1. Minterm = 0,1,2,5,6,7,8,9,10,14
DontCare =
Variable = a,b,c,d
using Quine-McCluskey


Solution:
Minterm = `sum m(0,1,2,5,6,7,8,9,10,14)`

Variable = a,b,c,d
1. min terms and their binary representations

Group A1		0   0000   `->`
Group A2		1   0001   `->` 2   0010   `->` 8   1000   `->`
Group A3		5   0101   `->` 6   0110   `->` 9   1001   `->` 10   1010   `->`
Group A4		7   0111   `->` 14   1110   `->`

2. merging of min term

Group B1 (A1,A2)		0,1   000-   `->` 0,2   00-0   `->` 0,8   -000   `->`
Group B2 (A2,A3)		1,5   0-01   ✓ 1,9   -001   `->` 2,6   0-10   `->` 2,10   -010   `->` 8,9   100-   `->` 8,10   10-0   `->`
Group B3 (A3,A4)		5,7   01-1   ✓ 6,7   011-   ✓ 6,14   -110   `->` 10,14   1-10   `->`

3. merging of min term pairs

Group C1 (B1,B2)		0,1,8,9   -00-   ✓ 0,2,8,10   -0-0   ✓
Group C2 (B2,B3)		2,6,10,14   --10   ✓

1. Prime implicant chart (ignore the don't cares)

PIs\Minterms	0	1	2	5	6	7	8	9	10	14	a,b,c,d
1,5		X		X							0-01
5,7				X		X					01-1
6,7					X	X					011-
0,1,8,9	X	X					X	X			-00-
0,2,8,10	X		X				X		X		-0-0
2,6,10,14			X		X				X	X	--10

Column-9 has only single X, so essential PI (0,1,8,9) is -00-. Now remove this PI Row and corresponding Minterm Column 0,1,8,9

Extracted essential prime implicants : -00-

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2. Reduced Prime implicant chart

PIs\Minterms	2	5	6	7	10	14	a,b,c,d
1,5		X					0-01
5,7		X		X			01-1
6,7			X	X			011-
0,2,8,10	X				X		-0-0
2,6,10,14	X		X		X	X	--10

Column-14 has only single X, so essential PI (2,6,10,14) is --10. Now remove this PI Row and corresponding Minterm Column 2,6,10,14

Extracted essential prime implicants : --10

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3. Reduced Prime implicant chart

PIs\Minterms	5	7	a,b,c,d
1,5	X		0-01
5,7	X	X	01-1
6,7		X	011-
0,2,8,10			-0-0

(`2^(nd)` Row) Row PI 5,7 has maximum(2) X, so essential PI (5,7) is 01-1. Now remove this PI Row and corresponding Minterm Column 5,7


Extracted essential prime implicants : 01-1

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All extracted essential prime implicants : -00-,--10,01-1

Minimal Quine-McCluskey Expression = b'c' + cd' + a'bd