University of Illinois at Urbana Champaign Dept of Electrical and Computer Engineering ECE 120 Introduction to Computing Don t Care Outputs Some Input Combinations May Not Matter Sometimes we don t care whether a particular input combination generates a 0 or a 1 For example when an input combination is impossible to generate or when outputs are ignored in the case of an input combination ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 1 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 2 For Such Inputs Use x to Indicate Don t Care Why Are Don t Cares Useful In such cases we use x called a don t care in place of the desired output Indicates that either 0 or 1 is acceptable However whatever we implement will generate a 0 or a 1 not a don t care So we need to be sure that we really do not care More choices often means a better answer for any choice of metric Say that you optimize a K map for a function F Then you consider several other functions G H and J If you have to pick one of the four functions F G H or J the choice can t get worse since you can always pick F but the best choice may be better than F ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 3 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 4 3 4 2018 1 N Don t Cares Allows 2N Different Functions An Example with Two Don t Cares Using x s for outputs means allowing more than one function to be chosen Each x can become a 0 or a 1 So optimizing with N x s means choosing from among 2N possible functions Let s do an example The function F appears to the right partially specified Let s say that we don t care about the value of F when AB 01 F C 0 0 1 1 AB 00 01 11 10 1 1 0 1 This notation means A 0 AND B 1 You can infer that AB in this case does not mean A AND B because the product AB has a single truth value 0 or 1 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 5 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 6 Solution for F with 0s AB B C Solution for F with a 0 and a 1 AB C One option is to fill the blanks with 0s F AB 00 01 11 10 Then we can solve F AB B C C 0 0 1 1 0 0 1 1 0 1 But we could have chosen values other than 0 too Without more information about F filling with 0s is no better nor worse than any other choice For example we could put a 0 and a 1 F AB 00 01 11 10 And then solve F AB C This function is better than the first one it has one fewer literal C 0 0 1 1 0 1 1 1 0 1 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 7 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 8 3 4 2018 2 Solution for F with Don t Cares B C Always Check that Don t Cares Have No Ill Effects Rather than solving for all four possibilities let s write x s into the K map F C 0 0 AB 00 01 11 10 x x 1 1 0 1 The x s can be 0s or 1s so to solve the K map we can grow loops to include x s but we do not need to cover x s 1 1 F B C the best possible answer 11 F 00 01 AB When designing with x s it s a good habit to verify that the 0s and 1s generated in place of x s do not cause any adverse effects For our function both x s become 1s because they are inside a loop We don t have any more context for this example so we are done 1 1 0 0 C 1 1 x 1 1 x 10 0 1 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 9 ECE 120 Introduction to Computing 2016 Steven S Lumetta All rights reserved slide 10 3 4 2018 3