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Yes, This is to capture measurements which will last nights and days, and whichever the stockage device that will be used, it won't be emptied every day. SDXC would be safer for us.
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I don't know what speed you need to access the SD card. if I were you I will consider to use a soft CPU core inside FPGA and have a uclinux or just Linux system run on it. By using the linux core i am sure there must be some support for exFAT. But for the low level driver and IP core I don't know if there is any differences between SD and SDXC.