K-Map (for Boolean expression simplification)

K-MAP:

   " K map provide a systematical method for the simplification of Boolean expressions. "

Basically there are two methods by which we can simplify the Boolean expression first one is from 12 laws and rules of Boolean algebra and the second is by using K-map. By using K-map we can easily simplify the Boolean than laws and rule of Boolean algebra.

  We have three type of K-map according to the width of the variable. That’s.

1.    3 variable K-map

2.    4 variable K-Map

3.    5 variable K-map

3 VARIABLES OF K-MAP:

            It consist of eight cell in which we distribute the three variable A, D and C. the total  cell is calculate by the number of variable by the power of 2. Such as for three variables the total cell is 2³ the total is 8. Like this for 4 variable K-map the total cell will be 2⁴ which are 16 and the 5 variables K-map the total cell will be 2⁵ which are 32.  We use grey code to calculate the Boolean expression in term of 1s and 0s.

Diagram:

3 variable k map

4 VARIABLES K-MAP:

For 4 variables K-map the total cell will be 2⁴ which are 16. Also use grey code to initiate the cells. We use the four variables A, B, C and D for this K-map.

Diagram:

4 variable k map

5 VARIABLES K-MAP:

For 5 variables k-map the total 32 cells can be made to evaluate the Boolean expression by distributing five variables A, B, C, D and E. Such that we make not a whole 32 cells we divide this into two maps such that both consist of sixteen cells. First k-map for A (1) and second for A-compliment (0).

Diagram:

5 variable k map

Example:

How can I simplify the Boolean expression A+A*B+A*C+'A*B*C?

How can I simplify the Boolean expression A+A*B+A*C+'A*B*C?