Boolean Simplification using K-map (with Example)

Boolean Function Simplification Using K-map

We want to simplify the Boolean function:

Fmin = A̅C̅ + A̅D + A̅B + B D

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Step 1: Identify Variables

We have 4 variables: A, B, C, D. We’ll use A and B for rows and C and D for columns in the K-map.

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Step 2: Minterms for Each Product Term

• A̅C̅ → A=0, C=0 → any B, any D → minterms: 0000, 0001, 0100, 0101
• A̅D → A=0, D=1 → any B, any C → minterms: 0001, 0011, 0101, 0111
• A̅B → A=0, B=1 → any C, any D → minterms: 0100, 0101, 0110, 0111
• B D → B=1, D=1 → any A, any C → minterms: 0101, 0111, 1101, 1111

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Step 3: K-map Layout

Placing 1's in the K-map according to minterms:

AB\CD	00	01	11	10
00	1	1	0	0
01	1	1	1	1
11	0	1	1	0
10	0	0	0	0

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Step 4: Group the 1s

• All 1s where A=0 → A̅(C̅ + B + D)
• 1s where B=1 and D=1 (even if A=1) → B D

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Step 5: Final Simplified SOP

Fmin = A̅(C̅ + B + D) + B D

This matches our earlier algebraic simplification.

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