Download - Physics Final 2
-
7/25/2019 Physics Final 2
1/16
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.
https://en.wikipedia.org/wiki/Electronicshttps://en.wikipedia.org/wiki/Boolean_functionhttps://en.wikipedia.org/wiki/Logical_operationhttps://en.wikipedia.org/wiki/Logical_operationhttps://en.wikipedia.org/wiki/Rise_timehttps://en.wikipedia.org/wiki/Fan-outhttps://en.wikipedia.org/wiki/Diodehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Switch#Electronic_switcheshttps://en.wikipedia.org/wiki/Vacuum_tubehttps://en.wikipedia.org/wiki/Relayhttps://en.wikipedia.org/wiki/Fluidic_logichttps://en.wikipedia.org/wiki/Pneumatics#Pneumatic_logichttps://en.wikipedia.org/wiki/Opticshttps://en.wikipedia.org/wiki/Molecular_logic_gatehttps://en.wikipedia.org/wiki/Analytical_enginehttps://en.wikipedia.org/wiki/Boolean_logichttps://en.wikipedia.org/wiki/Mathematicshttps://en.wikipedia.org/wiki/Multiplexerhttps://en.wikipedia.org/wiki/Processor_registerhttps://en.wikipedia.org/wiki/Arithmetic_logic_unithttps://en.wikipedia.org/wiki/Computer_storagehttps://en.wikipedia.org/wiki/Computer_storagehttps://en.wikipedia.org/wiki/Microprocessorhttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/MOSFEThttps://en.wikipedia.org/wiki/AND-OR-Inverthttps://en.wikipedia.org/wiki/Reversible_computinghttps://en.wikipedia.org/wiki/Toffoli_gatehttps://en.wikipedia.org/wiki/Functionally_completehttps://en.wikipedia.org/wiki/Relayhttps://en.wikipedia.org/wiki/Thermionic_valvehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Bipolar_transistorshttps://en.wikipedia.org/wiki/Resistor-transistor_logichttps://en.wikipedia.org/wiki/Boolean_functionhttps://en.wikipedia.org/wiki/Logical_operationhttps://en.wikipedia.org/wiki/Logical_operationhttps://en.wikipedia.org/wiki/Rise_timehttps://en.wikipedia.org/wiki/Fan-outhttps://en.wikipedia.org/wiki/Diodehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Switch#Electronic_switcheshttps://en.wikipedia.org/wiki/Vacuum_tubehttps://en.wikipedia.org/wiki/Relayhttps://en.wikipedia.org/wiki/Fluidic_logichttps://en.wikipedia.org/wiki/Pneumatics#Pneumatic_logichttps://en.wikipedia.org/wiki/Opticshttps://en.wikipedia.org/wiki/Molecular_logic_gatehttps://en.wikipedia.org/wiki/Analytical_enginehttps://en.wikipedia.org/wiki/Boolean_logichttps://en.wikipedia.org/wiki/Mathematicshttps://en.wikipedia.org/wiki/Multiplexerhttps://en.wikipedia.org/wiki/Processor_registerhttps://en.wikipedia.org/wiki/Arithmetic_logic_unithttps://en.wikipedia.org/wiki/Computer_storagehttps://en.wikipedia.org/wiki/Computer_storagehttps://en.wikipedia.org/wiki/Microprocessorhttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/MOSFEThttps://en.wikipedia.org/wiki/AND-OR-Inverthttps://en.wikipedia.org/wiki/Reversible_computinghttps://en.wikipedia.org/wiki/Toffoli_gatehttps://en.wikipedia.org/wiki/Functionally_completehttps://en.wikipedia.org/wiki/Relayhttps://en.wikipedia.org/wiki/Thermionic_valvehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Bipolar_transistorshttps://en.wikipedia.org/wiki/Resistor-transistor_logichttps://en.wikipedia.org/wiki/Electronics -
7/25/2019 Physics Final 2
2/16
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.
https://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Diode-transistor_logichttps://en.wikipedia.org/wiki/Transistor-transistor_logichttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/MOSFEThttps://en.wikipedia.org/wiki/PMOS_logichttps://en.wikipedia.org/wiki/NMOS_logichttps://en.wikipedia.org/wiki/CMOShttps://en.wikipedia.org/wiki/Transistor-transistor_logichttps://en.wikipedia.org/wiki/7400_serieshttps://en.wikipedia.org/wiki/Texas_Instrumentshttps://en.wikipedia.org/wiki/CMOShttps://en.wikipedia.org/wiki/4000_serieshttps://en.wikipedia.org/wiki/RCAhttps://en.wikipedia.org/wiki/Programmable_logic_devicehttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Programmable_logic_devicehttps://en.wikipedia.org/wiki/Field-Programmable_Gate_Arrayhttps://en.wikipedia.org/wiki/Gain_(electronics)https://en.wikipedia.org/wiki/Voltagehttps://en.wikipedia.org/wiki/Electronic_amplifierhttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Diode-transistor_logichttps://en.wikipedia.org/wiki/Transistor-transistor_logichttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/Field-effect_transistorhttps://en.wikipedia.org/wiki/MOSFEThttps://en.wikipedia.org/wiki/PMOS_logichttps://en.wikipedia.org/wiki/NMOS_logichttps://en.wikipedia.org/wiki/CMOShttps://en.wikipedia.org/wiki/Transistor-transistor_logichttps://en.wikipedia.org/wiki/7400_serieshttps://en.wikipedia.org/wiki/Texas_Instrumentshttps://en.wikipedia.org/wiki/CMOShttps://en.wikipedia.org/wiki/4000_serieshttps://en.wikipedia.org/wiki/RCAhttps://en.wikipedia.org/wiki/Programmable_logic_devicehttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Programmable_logic_devicehttps://en.wikipedia.org/wiki/Field-Programmable_Gate_Arrayhttps://en.wikipedia.org/wiki/Gain_(electronics)https://en.wikipedia.org/wiki/Voltagehttps://en.wikipedia.org/wiki/Electronic_amplifierhttps://en.wikipedia.org/wiki/Integrated_circuithttps://en.wikipedia.org/wiki/Integrated_circuit -
7/25/2019 Physics Final 2
3/16
*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
https://en.wikipedia.org/wiki/Fanouthttps://en.wikipedia.org/wiki/Propagation_delayhttps://en.wikipedia.org/wiki/Capacitancehttps://en.wikipedia.org/wiki/Fanouthttps://en.wikipedia.org/wiki/Propagation_delayhttps://en.wikipedia.org/wiki/Capacitance -
7/25/2019 Physics Final 2
4/16
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 &.
-
7/25/2019 Physics Final 2
5/16
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.
-
7/25/2019 Physics Final 2
6/16
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
-
7/25/2019 Physics Final 2
7/16
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
https://en.wikipedia.org/wiki/Circuit_boardshttps://en.wikipedia.org/wiki/Gate_arrayhttps://en.wikipedia.org/wiki/Circuit_boardshttps://en.wikipedia.org/wiki/Gate_array -
7/25/2019 Physics Final 2
8/16
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* #
' &
https://en.wikipedia.org/wiki/Field-programmable_gate_arrayhttps://en.wikipedia.org/wiki/Hardware_description_languagehttps://en.wikipedia.org/wiki/Veriloghttps://en.wikipedia.org/wiki/VHDLhttps://en.wikipedia.org/wiki/AND_gatehttps://en.wikipedia.org/wiki/AND_gatehttps://en.wikipedia.org/wiki/OR_gatehttps://en.wikipedia.org/wiki/Field-programmable_gate_arrayhttps://en.wikipedia.org/wiki/Hardware_description_languagehttps://en.wikipedia.org/wiki/Veriloghttps://en.wikipedia.org/wiki/VHDLhttps://en.wikipedia.org/wiki/AND_gatehttps://en.wikipedia.org/wiki/AND_gatehttps://en.wikipedia.org/wiki/OR_gatehttps://en.wikipedia.org/wiki/NOT_gatehttps://en.wikipedia.org/wiki/NOT_gate -
7/25/2019 Physics Final 2
9/16
& '
!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.
-
7/25/2019 Physics Final 2
10/16
*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
-
7/25/2019 Physics Final 2
11/16
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.
-
7/25/2019 Physics Final 2
12/16
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
-
7/25/2019 Physics Final 2
13/16
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 -
7/25/2019 Physics Final 2
14/16
*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.
-
7/25/2019 Physics Final 2
15/16
*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/ -
7/25/2019 Physics Final 2
16/16