.Using Karnaugh map simplify the following expressions:(i) F(A,B,C,D)=Σm(1,2,5,6,8,9)

To simplify the given expression using a Karnaugh map, follow these steps:

Step 1: Draw a 4-variable Karnaugh map. The variables A, B, C, and D can be arranged in the following order:

      CD
      00 01 11 10
    -------------
AB 00|   |   |   |   |
    -------------
   01|   |   |   |   |
    -------------
   11|   |   |   |   |
    -------------
   10|   |   |   |   |
    -------------

Step 2: Fill in the Karnaugh map with the given minterms. The minterms are given as Σm(1,2,5,6,8,9). This means that these minterms will be filled with 1s and the rest will be filled with 0s.

      CD
      00 01 11 10
    -------------
AB 00| 0 | 1 | 0 | 1 |
    -------------
   01| 0 | 1 | 1 | 0 |
    -------------
   11| 0 | 0 | 0 | 0 |
    -------------
   10| 1 | 1 | 0 | 0 |
    -------------

Step 3: Group the 1s in the Karnaugh map. The groups should be as large as possible and can overlap. Each group must be a rectangle (or square) and the number of cells in a group must be a power of 2 (1, 2, 4, 8, etc.).

In this case, we can make three groups: one group of two 1s at the top, one group of two 1s on the right, and one group of two 1s at the bottom.

Step 4: Write the simplified expression for each group.

• The top group can be represented as A'B'C.
• The right group can be represented as AC'.
• The bottom group can be represented as A'B'D.

Step 5: Combine these expressions with a + sign. The simplified expression is:

F(A,B,C,D) = A'B'C + AC' + A'B'D

This is the simplified expression of the given function using a Karnaugh map.