Question

3 variable kmap if the octal is present what is the expression​

Answer 1

Explanation:

3 variable Boolean expression using K map.

We know that the number of cells of the K-map is dependent on the number of variables. So, for 3 variable K map, the number of cells will be 23 i.e., 8.

Let us reduce the function given below using K-map

F (A, B, C) = Σm (0, 1, 2, 4, 7)

The figure below represents the K-map for 3 variables having 8 cells.

As we have already discussed earlier the reason behind the assigning of variables to the Karnaugh map. So, let us now proceed towards filling of bits to the minterm K-map.

The figure below shows the assigning of bits to the K-map:

Here, we can clearly see that for minterm K-map, 1 is assigned at m0, m1, m2, m4, m7, as given in the function.

So, firstly here we will check the priority, as we can see that neither 16, 8 nor 4 1’s is present in order to perform the grouping. So, we will check for grouping of 2 bits.

The figure below represents the grouping of bits for the above function:

Here, we can see that two 1, present at the 1st row of column 00 and 01 are forming pair. Similarly, two 1’s of the first column and rows 0, 1 are forming a pair. Also, the two corners, 1 at the first row is forming a group of 1.

However, still, a single 1 is left that is unable to participate in a grouping as no other 1 is present at its adjacent position. So, this 1 is considered to be as a group of single 1. As represented in the figure given above.

Let us now see how the above function is realized using K-map.

So, the function for all 4 implicants will be: