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What happens when the input of a flip flop changes exactly at the time of the clock pulse transition?

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At the time of clock pulse,whatever will be the input to the ff accordingly o/p will be produced.

so ,new state
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It depends upon implementation . say if its a D Flip flop then it will change the output (if 0 then 1 like that ), if J K then it may change or not ,

say both of J and K are attached to input . then input 1010101 , then for 0 (j=0 k= 0)it will not change the state .
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