quine mccluskey

7/21/2019 Quine McCluskey

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The Quine-McCluskeyMethod

Prepared by: Kimberly Rivera



Introduction



Given:

F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)



Step 1: Generate PrimeImplicant

A prime implicant i a product term t*atcannot be combined +it* anot*er to eliminatea variable



Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)

Group by t*enumber o- %.

0 0 0 0 0

4 0 1 0 0

8 1 0 0 0

10 1 0 1 0

12 1 1 0 0

11 1 0 1 1

13 1 1 0 1

15 1 1 1 1



Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)

0 0 0 0 0

4 0 1 0 0

8 1 0 0 0

10 1 0 1 0

12 1 1 0 0

11 1 0 1 1

13 1 1 0 1

15 1 1 1 1

/ero %.

0ne %.

1+o %.

1*ree %.

Four %.



Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)

0 0 0 0 0

4 0 1 0 0

8 1 0 0 0

10 1 0 1 0

12 1 1 0 0

11 1 0 1 1

13 1 1 0 1

15 1 1 1 1

A-ter 2roupin2 t*emby t*e number o- %.,+e no+ *ave to

compare eac*member o- one2roup to eac*member o- t*e it

ad3acent 2roup



Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)

0 0 0 0 0

4 0 1 0 0

8 1 0 0 0

10 1 0 1 0

12 1 1 0 0

11 1 0 1 1

13 1 1 0 1

15 1 1 1 1

4ou can only 2roup amember o- one2roup to a member

o- t*e ad3acent 2roupi- t*eir onlydi5erence i one

variable



Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)

0 0 0 0 0

4 0 1 0 0

8 1 0 0 0

10 1 0 1 0

12 1 1 0 0

11 1 0 1 1

13 1 1 0 1

15 1 1 1 1

67ample, *ere+e compare t*e2roup o- /ero %.to t*e 2roup o-

0ne %.

} (",#) """" "%""

Replace t*e variable t*atc*an2ed +it* a DA89

"""



;e do t*i -or t*e ret o- t*e member 1*en+e.ll arrive +it* t*i table

(0,4) 0 - 0 0

(0,8) - 0 0 0

(4,12) - 1 0 0

(8,10) 1 0 - 0

(8,12) 1 - 0 0

(10,11) 1 0 1 -

(12.13) 1 1 0 -

(11,15) 1 - 1 1

(13,15) 1 1 - 1

<o+, +e.ll repeat t*e

ame tep, but t*i time,+e.ll 2roup t*oe t*at*ave t*e da*e in t*eame poition



(0,8) - 0 0 0

(4,12) - 1 0 0

(0,4) 0 - 0 0

(8,12) 1 - 0 0

(11,15)

1 - 1 1

(8,10) 1 0 - 0

(13,15) 1 1 - 1

(10,11) 1 0 1 -

(12,13) 1 1 0 -

A2ain +ecompare, but

t*i time, +eonly compare t*emember +it*in

one 2roup

}



(0,8) - 0 0 0

(4,12) - 1 0 0

(0,4) 0 - 0 0

(8,12) 1 - 0 0

(11,15)

1 - 1 1

(8,10) 1 0 - 0

(13,15) 1 1 - 1

(10,11) 1 0 1 -

(12,13) 1 1 0 -

} (",$,#,%&) """ %""

=ut li>e be-ore, +eput a da* in

replacement -or t*evariable t*atc*an2ed

""



A-ter pairin2 eac* member, +e.ll arrive +it*t*i table

(0,8,4,12) - - 0 0

(0,4,8,12) - - 0 0

;e only 2ot to pair -our

prime implicant in t*epreviou table Reultin2 toonly t+o prime implicant int*i table



;*at +ill *appen to t*oe t*at are not paired?

(0,8) - 0 0 0

(4,12) - 1 0 0

(0,4) 0 - 0 0

(8,12) 1 - 0 0

(11,

15)1 - 1 1

(8,10) 1 0 - 0

(13,15) 1 1 - 1

(10,11) 1 0 1 -

(12,13) 1 1 0 -

1*ey +ill be

included in t*ePrimeImplicant 1able



Step 2: Contruct Prime Implicant 1able

(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0

4

8

10

11

12

13

15




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X

10

11

12 X

13

15




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X

11

12 X

13

15




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X X

11 X

12 X

13

15




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X X

11 X X

12 X

13

15 X




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X X

11 X X

12 X X

13 X

15 X




(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X X

11 X X

12 X X

13 X X

15 X X



Step 3: Reduce Prime Implicant 1able

(a.) Remoe !ssential "#ime $mplicants



(0,4,8,12)

(8,10) (10,11 )

(11,15 )

(12,13 )

(13,15 )

0 X

4 X

8 X X

10 X X

11 X X

12 X X

13 X X

15 X X

.) Remoe !ssential "#ime $mplicants

(",#,$,%&) - - % % C&'&



;e re+rite t*e table +it*out t*e eliminated ro+and column

(8,10) (10,11) (11,15) (12,13) (13,15)

10 X X

11 X X

13 X X

15 X X



(8,10) (10,11) (11,15) (12,13) (13,15)

10 X X

11 X X

13 X X

15 X X

e.) Ro+ 'ominance ,# (c.) Column 'ominan



(8,10) (10,11) (11,15) (12,13) (13,15)

10 X X

11 X X

13 X X

15 X X

Ro+ dominance i not applicable in t*i table, t*ere-ore, +e uecolumn dominance 1*en, +e remove t*e dominated column



(10,11) (11,15) (13,15)

10 X

11 X X

13 X

15 X X

;e re+rite t*e table +it*out t*e dominated columnAnd a2ain, column dominance can be applied



(10,11) (13,15)

10 X

11 X

13 X

15 X

Ro+ dominance and Removin2 o- 6ential Prime Implicant caneit*er be applied in t*i table *o+ever, +e +ill be able toimpli-y it -ater by Removin2 t*e eential prime implicant



(10,11) (13,15)

10 X

11 X

13 X

15 X

(%",%%) 1 %1 - &C

(%',%) 1 1- 1 '



Remember:

Step / 8olve Prime Implicant 1able

(",#,$,%&) - - % % C&'&(%",%%) 1 % 1 -

&C(%',%) 1 1 - 1 '

0 C&'& &C '



Ro+ 'ominance

(1,2,3) (1,5) (1,3,5,7) (2,3,7)

1 X X X

2 X X

3 X X X

5 X X

7 X X



67ercie:

%F(A,B,C,D)!m(",%,&,',,@$,%",%#,%)

0 &'& &' C



6nd

quine mccluskey

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