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7/21/2019 Quine McCluskey
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The Quine-McCluskeyMethod
Prepared by: Kimberly Rivera
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Introduction
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Given:
F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
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Step 1: Generate PrimeImplicant
A prime implicant i a product term t*atcannot be combined +it* anot*er to eliminatea variable
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Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
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
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Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
0 0 0 0 0
4 0 1 0 0
8 1 0 0 0
10 1 0 1 0
12 1 1 0 0
11 1 0 1 1
13 1 1 0 1
15 1 1 1 1
/ero %.
0ne %.
1+o %.
1*ree %.
Four %.
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Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
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
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Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
0 0 0 0 0
4 0 1 0 0
8 1 0 0 0
10 1 0 1 0
12 1 1 0 0
11 1 0 1 1
13 1 1 0 1
15 1 1 1 1
4ou can only 2roup amember o- one2roup to a member
o- t*e ad3acent 2roupi- t*eir onlydi5erence i one
variable
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Given:F(A,B,C,D)!m(",#,$,%",%%,%&,%',%)
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
"""
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;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
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(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
}
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(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
""
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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
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;*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
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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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 2: Contruct Prime Implicant 1able
(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
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Step 3: Reduce Prime Implicant 1able
(a.) Remoe !ssential "#ime $mplicants
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(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&'&
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;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
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(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
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(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
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(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
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(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
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(10,11) (13,15)
10 X
11 X
13 X
15 X
(%",%%) 1 %1 - &C
(%',%) 1 1- 1 '
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Remember:
Step / 8olve Prime Implicant 1able
(",#,$,%&) - - % % C&'&(%",%%) 1 % 1 -
&C(%',%) 1 1 - 1 '
0 C&'& &C '
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Ro+ 'ominance
(1,2,3) (1,5) (1,3,5,7) (2,3,7)
1 X X X
2 X X
3 X X X
5 X X
7 X X
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67ercie:
%F(A,B,C,D)!m(",%,&,',,@$,%",%#,%)
0 &'& &' C
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6nd
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