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As I only require a single address (the base address) for the read, I removed the address signals from the template - this resulted in a Warning: 's0: Slave has data signal but no address signal'. Does this matter?
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Yes it does matter. The processor identifies the peripherals by address mapping so you need to specify an address line.
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Also, in address map, I note that 1K of address space has been allocated to this component (0x00000000 to 0x000003FF). Why is this?
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Even if there is a single address that you want for your peripheral, there would always be atleast two addresses possible for the peripheral. This is because if you have only one address line, it will always result in two different addresses ('0' and '1' with appropriate prefixes; an enlargement of this space depends on specific processor bus arbitration rules). Since Nios has dedicated component signals, you need to bear with this ambiguity though it really doesn't affect the operation of either Nios or the peripheral.