Simplify the following using Quine - McCluskey's method. F(W, X, Y, Z) = Σ(0, 1, 2, 8, 10, 11, 14, 15)

The Quine-McCluskey method is a tabulation method used in digital logic to minimize Boolean expressions. It is a step-by-step procedure used to reduce a given Boolean function to its simplest form.

Let's simplify the given function F(W, X, Y, Z) = Σ(0, 1, 2, 8, 10, 11, 14, 15) using Quine-McCluskey's method.

Step 1: Write the minterms in binary form

Minterm	Binary
0	0000
1	0001
2	0010
8	1000
10	1010
11	1011
14	1110
15	1111

Step 2: Group the minterms based on the number of 1's in their binary representation

Group 0	Group 1	Group 2	Group 3	Group 4
0000	0001	0010	1011	1111
		1010	1110
		1000

Step 3: Compare each element in a group with the elements of the next group. If they differ by a single bit, combine them and mark them. The bit position where they differ is replaced by '-'

Group 0-1	Group 1-2	Group 2-3	Group 3-4
000-	00-0	10-0	111-
	10-0	101-
		11-0

Step 4: Repeat the process for the newly formed groups until no more groups can be combined

Group 0-1-2	Group 1-2-3	Group 2-3-4
0-0-	10--

Step 5: Write down the prime implicants which are not marked

Prime Implicants
000-
00-0
10-0
101-
111-
0-0-
10--

Step 6: Construct a prime implicant table and find the essential prime implicants

Minterm	000-	00-0	10-0	101-	111-	0-0-	10--
0	x	x				x
1	x					x
2		x	x			x
8			x				x
10				x			x
11				x	x
14					x
15					x

The essential prime implicants are those that cover at least one minterm that is not covered by any other prime implicant. From the table, we can see that the essential prime implicants are 000-, 101-, 111-, and 10--.

Step 7: Write the simplified function in terms of the variables

The simplified function is F = W'X' + WY'Z + WXYZ + WX'Z'

So, the given function F(W, X, Y, Z) = Σ(0, 1, 2, 8, 10, 11, 14, 15) simplifies to F = W'X' + WY'Z + WXYZ + WX'Z' using Quine-McCluskey's method.