Question

Please, multiply the highlighted yellow digit by 6 first then solve. thank you!

Given: An 8-bit computer system with 4 MB of main memory. It has a 16K-words direct-mapped cache with a block size of 16 Bytes. Sought: Calculate the cache line number when Byte address 5678ten from main memory is mapped to cache. Consider that numbering of main memory blocks and cache lines starts from zero. Express your answer in hexadecimal. It is required to show ALL incremental steps of the solution.

Answer 1

Given,

The computer system is an 8 bit system.

So, size of 1 word = 8 bits = 1 word.

Size of memory = 4MB

Number of bits used to represent byte address = log ( Size of memory ) = log ( 4 MB ) = 22 bits

Block size = 16 Bytes

Number of bits used to represent block offset = log ( Block Size ) = log 16 = 4 bits

Size of the cache = 16 K words = 16 KB [ Since 1 word = 1 byte ]

Number of cache lines in the cache = Size of cache / Block Size = 16 KB / 16 Bytes = 1 K lines = 1024 lines

Number of bits used to represent cache line number = log ( Number of cache lines in the cache ) = log 1024 = 10 bits

Number of bits in the tag field = Address bits - ( Cache line number bits + Block offset bits )

= 22 - ( 10 + 4 ) = 8 bits

So, the address division in the direct mapped cache is :

Tag	Line Number	Block Offset
8 bits	10 bits	4 bits

The given byte address is ( 5678 * 6 ) = 34068 whose binary representation using 22 bits is :

0000001000010100010100

The first 8 bits from the left represent the tag, the 4 bits from the right represent the block offset and the remaining 8 bits represent the cache line number.

The cache line number is 0001010001 which is padded by extra 2 0s so that the number can be converted to hexadecimal form easily.

The binary number 000001010001 is divided into groups of size 4 in order to get the equivalent hexadecimal value as follows :

Binary value	0000	0101	0001
Hexadecimal value	0	5	1

Hence, the cache line number to which byte address 34068 is mapped is 0x051.