Some confusing concepts about cache and memory

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I am confused with true or false questions about computer caches and memory. There are 2 questions and my answer for each of them. Could you tell me whether my answer is right or wrong? thanks for reading!

  1. Direct mapped cache offers better hit time than set-associative caches.
    my answer: True (Because set associative cache needs more time to search all blocks per set)

  2. Fully set-associativity cache does not use index bits during search
    my answer : True(Because if cache is fully set-associative it only compare the address and cache's tag)

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