Help with latches but can't figure out why after several checks

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There are cases in your code where LED_out retains the previous value.

To avoid latches you need to always give LED_out a value that depends only on the process inputs (state, key*).

If you need LED_out to have memory, make it a flip-flop.

Same for LED_R

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Thanks for your quick reply rbugalho,

I am a beginner to vhdl, please an example will help me understand what you mean better.

Just one will do, thanks