> The only way to have a square output is to divide a frequency by
> an even number, this is why you need first to multiply the frequency
>  by 2
>
> Wagner

You could do the conversion to 50% duty cycle at the output too.
Take the pulse from the division counter to drive a flip flop, delay /Q
by a fixed amount (13us I think) with a small cap and  then use a
phase comparator on Q and /Q to x2, like you've done your x2 initially
with the EOR gate

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