After doing a past year paper on JK flip flop

I realized that there is an equation not in my syllabus:

Q+ = JQ'+K'Q

I UNDERSTAND it but I dont know how it is derived from the truth table. Can anybody teach me? Currently, I only know how to derive boolean equations when the output is 1 or 0

 

Hello hitmen,

Draw the characteristics table with J,K and Q and what you have to find is Qnext .Here we apply clock to get Qnext and hence remember that the values may either be 0 or 1 for Q under all possible combinations of J and K.We have 4 possible combinaations of J and K and for each combination of J,k Q takes two values 0 and 1.SO in all we get 8 combinations .

J k Q Qnext
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

Implement Qnext using k-map and you will get k'Q+JQ'.