K-Map Simplification Solution

Given Expression:

f(W,X,Y,Z) = W'X'Y'Z' + WX'YZ + WX'Y'Z + W'YZ + WX'Y'Z'

Step 1: Convert to Minterms

• W'X'Y'Z' = m0
• WX'YZ = m9
• WX'Y'Z = m8
• W'YZ = m3 and m7
• WX'Y'Z' = m8

f = Σ(0,3,7,8,9)

Step 2: K-Map Setup

      YZ
WX    00  01  11  10
00    1   0   1   0    (m0,m3)
01    0   0   1   0    (m7)
11    0   0   0   0    
10    1   1   0   0    (m8,m9)

Step 3: Group the 1s

• Group 1: m0 → W'X'Y'Z'
• Group 2: m3, m7 → YZ
• Group 3: m8, m9 → WX'Z

Step 4: Simplified SOP Expression

f(W,X,Y,Z) = W'X'Y'Z' + YZ + WX'Z

Step 5: Logic Diagram

Inputs: W, X, Y, Z

NOT gates: W' = NOT(W), X' = NOT(X), Y' = NOT(Y), Z' = NOT(Z)

AND gates:
- Term 1: W'X'Y'Z' (4 inputs)
- Term 2: YZ (2 inputs)
- Term 3: WX'Z (3 inputs)

OR gate: f = W'X'Y'Z' + YZ + WX'Z (3 inputs)

Final Answer:

SOP Expression: f(W,X,Y,Z) = W'X'Y'Z' + YZ + WX'Z

Gates needed: 4 NOT, 3 AND, 1 OR