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Given that, A machine with a byte - addressable main memory of 2 ^ 1 6 bytes and A block size of 8 bytes. A
Given that,
A machine with a byteaddressable main memory of bytes and
A block size of bytes.
A Direct mapped cache consisting of lines is used with this machine.
a
A bit memory address is divided into the tag, line number, and byte number as follows:
The byte number is the lowest bits of the address bits
The line number is the next bits of the address bits since there are lines in the cache.
The tag is the remaining bits of the address bits since it uniquely identifies the block of memory being cached.
Explanation:
First, we need to understand the concept of a cache block. A cache block is a contiguous chunk of bytes in main memory that is loaded into the cache as a unit. In this case, the cache block size is bytes, which means that every time the cache is loaded with data from main memory, it loads bytes at a time.
Next, we need to understand the concept of a cache line. A cache line is a group of bytes in the cache that corresponds to a specific block of bytes in main memory.
In this case, there are cache lines, which means that the cache can store up to different blocks of data from main memory.
Now, let's look at how a bit memory address is divided into tag, line number, and byte number:
The lowest bits of the address bits represent the byte number within a cache block. Since the cache block size is bytes, there are possible byte numbers within a block, ranging from in decimal to in decimal
The next bits of the address bits represent the line number within the cache. Since there are cache lines, there are possible line numbers, ranging from in decimal to in decimal
The remaining bits of the address bits represent the tag, which uniquely identifies the cache block being accessed. Since a cache block is bytes in size, the tag identifies the byte block of memory that the requested byte belongs to
To summarize, the byte number within a cache block is determined by the lowest bits of the address, the line number within the cache is determined by the next bits of the address, and the tag is determined by the remaining bits of the address.
Adm
b
To determine the line number for each of the given addresses, we look at the bits of the address the bits after the lowest bits, which determine the byte number The line number is the decimal value of these bits.
For the address the line number is
For the address the line number is
For the address the line number is
For the address the line number is
Explanation:
For a detailed explanation let's take the first address and determine which line it would be stored in:
The lowest bits of the address are which represents the byte number within a cache block.
The next bits of the address are which represents the line number within the cache. In decimal, this is
The remaining bits of the address are which represents the tag.
Since this is a directmapped cache, the byte at this address can only be stored in one line of the cache, which is line Specifically, it would be stored in the byte offset within the cache line that corresponds to the lowest bits of the address, which is byte within the line.
To summarize, the byte at address would be stored in line of the cache, with tag and byte offset
Adm
c
Since the block size is bytes, the other bytes stored along with it will be the bytes in the same block. To determine those byte addresses, we can simply increment the byte number from to while keeping the tag and line number the same:
Byte :
Byte :
Byte :
Byte :
Byte :
Byte :
Byte :
Byte :
Explanation:
In this case, the byte at address is the first byte in the block, so the other bytes are the bytes with addresses Other than remaining numbers in where block size is bytes
Since all of these bytes are in the same block of memory, they are all mapped to the same line in the cache, which is line Therefore, all of these bytes will be stored in the same line of the cache as the byte at address
Adm
d
In a direct mapped cache, each memory block maps to a specific cache line. The cache line size is equal to the block size.
In this case, the block size is bytes, so each cache line can hold bytes of memory.
The cache has lines, so the total number of bytes that can be stored in the cache is:
lines bytes per line bytes.
There
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