Can I use a single code on different FPGA boards.

In general, HDL languages are standards, so yes, you can take code from one device and move it to another. However, some code, such as that for IP, is usually optimized for a specific device architecture, so you would want to regenerate that code for the new architecture. Also, you need to recompile code for a new architecture because the output files from compilation (such as the programming file) will not work in the different device.

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