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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
$i"ital
%unda&entals'ent# Edition
Floyd
(#apter 4
2008 Pearson Education
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)ntroducci*n)ntroducci*n
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EstrucutraEstrucutra
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
+todo de -arnau"#+todo de -arnau"#
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
+todo de -arnau"#+todo de -arnau"#
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+todo de -arnau"#+todo de -arnau"#
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
!d.acencia de celdas!d.acencia de celdas
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!d.acencia de celdas!d.acencia de celdas
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
+ini&i/aci*n de la su&a de productos+ini&i/aci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de la su&a de productoseneraci*n del &apa de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de la su&a de productoseneraci*n del &apa de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de la su&a de productoseneraci*n del &apa de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de la su&a de productoseneraci*n del &apa de la su&a de productos
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Resu&nResu&n
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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Resu&nResu&n
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n de la su&a de productosSi&pli1icaci*n de la su&a de productos
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3tenci*n a partir de la tala de verdad3tenci*n a partir de la tala de verdad
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3tenci*n a partir de la tala de verdad3tenci*n a partir de la tala de verdad
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
3tenci*n a partir de la tala de verdad3tenci*n a partir de la tala de verdad
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EstructuraEstructura
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+ini&i/aci*n del producto de su&as+ini&i/aci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de producto de su&aseneraci*n del &apa de producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
eneraci*n del &apa de producto de su&aseneraci*n del &apa de producto de su&as
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eneraci*n del &apa de producto de su&aseneraci*n del &apa de producto de su&as
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Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
Si&pli1icaci*n del producto de su&asSi&pli1icaci*n del producto de su&as
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3tenci*n a partir de la tala de verdad3tenci*n a partir de la tala de verdad
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
3tenci*n a partir de la tala de verdad3tenci*n a partir de la tala de verdad
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(onversi*n entre 1or&as estndar(onversi*n entre 1or&as estndar
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts Reserved%lo.d, $i"ital %unda&entals, 0t#ed
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EstructurasEstructuras
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%unciones inco&pleta&ente especi1icadas%unciones inco&pleta&ente especi1icadas
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
)ndi1erencias en la su&a de productos)ndi1erencias en la su&a de productos
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
)ndi1erencias en la su&a de productos)ndi1erencias en la su&a de productos
di1 i d d
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
)ndi1erencias en productos de su&as)ndi1erencias en productos de su&as
di1 i d ddi1 i d d
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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts ReservedFloyd, Digital Fundamentals, 10thed
)ndi1erencias en productos de su&as)ndi1erencias en productos de su&as
EE
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EstructuraEstructura
(i i lid 6l i l(i i lid 6l i l
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(ircuitos con slida &6ltiple(ircuitos con slida &6ltiple
+t d d - # lti 1 i+t d d - # lti 1 i
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+todo de -arnau"# para &ulti1unciones+todo de -arnau"# para &ulti1unciones
Si li1i i* d l i 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi li1i i* d lti 1 i
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si li1i i* d lti 1 iSi&pli1icaci*n de & lti 1 nciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si&pli1icaci*n de & lti 1 ncionesSi&pli1icaci*n de &ulti 1unciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si&pli1icaci*n de &ulti 1uncionesSi&pli1icaci*n de &ulti 1unciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si&pli1icaci*n de &ulti 1uncionesSi&pli1icaci*n de &ulti 1unciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si&pli1icaci*n de &ulti 1uncionesSi&pli1icaci*n de &ulti 1unciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
Si&pli1icaci*n de &ulti 1uncionesSi&pli1icaci*n de &ulti 1unciones
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Si&pli1icaci*n de &ulti1uncionesSi&pli1icaci*n de &ulti1unciones
EstructuraEstructura
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EstructuraEstructura
%unciones con &s de cuatro variales%unciones con &s de cuatro variales
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%unciones con &s de cuatro variales%unciones con &s de cuatro variales
%unciones con &s de cuatro variales%unciones con &s de cuatro variales
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%unciones con &s de cuatro variales%unciones con &s de cuatro variales
EstructuraEstructura
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EstructuraEstructura
Resu&nResu&n
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Resu&nResu&n
Su&&ar.Su&&ar.
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'#e -arnau"# &ap -&ap is a tool 1or si&pli1.in"
co&inational lo"ic :it# ; or 4 variales %or ; variales,
8 cells are re
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0
00
0
0
AB
C
(ells are usuall. laeled usin" 0>s and >s to represent t#e
variale and its co&ple&ent
ra.
code
Su&&ar.Su&&ar.
-arnau"# &aps
3nes are read as t#e true variale
and /eros are read as t#e
co&ple&ented variale
'#e nu&ers are entered in "ra.
code, to 1orce ad=acent cells to edi11erent . onl. one variale
Su&&ar.Su&&ar.
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Su&&ar.Su&&ar.
ABC
ABC
ABC
ABC
ABC
ABC
ABC
ABC
AB
AB
AB
AB
C C
!lternativel., cells can e laeled :it# t#e variale
letters '#is &a?es it si&ple to read, ut it ta?es &ore
ti&e preparin" t#e &ap
-arnau"# &aps
C C
AB
AB
AB
AB
C C
AB
AB
AB
AB ABC
ABC
Read t#e ter&s 1or t#e.ello: cells
'#e cells areABCandABC
Su&&ar.Su&&ar.
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ed
roup t#e >s into t:o overlappin""roups as indicated
2 Read eac# "roup . eli&inatin" an.
variale t#at c#an"es across a
oundar.; '#e vertical "roup is readAC
Su&&ar.Su&&ar.
-&aps can si&pli1. co&inational lo"ic . "roupin"
cells and eli&inatin" variales t#at c#an"e
-arnau"# &aps
AB
C
00
02
22
20
0 2
2
2 2
A B
C
0 0
0 2
2 2
2 0
0 2
roup t#e >s on t#e &ap and read t#e &ini&u& lo"ic
Bc#an"es
across t#is
oundar.
Cc#an"es
across t#is
oundar.
4 '#e #ori/ontal "roup is readAB
X = AC +AB
Su&&ar.Su&&ar.
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ed
! 4variale &ap #as an ad=acent cell on eac# o1 its 1ouroundaries as s#o:n
AB
AB
AB
AB
CD CD CD CD
Eac# cell is di11erent onl. .
one variale 1ro& an ad=acent
cell
roupin" 1ollo:s t#e rules
"iven in t#e te@t
'#e 1ollo:in" slide s#o:s an
e@a&ple o1 readin" a 1ourvariale &ap usin" inar.
nu&ers 1or t#e varialesA
Su&&ar.Su&&ar.
-arnau"# &aps
Su&&ar.Su&&ar.
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ed
X
Su&&ar.Su&&ar.
-arnau"# &aps
roup t#e >s on t#e &ap and read t#e &ini&u& lo"ic
roup t#e >s into t:o separate
"roups as indicated2 Read eac# "roup . eli&inatin"
an. variale t#at c#an"es across a
oundar.
; '#e upper .ello: "roup is read as
AD.4 '#e lo:er "reen "roup is read as
AD
AB
CD
00
02
22
20
00 02 22 20
2 2
2 2
2
2
2
2
AB
CD
00
02
22
20
00 02 22 20
2 2
2 2
2
2
2
2
X = AD +AD
Bc#an"es
C c#an"es
Bc#an"es
Cc#an"es across
outer oundar.
Su&&ar.Su&&ar.
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ed
Su&&ar.Su&&ar.
Bard:are $escription Can"ua"es B$Cs
! Bard:are $escription Can"ua"e B$C is a tool 1ori&ple&entin" a lo"ic desi"n in a PC$ 3ne i&portant
lan"ua"e is called DB$C )n DB$C, t#ere are t#ree
approac#es to descriin" lo"ic
2 $ata1lo:
; Fe#avioral
Structural $escription is li?e a sc#e&atic
co&ponents and loc? dia"ra&s
$escription is li?e a sc#e&atic
co&ponents and loc? dia"ra&s
$escription is e
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ed
Su&&ar.Su&&ar.
Bard:are $escription Can"ua"es B$Cs
'#e data flow&et#od 1or DB$C uses Fooleant.pe state&ents '#ere
are t:oparts to a asic data 1lo: pro"ra& t#e entityand t#e
architecture '#e entit. portion descries t#e )G3 '#e arc#itecture
portion descries t#e lo"ic '#e 1ollo:in" e@a&ple is a DB$C pro"ra&
s#o:in" t#e t:o parts '#e pro"ra& is used to detect an invalid F($
codeentityF($)nv is
portF,(,$ in bitH I out bitH
endentityF($)nv
architecture)nvalid of F($)nvbegin
I K (B or C) and DH
endarchitecture)nvalidH
Su&&ar.Su&&ar.
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Su&&ar.Su&&ar.
Bard:are $escription Can"ua"es B$Cs
!not#er standard B$C is Derilo" )n Derilo", t#e )G3 and t#e lo"ic is
descried in one unit called a module Derilo" uses speci1ic s.&ols to
stand 1or t#e Foolean lo"ical operators
'#e 1ollo:in" is t#e sa&e pro"ra& as in t#e previous slide, :ritten
1or Derilo"
moduleF($)nv I, F, (, $H
inputF, (, $H
outputIH
assignI K F L (M$Hendmodule
Selected -e. 'er&sSelected -e. 'er&s
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ed
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Variable
Complement
Sum term
Product term
A symbol used to represent a logical quantity thatcan have a value of 1 or 0, usually designated by
an italic letter.
The inverse or opposite of a number. In Boolean
algebra, the inverse function, expressed with a barover the variable.
The Boolean sum of two or more literals
equivalent to an OR operation.
'#e Foolean product o1 t:o or &ore literals
e
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Sum-of-products (SOP)
Product of
sums (POS)
Karnaugh map
VHDL
! 1or& o1 Foolean e@pression t#at is asicall. t#e3Rin" o1 !N$ed ter&s
A form of Boolean expression that is basically the
ANDing of ORed terms.
An arrangement of cells representing combinations
of literals in a Boolean expression and used for
systematic simplification of the expression.
! standard #ard:are description lan"ua"e )EEE
Std 0799;
Recommended