Construction of four variable K map for a given Pairs

CONSTRUCTION OF FOUR VARIABLE K‒MAP FOR A GIVEN TRUTH TABLE

Let us consider a Table 2.17. In this, the input variable A,B,C & D and output variable Y forms a Truth Table.

Construction of 4‒ Variable K‒map in SOP form

Step 1: Look for output 1s in the Truth table (Table 2.17)

Step 2: Write the minterms.

The minterms are 

Step 3: Now enter 1s for the product

 and 0s in the remaining cells, the complete Karnaugh map looks like as shown in Fig.2.17A.

In another way the minterms  can be represented by function F(A,B,C,D) = Σm (1,6,7,10,14).

Here Σ and m represents SOP and minterms respectively and 1,6,7,10,14 are cell order values. The construction of Karnaugh map is as shown in Fig.2.17(B). Fig. 2.17(A) and 2.17(B) represents same SOP minterms for the Table 2.17.

Construction of 4‒ Variable K‒map in POS form

Step 1: Look for output 0s in the Truth table (Table 2.17)

Step 2: Write the Maxterms.

The Maxterms are

Step 3: Now enter 0s for the sum

and 1s in the remaining cells, the complete Karnaugh map for POS looks like as shown in Fig.2.18(A)

Fig. 2.18(A) and 2.18(B) represents same POS Maxterms for the Table 2.17

In another way the Maxterms

can be represented by function F(A,B,C,D) C,D) = Π M (0,2,3,4,5, 8,9,11,12,13,15).

Here Π and M represents POS and Maxterms respectively and 0,2,3,4,5,8,9,11,12,13,15 are cell order values. The construction of Karnaugh map is as shown in Fig.2.18(B).

Note: Σm (or) Σ both represents SOP

ΠM (or) Π both represents POS