Question

a computer system uses 16 bits memory address.it has 2k byte cache organized in a direct mapped manner with 64 bytes per cache block size of each memory word is 1 byte.calculate no. of bits in each of the tag ,block and word fields of memory address

Answer 1

A computer system uses 16-bit memory addresses. It has a 2K-byte cache organized in a direct-mapped manner with 64 bytes per cache block. Assume that the size of each memory word is 1 byte.

When a program is executed, the processor reads data sequentially from the following word addresses:

128, 144, 2176, 2180, 128, 2176

All the above addresses are shown in decimal values. Assume that the cache is initially empty. The cache hits ratio occur for for above given addresses is __________ .

(A) 0.333

(B) 0.666

(C) 0.353

(D) 0.535

Answer: (A)

Explanation: First, find word, block and tag size:

Block size = 64 bytes = 26 bytes = 26 words (since 1 word = 1 byte)

Therefore, Number of bits in the Word field = 6

Cache size = 2K-byte = 211 bytes

Number of cache blocks = Cache size / Block size = 211/26 = 25

Therefore, Number of bits in the Block field = 5

Total number of address bits = 16

Therefore, Number of bits in the Tag field = 16 – 6 – 5 = 5

For a given 16-bit address, the 5 most significant bits, represent the Tag, the next 5 bits represent the Block, and the 6 least significant bits represent the Word.

Answer 2

Concept:

A memory address in computing is a reference to a particular memory region that is used at different levels by hardware and software. Memory addresses are unsigned numbers that are often presented and handled as fixed-length digit sequences.

Given:

Here it is given that a computer system uses $16$ bits memory address.it has $2k$ byte cache organized in a direct mapped manner with $64$ bytes per cache block size of each memory word is $1$ byte.

Find:

We have to calculate no. of bits in each of the tag ,block and word fields of memory address.

Solution:

According to the question,

A computer system uses $16$-bit memory addresses. It has a $2K$-byte cache organized in a direct-mapped manner with $64$ bytes per cache block. Assume that the size of each memory word is $1$ byte.

When a program is executed, the processor reads data sequentially from the following word addresses:

$128, 144, 2176, 2180, 128, 2176$

All the above addresses are shown in decimal values. Assume that the cache is initially empty. The cache hits ratio occur for for above given addresses is $(A) 0.333$.

Hence the correct option of the question is $0.333$ and this is our final answer also.