COMPUTER ORGANIZATION
AND ARCHITECTURE
Sheet chapter 4
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صار فيه شي خطا تقولون افراح نزلته بالموقع
انا كنت اكتب معاها الحل تقريبا كله صح بس يمكن طريقة الحل تختلف
فنزلته لكم من باب المساعده واتمنى ماتحملوني مسؤلية الحل اول استاذه
ايمان ماترسل الحل برفعه لكم بس هذا الحل خذوه مبدئيا الن مافيه وقت
تذاكرون
تحياتي افراح
4.1 A set-associative cache consists of 64 lines, or slots, divided
into four-line sets. Main memory contains 4K blocks of 128 words
each. Show the format of main memory addresses.
Number of set=16 4 lines
Number of block in main memory=size of memory/size of block
Size of memory = Number of block in main memory× size of block
Size of memory=22×210 × 27
Size of memory=219
Tag Set Size of block
Size of block = 128=27 -> so size of block=7
Tag= size of memory – set – size of block
Tag=19-4-7
Tag=8
Tag Set Size of block
8 4 7
4.2 A two-way set-associative cache has lines of 16 bytes and
a total size of 8 kbytes.The 64-Mbyte main memory is byte
addressable. Show the format of main memory addresses.
Set 1 Block 1 Block 2
Set 2 Block 3 Block 4
Set 3 Block 5 Block6
Set 4 Block7 Block8
Set 5 Block9 Block10
Set 6 Block11 Block12
Set 7 Block13 Block14
Set 8 Block 15 Block16
Total block in the cache= 8kbytes/16 bytes=23×210/24=29= 512
Number of set =number of block in cache/2
Number of set=512/2
Number of set in cache=256
Number of set in cache =28
Number of set=8
Size block=16=24
Size of memory=26×220=226
Tag= size of memory – set-size of block
Tag=26-8-4
Tag=14
tag set Size of block
14 8 4
4.3 For the hexadecimal main memory addresses 111111,
666666,BBBBBB, show the following information, in
hexadecimal format:
a. Tag, Line, and Word values for a direct-mapped cache,
using the format of Figure 4.10
b. Tag and Word values for an associative cache, using the
format of Figure 4.12
c. Tag, Set, and Word values for a two-way set-associative
cache, using the format of
Figure 4.15
Figure 111111 666666 BBBBBB
a 11-444-1 66-1999-2 BB-2EEE-3
b 44444-1 199999-2 2EEEEE-3
c 22-444-1 CC-1999-2 177-EEE-3
4.5 Consider a 32-bit microprocessor that has an on-chip 16-
KByte four-way set-associative cache. Assume that the cache
has a line size of four 32-bit words. Draw a block diagram
of this cache showing its organization and how the different
address fields are used to determine a cache hit/miss.Where
in the cache is the word from memory location
ABCDE8F8 mapped?
Size of address CPU=32 bit
Total Block in cach=16k/16
Total Block in cache=24×210/24=210= 1024
Number of set in cache=total block/4
Number of set in cache=1024/4
Number of set in cache=256=28
Size of block =16=24
Tag= Size of address CPU-set-size of block
Tag=32-8-4=20
Tag set Size of block
20 8 4
Where in the cache is the word from memory location
ABCDE8F8 mapped?
Tag 20 Set 8 Size 4
1010 1011 1100 1101 1110 1000 1111 1000
So we select set 143 because the input to decoder is 10001111
and the output from decoder is set 143
4.8 Consider a machine with a byte addressable main memory of
216 bytes and block size of 8 bytes. Assume that a direct mapped
cache consisting of 32 lines is used with this machine.
a. How is a 16-bit memory address divided into tag, line
number, and byte number?
Tag line Size
8 5 3
b. Into what line would bytes with each of the following
addresses be stored?
0001 0001 0001 1011
1100 0011 0011 0100
1101 0000 0001 1101
1010 1010 1010 1010
0001 0001 0001 1011
Line 3
1100 0011 0011 0100
Line 6
1101 0000 0001 1101
Line 3
1010 1010 1010 1010
Line 21
c. Suppose the byte with address 0001 1010 0001 1010 is
stored in the cache.What are the addresses of the other bytes
stored along with it?
0001 1010 0001 1111 stored in the cach
d. How many total bytes of memory can be stored in the
cache?
28=255 byte
e. Why is the tag also stored in the cache?
The tag is used to distinguish between two items with two
different memory addresses Because it can stored in the same
place in the cache
COMPUTER ORGANIZATION
AND ARCHITECTURE
Sheet chapter 5
5.2 Consider a dynamic RAM that must be given a refresh
cycle 64 times per ms. Each refresh operation requires 150 ns;
a memory cycle requires 250 ns.What percentage of the
memory’s total operating time must be given to refreshes?
1ms refrech=64×150×10-6 =0.0096 Almost 1%
5.11 Suppose an 8-bit data word stored in memory 11000010.
Using the Hamming algorithm, determine what check bits
would be stored in memory with the data word.
M=8
k
2 -1>=k+m
24-1>=4+8
15>=12
1 2 3 4 5 6 7 8 9 10 11 12
1 0 1 1 1 0 0 1 0 0 1 0
The check bits are in bit numbers 1, 2,4, and 8.
Check bit 8 calculated by values in bit numbers: 9,10,11, and 12
Check bit 4 calculated by values in bit numbers: 5,6,7 and 12
Check bit 2 calculated by values in bit numbers: 3,6,7,10 and 11
Check bit 1 calculated by values in bit numbers: 3,5,7,9,10 and 11
Thus, the check bits are:1011
5.12 For the 8-bit word 00111001, the check bits stored with
it would be 0111. Suppose when the word is read fro memory,
the check bits are calculated to be 1101.What is the data word
that was read from memory?
0111
XOR
1101
1010=5 IN DICIMAL
SO the date read is 001100011 from 001110011
