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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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+todo de -arnau"#+todo de -arnau"#


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!d.acencia de celdas!d.acencia de celdas


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!d.acencia de celdas!d.acencia de celdas


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+ini&i/aci*n de la su&a de productos+ini&i/aci*n de la su&a de productos


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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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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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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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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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(onversi*n entre 1or&as estndar(onversi*n entre 1or&as estndar


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EstructurasEstructuras


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%unciones inco&pleta&ente especi1icadas%unciones inco&pleta&ente especi1icadas


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)ndi1erencias en la su&a de productos)ndi1erencias en la su&a de productos


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)ndi1erencias en la su&a de productos)ndi1erencias en la su&a de productos

di1 i d d


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)ndi1erencias en productos de su&as)ndi1erencias en productos de su&as

di1 i d ddi1 i d d


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)ndi1erencias en productos de su&as)ndi1erencias en productos de su&as

EE


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(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 li1i i* d lti 1 iSi&pli1icaci*n de & lti 1 nciones


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Si&pli1icaci*n de & lti 1 ncionesSi&pli1icaci*n de &ulti 1unciones


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Si&pli1icaci*n de &ulti 1uncionesSi&pli1icaci*n de &ulti 1unciones


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%unciones con &s de cuatro variales%unciones con &s de cuatro variales


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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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! 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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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.


'#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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ed

Su&&ar.Su&&ar.


!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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2009 Pearson Education, Upper Saddle River, NJ 07458 !ll Ri"#ts Reserved%lo.d, $i"ital %unda&entals, 0t#

ed


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;

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