SD card access

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The manual mentions using custom controllers to access the card in "SPI mode and SD Card 4-bit or 1-bit mode". What is meant by these?

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"Custom" in this sense means they don't supply the controller. You either design it yourself, or purchase Intellectual Property (IP) from one of the vendors such as SLS, Cast, Eureka, or El Camino that has developed it. Terasic may have one that they recommend.

If you're referring to the modes, those are standard means of communicating with SD cards. See here (http://en.wikipedia.org/wiki/secure_digital#transfer_modes).

There is an IP from altera called SPI 3 WIRE you can use it to connect to the SDCARD in the 1-bit mode (which means only 1 bit of data).

You can also try the 4-bits mode which is a lot faster with this: http://opencores.org/project,sdcard_mass_storage_controller

but i haven't tried myself.