Question

Arrange the following steps of K-Map simplification in the correct order.
• [A.] Write the minimized SOP/POS expression
• [B.] Plot the truth table outputs (1s and 0s) on the K-Map
• [C.] Identify the prime implicants and essential prime implicants
• [D.] Draw groups (loops) of adjacent 1s (or 0s) in powers of 2
Choose the correct answer from the options given below:

• A. A, B, C, D
• B. B, C, A, D
• C. C, A, B, D
• D. B, D, C, A

Hint:

K-Map order: Fill → Group → Identify → Simplify.

Answer 1

The Correct Option is D

Concept: Karnaugh Map (K-Map) is a graphical method used to simplify Boolean expressions by grouping adjacent cells.

Step 1: Plot outputs on K-Map.
First, the values from the truth table (1s for SOP or 0s for POS) are placed into the K-map grid.
\[ \text{This corresponds to step B.} \]

Step 2: Draw groups (loops).
Adjacent cells containing 1s (or 0s) are grouped in powers of 2 (1, 2, 4, 8...).
This helps reduce variables.
\[ \text{This corresponds to step D.} \]

Step 3: Identify prime implicants.
From the formed groups:
• Prime implicants are the largest possible groups.
• Essential prime implicants are those covering unique cells. \[ \text{This corresponds to step C.} \]

Step 4: Write minimized expression.
Finally, the simplified Boolean expression is written using the identified implicants.
\[ \text{This corresponds to step A.} \]

Step 5: Final correct sequence. \[ B \rightarrow D \rightarrow C \rightarrow A \] \[ \boxed{(4)} \]