Question

1- A 64-bit computer system employs a 16Gbyte main memory and a 32 Kilo word cache. Determine the number of bits in each field of the memory address register (MAR) as seen by cache in the following organizations (show your calculations): Fully associative mapping with line size of 2 words. A. Direct mapping with the line size of 8 words. B. C. 4-way associated mapping with the line size of 1 words.

Answer 1

A) FULLY ASSOCIATIVE

Given-

Cache memory size = 32 Kwords = 2¹⁵ words

Block size = Frame size = Line size = 2 words

Number of bits in block offset = 1 bit

Main memory size = 16GB = 2³⁴ BYTES

Thus, Number of bits in physical address = 34 bits

Number of bits in tag = Number of bits in physical address – Number of bits in block offset = 34 - 1 = 33

TAG	BLOCK OFFSET
33	34

B) DIRECT MAPPING

Cache memory size = 32 Kwords = 2¹⁵ words

Number of bits in physical address = 34 bits

Block size = 8 WORDS = 2³

Thus, Number of bits in block offset = 3 bits

Total number of lines in cache

= Cache size / Line size

= 2¹⁵ / 2³

= 2¹² lines

Thus, Number of bits in line number = 12 bits

Number of bits in tag

= Number of bits in physical address – (Number of bits in line number + Number of bits in block offset)

= 34 bits – (12 bits + 3 bits)

= 19 bits

Thus, Number of bits in tag = 20 bits

TAG	LINE NUMBER	BLOCK OFFSET
19	12	3

C) 4-way set Associated mapping

Given-

• Set size = 4
• Cache memory size = 16 Kwords =2¹⁵words
• Block size = Frame size = Line size = 1word = 2⁰

Thus, Number of bits in block offset = 0 bits

• Main memory size = 16GB = 2³⁴ BYTES

Thus, Number of bits in physical address = 34 bits

Total number of lines in cache

= Cache size / Line size

= 2¹⁵ / 2⁰

= 2¹⁵ lines

Total number of sets in cache

= Total number of lines in cache / Set size

= 2¹⁵ / 2²

= 2¹³ sets

Thus, Number of bits in set number = 13 bits

Number of tag bits = Number of bits in physical address – (Number of bits in set number + Number of bits in block offset)

=34 - (13+0)

=21 bits

TAG	SET NUMBER	LINE OFFSET
21	13	0