To simply and verify the Boolean expression using K-map.

Aim

To simply and verify the Boolean expression using K-map.

Apparatus Required:

Logic trainer kit, logic gates / ICs, wires.

Theory:

Karnaugh maps: Karnaugh maps or K-maps for short, provide another means of simplifying and optimizing logical expressions. This is a graphical technique that utilizes a sum of product (SOP) form. SOP forms combine terms that have been ANDed together that then get ORed together. This format lends itself to the use of De Morgan's law which allows the final result to be built with only NAND gates. The K-map is best used with logical functions with four or less input variables. One of the advantages of using K-maps for reduction is that it is easier to see when a circuit has been fully simplified. Another advantage is that using K-maps leads to a more structured process for minimization. In order to use a K-map, the truth table for a logical expression is transferred to a K-map grid. The grid for two, three, and four input expressions are provided in the tables below. Each cell corresponds to one row in a truth table or one given state in the logical expression. The order of the items in the grid is not random at all; they are set so that any adjacent cell differs in value by the change in only one variable. Because of this, items can be grouped together easily in rectangular blocks of two, four, and eight to find the minimal number of groupings that can cover the entire expression. Note that diagonal cells require that the value of more than two inputs change, and that they also do not form rectangles.

Given expression

F(C,A,B) = CAB + C'AB + CA'B + C'A'B

Simplification Using Boolean Properties

CAB + C'AB + CA'B + C'A'B = AB(C + C') + A'B(C + C') Distributive Property

= AB + A'B C + C' is always true

= (A + A')B Distributive Property

= B A + A' is always true

Simplification using K- Map

Procedure:

1. Connect the trainer kit to ac power supply.
2. Connect the circuit based on the given logic functions to be simplified.
3. Connect the inputs of first stage to logic sources and output of the last gate to logic indicator.
4. Apply various input combinations and observe output for each one.
5. Verify the output before and after reducing the expression.
6. Switch off the ac power supply.

Result

Post Lab Questions

1. Simply the expression F=AB+AB'
2. Name the different reduction techniques
3. Give the merits and demerits of K-map
4. What are differences between K-map and Quine McCluskey?
5. Give steps for reducing two variable expression using K-map?