Karnaugh Map Dont Care Conditions - Logic?

Could somebody please clarify for me do any of the following have don't care conditions? I'm a little confused what is meant by this? If so could you explain how you established these? The truth table e.t.c (Note: + = OR, . = AND, ¬ = NOT)





1) F = A . B


2) F = A + B


3) F = A . ¬B . C + ¬(B.(¬C + D))





Thanks.


David

Karnaugh Map Dont Care Conditions - Logic?
Logic equations don't have "don't cares".





Rather, a problem may provide "don't care"


situations which can be used to minimize the


necessary circuit needed to solve it.





Consider an input device which can be used


to register the number of human fingers that


someone presses on it. The value can be


the 11 values from 0 to 10.





Now consider a circuit which is supposed


to generate a 1 on output for any value


from this device which has exactly 2


bits set to 1. The truth table is:





abcd ==%26gt; output


0000 ==%26gt; 0


0001 ==%26gt; 0


0010 ==%26gt; 0


0011 ==%26gt; 1


0100 ==%26gt; 0


0101 ==%26gt; 1


0110 ==%26gt; 1


0111 ==%26gt; 0


1000 ==%26gt; 0


1001 ==%26gt; 1


1010 ==%26gt; 1





If you map that onto a Kmap, you get the


sum of products:





f = a'b'cd + a'bc'd + a'bcd' + ab'c'd + ab'cd'





Further consider that the input device


can *never* generate the values 11, 12,


13, 14, or 15. Therefore, you don't care


what your circuit does when given those


inputs.





1011 ==%26gt; ? (don't care)


1100 ==%26gt; ? (don't care)


1101 ==%26gt; ? (don't care)


1110 ==%26gt; ? (don't care)


1111 ==%26gt; ? (don't care)





After inspecting the Kmap, you might


*choose* to have these interpretted as:





1011 ==%26gt; 1


1100 ==%26gt; 0


1101 ==%26gt; 1


1110 ==%26gt; 1


1111 ==%26gt; 1





This would lead to a reduced expression of:





f = ad + ac + bc'd + bcd' + b'cd





The point about "don't cares" is that you


have the freedom to chose what the circuit


output will be (in order to minimize the


logic) becuase you truly "don't care" what


the output will be.

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