Consider a direct mapped cache of size 16 KB with block size of 256 bytes. The size of main memory is 128 KB

Numerical problem on Direct mapping

Q. Consider a direct mapped cache of size 16 KB with block size of 256 bytes. The size of main memory is 128 KB.

1. Find number of bits in tag

2. Find tag directory size

Ans. Cache of size = 16 KB = 2¹⁴ bytes => Its having 14 bits

Block size = 256 bytes = 2⁸ bytes => Its having 8 bits

Main memory size = 128 KB = 2¹⁷ bytes => Its having 17 bits

Number of bits in Line number  = Cache size / Block size

                                    = 2¹⁴ bytes / 2⁸ bytes

                                    = 2⁶ 

Line number having 6 bits.

Number of bits in Tag = 

Number of bits in main memory - number of bits in line number - number of bits in block

= 17 – Line bits – Block bits

= 17 – 6 – 8 =3

Tag directory size

Size of line number X Number of bits in tag

=2⁶ X 3 bits

= 192 bits

= 192 / 8 bytes

= 24 bytes

More topics from Computer Organization to read

Computer Organization and Architecture:

EasyExamNotes.com covered following topics in these notes.

1. Structure of desktop computers
2. Logic gates
3. Register organization
4. Bus structure
5. Addressing modes
6. Register transfer language
7. Direct mapping numericals
8. Register in Assembly Language Programming
9. Arrays in Assembly Language Programming

References:

1. William stalling ,“Computer Architecture and Organization” PHI
2. Morris Mano , “Computer System Organization ”PHI