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MINISTERUL EDUCAȚIEI AL REPUBLICII MOLDOVA

UNIVERSITATEA TEHNICĂ A MOLDOVEI

Lucrare de laborator nr.1Anal!a " #nte!a d#$o!t%elor nu&erceTema: Sinteza circuitelor logice

comina!ionale

A e'ectuat lucrarea (Student )r. TI*1+, U&ane-A.A %ercat lucrarea (Lector un%. Munteanu S.

C/"n0u 213

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Lucrare "e laorator Nr#$

Tema lucr%rii : Sinteza circuitelor logice comina!ionale

Sco&ul lucr%rii: 'tu"ierea &ractic% (i cercetarea

&roce'ului "e 'intez% a circuitelor logice comina!ionale#

Varianta )$

*$ + ,-./$/0/1/2/3/4/$./$)/$567

*) + ,-$/)/5/8/0/1/3/4/$$/$8/$067

$# Con#tru- tabelul de ade%0r $entru 'unc-le lo)ce 41 " 4 (

5 + 161

6

6,

6+

41

4

2 2 2 2 2 1 21 2 2 2 1 1 1 2 2 1 2 2 1, 2 2 1 1 2 1+ 2 1 2 2 2 13 2 1 2 1 1 1

7 2 1 1 2 1 18 2 1 1 1 1 25 1 2 2 2 1 19 1 2 2 1 1 112

1 2 1 2 1 2

11

1 2 1 1 2 1

1

1 1 2 2 1 2

1,

1 1 2 1 1 2

1+

1 1 1 2 2 1

1 1 1 1 1 2 1

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3Ta#$ Tabelul de ade%0r

)# E'ectua- &n&!area 'unc-lor 41 " 4 $entru unt0- "!erour (

 y1

=(   ´ x3

∙ x4 )+( x1

∙   ´ x3 )+(   ´ x

1∙ x

2∙ x

3 )+ (  ´ x2

∙   ´ x3

∙   ´ x4 )+( x1

∙   ´ x2

∙   ´ x4 )

 y2

=( x1∙   ´ x

2∙   ´ x

3)+ ( x1∙ x

3∙ x

4 )+( x2∙ x

3∙   ´ x

4 )+(   ´ x1

∙ x3

∙   ´ x4 )+(   ´ x

1∙   ´ x

2∙ x

4 )+(   ´ x1

∙ x2

∙   ´ x3 )

 y1a=( x1+ x

3+ x4 ) ( x1+ x

2+ x3 ) (   ´ x

1+ x2+ ´ x

3+ ´ x4 ) (   ´ x

1+ ´ x2+ x

3 )

 y2a

=( x1+ x

2+ ´ x

3 ) ( x1+ ´ x

2+ x

3+ ´ x

4 ) (  ´ x1

+ x2

+ x3

+ x4 ) (  ´ x

1+ ´ x

2+ x

3+ ´ x

4 )

5# Utl!:nd $ro$ret0-le de;Mor)an tran#'or&a- 'or&ad#<unct%0 $rn #etul de ele&ente(

,

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 y1=  ´(   ´ x3∙ x 4 )+( x1 ∙   ´ x3 )+(   ´ x1 ∙ x 2∙ x 3 )+ (  ´ x2∙   ´ x3 ∙   ´ x4 )+( x1 ∙   ´ x2 ∙   ´ x 4 )

 y1

=  ´(   ´´ x

3∙ x

4 ) ∙ (   ´ x1

∙   ´ x3 ) ∙(   ´´ x

1∙ x

2∙ x

3 ) ∙ (   ´´ x2

  ´ x3

  ´ x4 ) ∙(   ´ x

1  ´ x2

  ´ x4)

 y2=   ´( x1∙   ´ x2∙   ´ x3)+ ( x1∙ x3 ∙ x4 )+( x2∙ x3 ∙   ´ x 4 )+(   ´ x1∙ x3 ∙   ´ x4 )+(   ´ x1 ∙   ´ x2∙ x 4 )+(   ´ x1∙ x 2 ∙   ´ x3 )

 y2

=  ´(   ´ x

1∙   ´ x

2∙   ´ x

3 ) ∙ (   ´ x1

∙ x3

∙ x4 ) ∙ (   ´ x

2∙ x

3∙   ´ x

4 ) ∙(   ´´ x1

∙ x3

∙   ´ x4 ) ∙ (   ´´ x

1∙   ´ x

2∙ x

4 ) ∙ (   ´´ x1

∙ x2

∙   ´ x3 )

8# Con#tru- #c/e&a crcutulu lo)c $entru 'unc-le 41 " 4 =n#etul de ele&ente >I*NU(

+

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9ig#$ Sc/e&a crcutulu lo)c $entru 'unc-le 41

3

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9ig#) Sc/e&a crcutulu lo)c $entru 'unc-le 4

0# Pentru ecare crcut lo)c deter&na- co#tul " t&$ul dere-nere(Pentru 41 ( C ? 15@ Td ? Pentru 4 ( C ? 7@ Td ?

1# Pentru 'unc-a 41 deter&na- 'unc-a (canonc*d#<unct%0(

 y1

=(   ´ x3

∙ x4 )+( x1

∙   ´ x3 )+(   ´ x

1∙ x

2∙ x

3 )+ (  ´ x2

∙   ´ x3

∙   ´ x4 )+( x1

∙   ´ x2

∙   ´ x4 )

'or&a canonc*con<unct%0( y

1=( x1

+ x3

+ x4 )(  x

1+ x

2+ x

3 ) (   ´ x1

+ x2

+ ´ x3

+ ´ x4 ) (   ´ x

1+ ´ x

2+ x

3 )

7

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2# Pentru 'unc-a 4 #cre- toate cele 5 'or&e $e care lecunoa"te-(

adn 'or&a d#<unct%0 nor&al0(

'or&a >ISAU( y2

=( x1∙   ´ x

2∙   ´ x

3)+ ( x1∙ x

3∙ x

4 )+( x2∙ x

3∙   ´ x

4 )+(   ´ x1

∙ x3

∙   ´ x4 )+(   ´ x

1∙   ´ x

2∙ x

4 )+(   ´ x1

∙ x2

∙   ´ x3 )

'or&a >I*NU>I*NU( y

2=

  ´(   ´ x1

∙   ´ x2

∙   ´ x3 ) ∙ (   ´ x

1∙ x

3∙ x

4 ) ∙ (   ´ x2

∙ x3

∙   ´ x4 ) ∙(   ´´ x

1∙ x

3∙   ´ x

4 ) ∙ (   ´´ x1

∙   ´ x2

∙ x4 ) ∙ (   ´´ x

1∙ x

2∙   ´ x

3 )

'or&a SAU>I*NU( y2=

  ´(   ´ x1+ x2+ x3 ) (   ´ x1+   ´ x3+   ´ x4 ) (   ´ x2+ ´ x3+ x4 )(  x1+   ´ x3+ x4 ) ( x1+ x2+   ´ x4 ) ( x1+   ´ x2+ x3 )

'or&a SAU*NUSAU(

 y2=(  ´

´ x1+ x2+ x3

)+ (  ´

´ x1+ ´ x3+ ´ x4

)+ (  ´

´ x2+ ´ x3+ x4

)+(  ´

 x1+ ´ x3+ x4

)+(  ´

 x1+ x2+ ´ x4

)+(  ´

 x1+ ´ x2+ x3

)

bdn 'or&a con<unct%0 nor&al0('or&a SAU>I(

 y2

=( x1+ x

2+ ´ x

3 ) ( x1+ ´ x

2+ x

3+ ´ x

4 ) (  ´ x1

+ x2

+ x3

+ x4 ) (  ´ x

1+ ´ x

2+ x

3+ ´ x

4 )

'or&a >I*NU>I( y

2=(   ´´ x

1∙   ´ x

2∙ x

3 ) (   ´´ x1

∙ x2

∙   ´ x3

∙ x4 ) (   ´ x

1∙   ´ x

2∙   ´ x

3∙   ´ x

4 ) (   ´ x1

∙ x2

∙ x3

∙ x4 )

'or&a >ISAU*NU( y2=  ´(   ´ x1∙   ´ x2∙ x 3)+ (  ´ x1∙ x2 ∙   ´ x3 ∙ x4 )+ ( x1 ∙   ´ x2 ∙   ´ x3∙   ´ x4 )+( x1 ∙ x2∙ x 3∙ x 4 )

'or&a SAU*NUSAU*NU( y

2=

  ´(   ´ x1

+ x2

+ ´ x3 )+ (   ´ x

1+ ´ x

2+ x

3+ ´ x

4 )+(   ´´ x1

+ x2

+ x3

+ x4)+(   ´´ x

1+ ´ x

2+ x

3+ ´ x

4 )

Concluzie(n ur&a ace#te lucr0r de laborator a& a$lcat =n $ractc0 " a&

cercetat $roce#ul de #nte!0 a crcutelor lo)ce co&bna-onaleF a&e'ectuat &n&!area 'unc-lor lo)ce du$0 care a& real!at #ne!acrcutulu lo)c =n #etul de ele&ente >I*NUF " a& re$re!entat ace#te'unc- =n toate cele o$t 'or&e nor&ale.

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