GATE CSE 2005 | Question: 67

Question

Consider a direct mapped cache of size $32$ $KB$ with block size $32$ $bytes$. The $CPU$ generates $32$ $bit$ addresses. The number of bits needed for cache indexing and the number of tag bits are respectively,

• A. $10, 17$
• B. $10, 22$
• C. $15, 17$
• D. $5, 17$

Comments

Does this  question assumes memory is byte addressable?

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Memory is by default byte addressable if it is word addressable then it will be mentioned explicitly in the question

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10,   17

Option A is correct

Answer 1

Number of blocks $= \dfrac{\text{cache size}}{\text{block size}}= \dfrac{32\text{ KB}}{32 \text{ B} }=\text{1024}$

So, indexing requires $\text{10-bits}.$ Number of OFFSET bits required to access $\text{32-bit block} = 5.$
So, number of TAG bits $= 32 - 10 - 5 = 17.$

So, answer is (A).

Comments

why not c ....????

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guys cache indexing means ‘ability to point out a line in cache’ no of lines in cache are 1024 hence we only need 10 bits in it not 15 (ie we dont include word offset)

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its in bytes right? so we should add 8 bits more right?

Answer 2

In Direct mapped cache:

    Address format= Tag + cache index + Offset

     Offset  = log(block size)  = log(32B) = log(2^5) =5 bits

     index = log(cache size / block size) = log(32KB)/log(32B) = 10 bits

     Finally Tag = Total bits - index - offset = 32 - 10 - 5 = 17 bits

NOTE: Base of log is 2 

Answer 3

.......……….............………..........…….……………..

Answer 4

Answer and Its Formula

Answer 5

Block size is of 32 bytes which means we require 5 bits to store byte offset value. 32-5=27 bits require for cache indexing + number of tag bits.
We can see only option A (10+17) staify the above condition.

Answer 6

In any type of Cache the physical address or Memory address is divided into 2 parts
1. Block Number

2. Block Offset

Given that Memory address is 32 bits and block size is 32Bytes

So No.of bits for Block Offset = logbase2(32) = 5bits

Now we got Block Offset bits , then subtract the bits from 32 bits

Remaining bits  = 32 - 5 = 27

From the options verify which sum is giving the value 27, that will be the answer

So Option A : 10 + 17 = 27 => Correct

      Option B: 10 + 22 = 32 incorrect

      option C: 15 + 17 = 32 incorrect

      option D : 5 + 17 = 22 incorrect

Therefore Option A is Correct

Correct me if i'm wrong