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Using Quine McClusky method, minimize the following : F(A,B,C,D,E)= Σm(0,1,3,7,8,9,11,15,22,24,27)+d(6,16)
written 4.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 4.5 years ago
digital electronics
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written 4.5 years ago by gravatar for teamques10 teamques10 ★ 70k

Step 1: Input Grouping the minterms/don't care terms based on number of 1's

Group Minterm/Don’t care terms Binary Representation
0 0 0 0 0 0 0
1 1 0 0 0 0 1
8 0 1 0 0 0
16 1 0 0 0 0
2 3 0 0 0 1 1
6 0 0 1 1 0
9 0 1 0 0 1
11 0 1 0 1 0
24 1 1 0 0 0
3 7 0 0 1 1 1
22 1 0 1 1 0
4 15 0 1 1 1 1
27 1 1 0 1 1

 

Step 2: First Comparison Group the terms in pairs:

Group Pairs Binary Representation
0 (0,1) 0 0 0 0 -
(0,8) 0 - 0 0 0
(0,16) - 0 0 0 0
1 (1,9) 0 - 0 0 1
(8,9) 0 1 0 0 -
(8,24) - 1 0 0 0
(16,24) 1 - 0 0 0
2 (9,11) 0 1 0 - 1
(6,7) 0 0 1 1 -
(6,22) - 0 1 1 0
3 (7,15) 0 - 1 1 1
(11,15) 0 1 - 1 1
(11,27) - 1 0 1 1

Step 3: Second Comparison

Group Pairs Binary Representation
0 (0,1,8,9) 0 - 0 0 -
(0,8,16,24) - - 0 0 0

Step 4: Prime Implicants:

( 9 , 8 , 1 , 0 ) 0 - 0 0 -

( 24 , 16 , 8 , 0 ) - - 0 0 0

( 11 , 9 ) 0 1 0 - 1

( 7 , 6 ) 0 0 1 1 -

( 22 , 6 ) - 0 1 1 0

( 15 , 7 ) 0 - 1 1 1

( 15 , 11 ) 0 1 - 1 1

( 27 , 11 ) - 1 0 1 1

Step 4: Coverage Table

0-00- --000 010-1 0011- -0110 0-111 01-11 -1011
0 x x
1 x
7 x x
8 x x
9 x x
11 x x x
15 x x
22 x
24 x
27 x

$\bar{A}\bar{B}CD + A\bar{C}D$

Verify the output using this handy tool
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