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Cache Memory
Exercises
Questions I
• Given:– memory is little-endian and byte addressable;
memory size;– number of cache blocks, size of cache block– An instruction lw $t0, x or lbu $t0, x;
• Determine – HIT or MISS?– What value is in $t0?; and– Show the cache after word is brought in if needed
Address (binary)
Contents (Hex)
000000 aa bb cc dd
000100 00 11 00 33
001000 ff ee 01 23
001100 45 67 89 0a
010000 bc de f0 1a
010100 2a 3a 4a 5a
011000 6a 7a 8a 9a
011100 1b 2b 3b 4b
100000 b2 b3 b4 b5
100100 c1 c2 c3 c4
101000 d1 d2 d3 d4
101100 e1 e2 e3 e4
110000 f1 f2 f3 f4
110100 a1 a2 a3 a4
111000 2c 3c 4c 5c
111100 2d 3d 4d 5d
V Tag data(hex)
0 10 11 11 00 01
1 00 00 01 01 33
0 11 11 11 11 11
1 00 45 67 89 0a
lbu $t0, x # x = 001101
Question 1: cache HIT or MISS? What is in $t0?
Draw the cache after data is brought in
00
01
10
11
Assume memory is little-endian and byte addressable; cache block = 1 word;
Cache holds 4 blocks of data ( 4 words)
Address (binary)
Contents (Hex)
000000 aa bb cc dd
000100 00 11 00 33
001000 ff ee 01 23
001100 45 67 89 0a
010000 bc de f0 1a
010100 2a 3a 4a 5a
011000 6a 7a 8a 9a
011100 1b 2b 3b 4b
100000 b2 b3 b4 b5
100100 c1 c2 c3 c4
101000 d1 d2 d3 d4
101100 e1 e2 e3 e4
110000 f1 f2 f3 f4
110100 a1 a2 a3 a4
111000 2c 3c 4c 5c
111100 2d 3d 4d 5d
V Tag data(hex)
0 10 11 11 00 01
0 00 00 01 01 11
0 00 Ffee 01 23
0 00 00 00 00 00
lbu $t0, x # x = 001010
Question 2: cache HIT or MISS? What is in $t0?
Draw the cache after data is brought in
00
01
10
11
Assume memory is little-endian and byte addressable; cache block = 1 word;
Cache holds 4 blocks of data ( 4 words)
Address (binary)
Contents (Hex)
000000 aa bb cc dd
000100 00 11 00 33
001000 ff ee 01 23
001100 45 67 89 0a
010000 bc de f0 1a
010100 2a 3a 4a 5a
011000 6a 7a 8a 9a
011100 1b 2b 3b 4b
100000 b2 b3 b4 b5
100100 c1 c2 c3 c4
101000 d1 d2 d3 d4
101100 e1 e2 e3 e4
110000 f1 f2 f3 f4
110100 a1 a2 a3 a4
111000 2c 3c 4c 5c
111100 2d 3d 4d 5d
V Tag data(hex)
0 10 11 11 00 01
1 00 00 11 00 33
0 11 11 11 11 11
1 00 00 00 00 00
lbu $t0, x # x = 000111
Question 3: cache HIT or MISS? What is in $t0?
Draw the cache after data is brought in
00
01
10
11
Assume memory is little-endian and byte addressable; cache block = 1 word;
Cache holds 4 blocks of data ( 4 words)
Address (binary)
Contents (Hex)
000000 11 11 00 01
000100 00 11 00 33
001000 ff ee 01 23
001100 45 67 89 0a
010000 bc de f0 1a
010100 2a 3a 4a 5a
011000 6a 7a 8a 9a
011100 1b 2b 3b 4b
100000 b2 b3 b4 b5
100100 c1 c2 c3 c4
101000 d1 d2 d3 d4
101100 e1 e2 e3 e4
110000 f1 f2 f3 f4
110100 a1 a2 a3 a4
111000 2c 3c 4c 5c
111100 2d 3d 4d 5d
V Tag data(hex)
0 01 11 11 00 01
1 00 00 01 01 11
0 11 11 11 11 11
1 00 00 00 00 00
lbu $t0, x # x = 010010
Question 4: cache HIT or MISS? What is in $t0?
Draw the cache after data is brought in
00
01
10
11
Assume memory is little-endian and byte addressable; cache block = 1 word;
Cache holds 4 blocks of data ( 4 words)
Address (binary)
Contents (Hex)
000000 aa bb cc dd
000100 00 11 00 33
001000 ff ee 01 23
001100 45 67 89 0a
010000 bc de f0 1a
010100 2a 3a 4a 5a
011000 6a 7a 8a 9a
011100 1b 2b 3b 4b
100000 b2 b3 b4 b5
100100 c1 c2 c3 c4
101000 d1 d2 d3 d4
101100 e1 e2 e3 e4
110000 f1 f2 f3 f4
110100 a1 a2 a3 a4
111000 2c 3c 4c 5c
111100 2d 3d 4d 5d
V Tag data(hex)
0 10 11 11 00 01
0 00 00 01 01 11
0 11 11 11 11 11
0 00 00 00 00 00
lbu $t0, x # x = 011011
Question 5: cache HIT or MISS? What is in $t0?
Draw the cache after data is brought in
00
01
10
11
Assume memory is little-endian and byte addressable; cache block = 1 word;
Cache holds 4 blocks of data ( 4 words)
Cache Question II-1
• Suppose: 256 bytes of memory, cache holds 4 blocks, each block is 1 word. What is the cache size?
• Answer:
aaaaaaaa t t t t i i o o
cache: valid tag data
Cache size: 1 4 32
(4+1+32)*4 bits
Cache Question II-2
• Suppose: 256 bytes of memory, cache holds 8 blocks , each block is 1 word. What is the cache size?
• Answer:
aaaaaaaa t t t i i i o o
cache: valid tag data
Cache size: 1 3 32
(3+1+32)*8 bits
Question II-3
• What is the cache size (total number of bits) for a cache that holds 64KB of data (block == 1 word; 2**32 bytes of memory)
• Answer:• 64KB == 16K words;
– 16K = (2**4) *(2**10) = 2**14– So 14 bits are needed for the cache index
• Tag size = 32 – 14 -2 = 16 bits• Cache size = (1 + (32-14-2) + 32) * (2**14)
= 784 K bits = 98 KB
