I can\'t understand how the Quine – McCluskey method is used to solve this quest
ID: 3669265 • Letter: I
Question
I can't understand how the Quine–McCluskey method is used to solve this question or what format the question is wanting. I've attached a picture of the actual question to provide more detail of what I'm having trouble solving. I'm really lost on how to work this or where to even begin.
Note: My apologies about the rotation of the picture. I kept saving it in the correct rotation, but for some reason it goes back to the way it originally was when I upload it to Chegg. :( Ugh!
5. Using the Quine-McClusky method, find for a. the set of prime implicants b. the set of essential P.l. and c. all minimal expressionsExplanation / Answer
Step 1 : Divide all the minterms (and don’t cares) of function into group
For Min terms For don’t cares
Don’t cares
a b c d
4
9
11
0 1 0 0
1 0 0 1
1 0 1 1
Min terms
a b c d
1
3
5
6
7
8
15
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 1 1 1
Step 1 : Divide all the minterms (and don’t cares) of a function into groups
Group
Min term ID
a b c d
Merge mark
G0
1
4
8
0 0 0 1
0 1 0 0
1 0 0 0
G1
3
5
6
9
11
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
G2
7
0 1 1 1
G3
15
1 1 1 1
Step 2: Merge minterms from adjacent groups to form a new implicant table
Group
Minterm ID
a b c d
G0’
1,3
1,5
1,9
4,5
4,6
8,9
0 0 d 0
0 1 0 d
d 0 0 1
0 1 0 d
0 1 d 0
1 0 0 d
G1’
3,7
5,7
6,7
0 d 1 1
0 1 d 1
0 1 1 d
G2’
7,15
d 1 1 1
Step 3: Repeat step 2 until no more merging is possible
Group
Minterm ID
a b c d
G0”
1,5,6,7
4,5,6,7
4,6,5,7
0 1 d d
0 1 d d
0 1 d d
No merging is possible final table is
Step4.Put all prime implicant in a cover table(don’t care excluded)
Don’t cares
a b c d
4
9
11
0 1 0 0
1 0 0 1
1 0 1 1
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