Final answer:
The time required to transfer 1000 words from the disk controller to main memory using DMA depends on the mode used: word-at-a-time mode is ((t1 + t2) * 1000 + 2*t1), where t1 is the bus acquisition time and t2 is the transfer time per word; burst mode is (t1 + (t2 * 1000) + 2*t1).
Step-by-step explanation:
The question concerns how long it will take to transfer 1000 words from the disk controller to main memory using direct memory access (DMA) considering different transfer modes. We need to account for the time to acquire the bus () and the time to transfer one word (), where it's given that is significantly larger than .
For word-at-a-time mode, each word transfer requires acquiring the bus, so the total time would be:
Total time (word-at-a-time) = (t1 + t2) * 1000
In burst mode, the bus is acquired once for the entire block of 1000 words. Therefore, the time would include a single bus acquisition time plus the time to transfer all words:
Total time (burst mode) = t1 + (t2 * 1000)
Note that there are additional overheads for starting and acknowledging the transfer, which must also be considered. Assuming that each of these actions is equivalent to transferring one word, the equations would further include two extra 't1' times for both modes. Adjusting for this overhead, the revised formulas become:
Total time (word-at-a-time, with overhead) = (t1 + t2) * 1000 + 2*t1
Total time (burst mode, with overhead) = t1 + (t2 * 1000) + 2*t1