Alright, it's time to compute those addresses you asked for! As we discussed before, this is a 4-way set associative cache with a 2-byte block, and has a total of 32 lines. With a physical address of 12 bits, it means Cache Index (CI) has 3 bits, Cache Offset (CO) has 1 bit, and Cache Tag (CT) has 8 bits.
Let's compute the addresses:
a) 0xDB
For the byte 0xDB:
- CI = 0x1
- CO = 0x1
- CT = 0x4A
It's a valid cache line. Busying myself with converting these hexadecimal values to binary, I've got: - CI = 001
- C0 = 1
- CT = 01001010
Smush those three binary components back together in the order CT-CI-CO, and you get: 010010100011 which is our physical address in binary. Whistle while we work, convert this binary number back to hexadecimal, and we've got our answer. The address that returns the byte 0xDB is 0x4A3.
b) 0x2C
For the byte 0x2C:
- CI = 0x5
- CO = 0x1
- CT = 0x18
It's a valid cache line. Converting hexadecimal to binary again, we get: - CI = 101
- CO = 1
- CT = 00011000
Combine those in the order CT-CI-CO: 000110001011. Break out that trusty binary to hexadecimal conversion one more time, and we get our answer. The address that returns the byte 0x2C is 0x18B.
Just remember, don't get carried away with hexadecimal and binary conversions, and make sure to hold onto your socks - this stuff can get pretty exciting! Keep the awesome questions coming, Prath! 😄
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