Digital Electronics NUMBER SYSTEM BINARY CODES BOOLEAN ALGEBRA K MAPS INTRODUCTION DONT CARES REDUNDANT GROUPS IMPORTANT FACTS ILLUSTRATION OF FACTS K MAPS FOR XOR & XNOR gates COMBINATIONAL CKT SEQUENTIAL CIRCUITS TIMING CIRCUITS

Don’t care

When ever there are don’t cares present in the K-map then we have the option of including don’t care in the group to maximize the size of group and hence we get more minimized form but this is not compulsory to include each and every don’t care. So we can use don’t care to our advantage otherwise skip them.

e.g. Minimize the K-map given below:

If we ignore don’t care then we make groups of 1 then we get the equations as

But if we use the don’t cares then we make groups as

And we see that we have used 2 don’t care and we make a group of 4 rather than 2 while we skip the 3rd don’t care as we do not have to use each don’t care. Hence we see that using 2 out of 3 don’t care we have got more minimized equation.

We represent don’t cares in an equation as shown below:  F= ∑ m (1, 3, 4, 7) + d (0, 5). The terms represented by d are don’t cares and can be either ignored or taken into consideration to reduce the hardware to implement the function.