I thought the same as you.I read this:
as you thinking he wants to create an output that is 1:11, while my read of his question is that he has an *input* that is 1:11, and he wants to create an output that is 12:12.
Did I misread?
ak
It needs to toggle at the rising edge of an input that will be active high for 1 hour then active low for 11 hours


