Question

Sequence of steps for Boolean function simplification using K-map : A. Write truth table B. Plot minterms on K-map C. Group adjacent 1's D. Write simplified equation Choose the correct answer from the options given below :

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

Hint:

Standard K-map simplification sequence: \[ \text{Truth Table} \rightarrow \text{Plot Minterms} \rightarrow \text{Group Adjacent 1's} \rightarrow \text{Simplified Expression} \] Always form groups in powers of: \[ 2^n \] such as \(1,2,4,8\).

Answer 1

The Correct Option is B

Concept: Karnaugh Map (K-map) is a graphical method used for simplifying Boolean expressions. The simplification process follows a systematic sequence:
• Obtain truth table
• Plot values on K-map
• Group adjacent cells
• Derive simplified expression Following the correct order is important to avoid logical errors during minimization.

Step 1: Write the truth table. The first step is: \[ \text{Write truth table} \] The truth table identifies:
• Input combinations
• Output values
• Required minterms Hence: \[ A \] comes first.

Step 2: Plot minterms on the K-map. After obtaining the truth table:
• Corresponding 1's are placed in K-map cells.
• Each cell represents a minterm. Thus: \[ B \] comes next.

Step 3: Group adjacent 1's. After plotting:
• Adjacent cells containing 1's are grouped.
• Groups are formed in powers of 2: \[ 1,2,4,8,\ldots \] This step reduces variables and simplifies the logic expression. Therefore: \[ C \] comes after plotting.

Step 4: Write the simplified equation. Finally:
• Simplified Boolean terms are extracted from groups.
• Reduced Boolean expression is written. Thus: \[ D \] comes last.

Step 5: Write the complete sequence. Therefore, the correct order is: \[ A \rightarrow B \rightarrow C \rightarrow D \] Hence, the correct option is: \[ \boxed{(B)\ A,B,C,D} \]