Lesson-3-Karnaugh-Map PDF

ECE 311 LOGIC CIRCUITS AND SWITCHING THEORY  Karnaugh Map ENGR. ANGELICA L. BONGCAYAO, LPT Instructor Karnaugh Map (K-map)  A Karnaugh map provides a systematic method for simplifying Boolean expressions and, if properly used...

ECE 311 LOGIC CIRCUITS AND SWITCHING THEORY  Karnaugh Map ENGR. ANGELICA L. BONGCAYAO, LPT Instructor Karnaugh Map (K-map)  A Karnaugh map provides a systematic method for simplifying Boolean expressions and, if properly used, will produce the simplest SOP or POS expression possible, known as the minimum expression.  The purpose of a Karnaugh map is to simplify a Boolean expression.  A Karnaugh map is similar to a truth table because it presents all of the possible values of input variables and the resulting output for each value. Instead of being organized into columns and rows like a truth table, the Karnaugh map is an array of cells in which each cell represents a binary value of the input variables.  The cells are arranged in a way so that simplification of a given expression is simply a matter of properly grouping the cells. The 3-Variable Karnaugh Map Karnaugh Map ---- Rules of Simplification Groups may wrap around the table. The leftmost cell in a row may be grouped with the rightmost cell and the top cell in a column may be grouped with the bottom cell. There should be as few groups as possible, as long as this does not contradict any of the previous rules. Summary: 1. No zeros allowed. 2. No diagonals. 3. Only power of 2 number of cells in each group. 4. Groups should be as large as possible. 5. Every one must be in at least one group. 6. Overlapping allowed. 7. Wrap around allowed. 8. Fewest number of groups possible. Ans: Ans: Ans: Ans: Ans: Ans: Ans: When a quad is looped, the resultant term will contain only the variables that do not change form for all the squares in the quad. Ans: Ans: Ans: Ans: Ans: Ans: An s: Ans: Ans:  Let’s Solve! No.1 No.2 No.3