current to flow "in either direction% etween

its input and its output. *he semiconductor logic gate, on the other hand,

acts as a high-gainvoltageamplifier, which sin2s a tiny current at its

input and produces a low-impedance voltage at its output. It is not

possile for current to flow etween the output and the input of a

semiconductor logic gate.

#nother important advantage of standardized integrated circuitlogic

families, such as the 45'' and 5''' families, is that they can e

cascaded. *his means that the output of one gate can e wired to the

inputs of one or several other gates, and so on. ystems with varyingdegrees of complexity can e uilt without great concern of the designer

for the internal wor2ings of the gates, provided the limitations of

each integrated circuitare considered.
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*he output of one gate can only drive a finite numer of inputs to other

gates, a numer called the 7fanoutlimit7. #lso, there is always a delay,

called the 7propagation delay7, from a change in input of a gate to the

corresponding change in its output. !hen gates are cascaded, the total

propagation delay is approximately the sum of the individual delays, aneffect which can ecome a prolem in high-speed circuits. #dditional

delay can e caused when a large numer of inputs are connected to an

output, due to the distriuted capacitanceof all the inputs and wiring and

the finite amount of current that each output can provide.

Boolean ALGEBRA

Boolean #lgera is the mathematics we use to analyse digital gates and

circuits. !e can use these 9Laws of Boolean: to oth reduce and

simplify a complex Boolean expression in an attempt to reduce the

numer of logic gates re8uired. Boolean #lgera is therefore a system

of mathematics ased on logic that has its own set of rules or lawswhich are used to define and reduce Boolean expressions.

*he variales used in Boolean #lgera only have one of two possile

values, a logic 9': and a logic9&: ut an expression can have an

infinite numer of variales all laelled individually to represent inputs
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to the expression, (or example, variales #, B, / etc, giving us a

logical expression of # B < /, ut each variale can 0L= e a ' or

a &.

# set of rules or Laws of Boolean #lgera expressions have een

invented to help reduce the numer of logic gates needed to perform aparticular logic operation resulting in a list of functions or theorems

2nown commonly as the Laws of Boolean #lgera.

*he asic Laws of Boolean #lgera that relate to the /ommutative

Law allowing a change in position for addition and multiplication, the

#ssociative Law allowing the removal of rac2ets for addition and

multiplication, as well as the Distriutive Law allowing the factoring of

an expression, are the same as in ordinary algera.

)ach of the Boolean Laws aove are given with >ust a single or two

variales, ut the numer of variales defined y a single law is not

limited to this as there can e an infinite numer of variales as inputstoo the expression. *hese Boolean laws detailed aove can e used to

prove any given Boolean expression as well as for simplifying

complicated digital circuits.

Rules in Boolean Algebra :(ollowing are the important rules used in Boolean algera.

?ariale used can have only two values. Binary & for @I6@ and

Binary ' for L!.

/omplement of a variale is represented y an over ar "-%. *hus,

complement of variale B is represented as . *hus if B < ' then

< & and B < & then < '.

1ing of the variales is represented y a plus "% sign etween

them. (or example 1ing of #, B, / is represented as # B /.

Logical #0Ding of the two or more variale is represented y

writing a dot etween them such as #.B./. ometime the dot may

e omitted li2e #B/.

Description of the Laws of Boolean AlgebraAnnulment Law # term #0DAed with a 9': e8uals ' or 1

Aed with a 9&: will e8ual &.


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o # . ' < ' # variale #0Ded with ' is always e8ual to '.

o # & < & # variale 1ed with & is always e8ual to &.

Identity Law # term 1Aed with a 9': or #0DAed with a

9&: will always e8ual that term.

o # ' < # # variale 1ed with ' is always e8ual to the

variale.

o #. & < # # variale #0Ded with & is always e8ual to the

variale.

Idempotent Law #n input that is #0DAed or 1Aed with

itself is e8ual to that input.

o # # < # # variale 1ed with itself is always e8ual to the

variale.

o # . # < # # variale #0Ded with itself is always e8ual to the

variale.

Complement Law # term #0DAed with its complemente8uals 9': and a term 1Aed with its complement e8uals 9&:.

o #. # < ' # variale #0Ded with its complement is always

e8ual to '.

o # # < & # variale 1ed with its complement is always

e8ual to &.

Commutative Law *he order of application of two separate

terms is not important.

o #. B < B . # *he order in which two variales are #0Ded

ma2es no difference.

o

# B < B # *he order in which two variales are 1edma2es no difference.

Double egation Law # term that is inverted twice is

e8ual to the original term.


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o # < # # doule complement of a variale is always e8ual to

the variale.

Distributive Law *his law permits the multiplying or

factoring out of an expression.

o #"B /% < #.B #./ "1 Distriutive Law%

o # "B./% < "# B%."# /% "#0D Distriutive Law%

Absorptive Law *his law enales a reduction in a

complicated expression to a simpler one y asoring li2e terms.

o

# "#.B% < # "1 #sorption Law%o #"# B% < # "#0D #sorption Law%

Associative Law *his law allows the removal of rac2ets

from an expression and regrouping of the variales.

o # "B /% < "# B% / < # B / "1 #ssociate

Law%o #"B./% < "#.B%/ < # . B . / "#0D #ssociate Law%

TYPES OF LOGIC GATES :

AND Gate

*he #0D gate is an electronic circuit that gives a high output only if allits input are high. # dot".% is used to show the #0D operation. i.e. #.B

Symbol Truth Table

A B A.B

0 0 0

0 1 0

1 0 0


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1 1 1

Boolean Expression Q = A.B Read as A AND B gives Q

OR (Inclusive OR) Gate

*he 1 gate is an electronic circuit that gives a high output only if one

or more of its input are high. *he 3lus "% is used to show the 1

operation.

Symbol Truth Table

A B AB

0 0 0

0 1 1

1 0 1

1 1 1

Boolean Expression Q = AB Read as A !R B gives Q

NOT Gate

*he 0* gate is an electronic circuit that produces an inverted version of

the output at its input. It is also 2nown as inverter. If the input variale is

#, the inverted output is 2nown as 0* #.

Symbol Truth Table

# C

0 1

1 0

Boolean Expression Q = N!T A or A Read as inversion o" A gives Q

In the &E's, schematics were the predominant method to design

oth circuit oardsand custom I/s 2nown as gate arrays. *oday custom
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I/s and the field-programmale gate arrayare typically designed

with @ardware Description Languages"@DL% such as ?erilogor ?@DL.

#

Distin#tive shape

$%EEE Std &'(&'a)

'&&'*

Re#tangular shape

$%EEE Std &'(&'a)'&&'

%E+ ,-,')'/ 0 '&&*

Boolean algebra bet1een A 2B

Truth table

AN

D

INPUT OUTPUT

# B # #0D B

' ' '

' & '

& ' '

& & &

!R

INPUT OUTPUT

# B # 1 B

' ' '

' & &

& ' &

& & &

N!

TINPUT OUTPUT

# 0* #

' &
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& '

!ummary ofLogic "ates :

*he following *ruth *ale compares the logical functions of the F-inputlogic gates aove.

%nputs Truth Table !utputs 3or Ea#h 4ate

A B AND NAND OR NOR EX-OR EX-NOR

0 0 0 1 0 1 0 1

0 1 0 1 1 0 1 0

1 0 0 1 1 0 1 0

1 1 1 0 1 0 0 1

*he following tale gives a list of the common logic functions and their

e8uivalent Boolean notation.

!ome Common Applications of Logic "ates

$nder Digital )lectronics During the course of discussion aoutvarious digital logic gates, we have mainly discussed aout the design,

property and operation of them. In this article we will loo2 at various

applications of logic gates. *heir applications are determined mainly

ased upon their truth tale i.e. their mode of operations. In the

following discussion we will loo2 at the applications of asic logic

gates as well as many other normal logic gates as well.

Appli#ation o" !R 4ates 0

!herever the occurrence of any one or more than one event is needed

to e detected or some actions are to e ta2en after their occurrence, in

all those cases 1 gates can e used. It can e explained with an

example. uppose in an industrial plant if one or more than oneparameter exceeds the safe value, some protective measure is needed to

e done. In that case 1 gate is used. !e are going to show this with

the help of a diagram.


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*he aove figure is a typical schematic diagram where an 1 gate is

used to detect exceed of temperature or pressure and produce commandsignal for the system to ta2e re8uired actions.

Appli#ation o" AND 4ates 0

*here are mainly two applications of #0D gate as )nale gate and

Inhiit gate. )nale gate means allowance of data through a channel

and Inhiit gate is >ust the reverse of that process i.e. disallowance of

data through a channel. !e are going to show an enaling operation to

understand it in an easier way. uppose in the measurement of

fre8uency of a pulsed waveform. (or measurement of fre8uency a

gating pulse of 2nown fre8uency is sent to enale the passage of the

waveform whose fre8uency is to e measured. *he diagram elow

shows the arrangement of the aove explained operation.

Appli#ation o" N!T 4ates or %nverters 0

0* gates are also 2nown as inverter ecause they invert the output

given to them and show the reverse result. 0ow the /+ inverters


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are commonly used to uild s8uare wave oscillators which are used for

generating cloc2 signals. *he advantage of using these is they consume

low power and their interfacing is very easy compared to other logic

gates.

*he aove figure shows the most fundamental circuit made of ring

configuration to generate s8uare wave oscillator. *he fre8uency of this

type generator is given y !here n represents the numer ofinverters and tp shows the propagation delay per gate.

#niversal logic gates :

*he 45'' chip, containing four 0#0Ds. *he two additional pins supply

power "G ?% and connect the ground. /harles anders 3eirce "winter of&EE'E&% showed that 01 gates alone "or alternatively 0#0D gates

alone% can e used to reproduce the functions of all the other logic gates,

ut his wor2 on it was unpulished until &HH.*he first pulished proof

was y @enry +. heffer in &&H, so the 0#0D logical operation is

sometimes called heffer stro2e; the logical 01 is sometimes called

Peirce's arrow.

/onse8uently, these gates are sometimes called universal logic Gates.


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Digital Logic "ates:

# Digital Logic 6ate is an electronic device that ma2es logical decisions

ased on the different cominations of digital signals present on its

inputs. Digital logic gates may have more than one input ut generally

only have one digital output. Individual logic gates can e connected

together to form cominational or se8uential circuits, or larger logic gate

functions.

tandard commercially availale digital logic gates are availale in two

asic families or forms, **L which stands for Transistor-Transistor

Logicsuch as the 45'' series, and /+ which stands for

Complementary Metal-Oxide-Siliconwhich is the 5''' series of chips.

*his notation of **L or /+ refers to the logic technology used to

manufacture the integrated circuit, "I/% or a 9chip: as it is more

commonly called.

*he 45'' chip, containing four 0#0Ds. *he two

additional pins supply power "G ?% and connect

the ground


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Digital Logic "ate

6enerally spea2ing, **L logic I/s use 030 and 303 type Bipolar

unction *ransistorswhile /+ logic I/s use complementary

+()* or ()* type (ield )ffect *ransistorsfor oth their input andoutput circuitry.

#s well as **L and /+ technology, simple Digital Logic 6atescan

also e made y connecting together diodes, transistors and resistors to

produce 1*L, 1esistor-*ransistor logic gates, D*L, Diode-*ransistorlogic gates or )/L, )mitter-/oupled logic gates ut these are less

common now compared to the popular /+ family.

De$%organ&s theorems:

Before discussingDe$%organ&s theoremswe should 2now aoutcomplements. /omplements are the reverse value of the existing value.

!e are trying to say that as there are only two digits in inary numersystem ' J &. 0ow if # < ' then complement of # will e & or # < &

*here are actually two theorems that were put forward y De-+organ.

De +organs theorem can e stated as followsK-

'heorem ( :

The compliment of the product of two variables is equal to the

sum of the compliment of each variable.

*hus according to De-+organ7s laws or De-+organ7s theorem if # andB are the two variales or Boolean numers.
http://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.amazon.com/Introduction-Digital-Electronics-Essential-Series/dp/0340645709?tag=basicelecttut-20http://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.electronics-tutorials.ws/transistor/tran_1.htmlhttp://www.amazon.com/Introduction-Digital-Electronics-Essential-Series/dp/0340645709?tag=basicelecttut-20


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*he left hand side "L@% of this theorem represents a 0#0D gate

with inputs # and B, whereas the right hand side "1@% of thetheorem represents an 1 gate with inverted inputs.

*his 1 gate is called as Bubbled OR.

*ale showing verification of the De +organ7s first theorem

'heorem ):

The compliment of the sum of two variables is equal to the

product of the compliment of each variable.*hus according to De +organs theorem if # and B are the two variales

then.

*he L@ of this theorem represents a 01 gate with inputs # and

B, whereas the 1@ represents an #0D gate with inverted inputs.


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*his #0D gate is called as Bubbled AND.

*ale showing verification of the De +organ7s second theorem

(or my pro>ect I have ta2en help from following sources;

&./omprehensive "3hysics 3ractical MII%

F.Internet - www.wi2ipedia.com,

www.encylopedia.com

H.0/)1* 3hysics *extoo2s

5.Dinesh "3hysics 3ractical MII%
http://www.wikipedia.com/http://www.encylopedia.com/http://www.wikipedia.com/http://www.encylopedia.com/


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Physics Final 2