The explanation of gray code “quadrant” technique

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Another question is if i insist to use binary counter in my FIFO implementation and i manage to close all the timing through STA.

Does this indicate it is safe to use binary counter? :p

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If your fifo is dual clock and its two clocks are unrelated then your assumption of closing timing can't be true across clock domain.

BTW, if you set megawizard to fifo with no flag detection then you are done a simple fifo that does not care about clock domain and leaves control to you. I assume we will get a fifo with just binary addressing for write and read.