Caches 20 points 1 consider a machine with a direct

Problem 5: Caches (20 points)
1. Consider a machine with a direct mapped cache that has 8-sets and has a block size of 4-bytes.
Memory addresses are 13-bits and each memory access from a processor requests a byte from the
cache. The contents of the cache are as follows, with all numbers in hexadecimal.
Cache Line
Set Index Tag Valid Byte 0 Byte 1 Byte 2 Byte 3
0 09 1 30 F4 72 AB
1 38 1 78 3F 92 D4
2 6E 0 - - - -
3 06 0 1F DA 40 C5
4 C7 1 - - - -
5 71 1 D3 9A 0B 12
6 91 1 - - - -
7 46 0 5C 80 B3 59
(a) (2 points) Calculate the size of the cache in bytes.
(b) (3 points) Indicate the number of bits used to determine
• the block offset:
• set index:
• tag:
(c) (10 points) A program running on this machine makes memory references at the addresses
specified in the first column of the following table. For each memory reference indicate what
is the block offset, set index and tag. Furthermore, indicate whether a cache hit occurs and the
byte returned. The byte returned is - for a miss.
Address Set index Block offset Tag Cache hit? (Y/N) Byte returned
0x0E35
0x0DD5
0x1FE4
0x0705
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(d) (3 points) If we redesign the cache by increasing the associativity to 4 while keeping the total
cache size exactly the same as above, how many bits will you use for the following:
• Tag:
• Set index:
• Block offset:
(e) (2 points) What is spatial locality and temporal locality?
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A B C
A B C
A B C
Figure 2: Examples of cycles for a linked list with 3 nodes.
Extra Credit Questions
Extra Credit 1: C Programming (15 points)
You are given a pointer to a singly linked list. The singly linked list has cycles due to a programming error.
Write a C program to detect whether the linked list has cycles without storing all the pointers to the
nodes . The function detect_cycles should return 1 when a cycle is found and 0 when there are no cycles.
Your code should handle all corner cases carefully and should not cause segmentation fault.
Figure shows various examples of cycles for a list with 3 nodes. The number of nodes in the input list
can range from 0 to a billion nodes.
struct node{
void* data;
struct node* next;
};
int detect_cycles(struct node* list){
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/* another page for work */
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