Homework #3 Solution

Instructions           1.    There are 7 questions with total 10 points.

2.    Please create electronic document with your answer.

3.    There is no need to include the question itself. However, you MUST include question number and sub-part index if any. Example: 9(b)

4.    Please create a PDF document  hw3.pdf and upload that in Canvas assignment page by the due date.

5.    NO handwritten document is accepted.

6.    NO LATE SUBMISSION.

 

1.   Assume an word addressable memory and a register file on a computing system contains the following data at an instance of time during running of a program. What is the operand value retrieved if : [2.5pts]

 

(a)  Next instruction is direct addressing with memory address 0x10003010? (b)  Next instruction is indirect addressing with memory address 0x10003010? (c)  Next instruction is register addressing with register address 7?

(d)  Next instruction is register indirect addressing with register address 7?

(e)  Next instruction is displacement addressing with register address 20 and offset address as 0xF6 (8-bit 2's complement format for offset) ?

 

 

MEM ADDR        CONTENT

0x1000301B        0x00000005

0x1000301A        0x00000006

0x10003019         0x00000007

0x10003018         0x00000008

0x10003017         0x00000009

0x10003016         0x00000010

0x10003015         0x00000011

0x10003014         0x00000012

0x10003013         0x00000010

0x10003012         0x00000011

0x10003011         0x00000012

0x10003010         0x10003014

0x1000300F         0x10003015

0x1000300E        0x00000001

0x1000300D        0x00000002

0x1000300C        0x00000003

 

 

 

 

REG       CONTENT            REG       CONTENT

R00        0x00000000         R16        0x90003024

R01        0x00000001         R17        0x90003025

R02        0x00000002         R18        0x90003026

R03        0x00000003         R19        0x90003027

R04        0x00000004         R20        0x10003018

R05        0x00000005         R21        0x10003027

R06        0x00000006         R22        0x10003028

R07        0x10003013         R23        0x10003029

R08        0x90003024         R24        0x10003030

R09        0x00000006         R25        0x10003031

R10        0x00000007         R26        0x10003032

R11        0x00000008         R27        0x10003033

R12        0x00000009         R28        0x10003034

R13        0x00000010         R29        0x10003035

R14        0x00000011         R30        0x10003036

R15        0x00000012         R31        0x10003037

 

2. A NUMA computer cluster has 200 computing nodes with each node associated with 128GB RAM. Average local memory access time is 50ns and average remote memory access time is 180ns. Assume a program is running on one node in this cluster. It is consuming total of 230GB with local memory occupancy as 100GB. If there are 1

million (1,000,000) memory access in this program with probability of accessing a remote memory location as 0.25 what is the total time the program is busy accessing memory in millisecond (ms) unit ? [1pts]

 

3.   A computing system with traditional disk (rotating hard disk) transfer data to main memory at minimum unit of

2KB of block of data (i.e. it has to adjust read/write head per 2KB block data access). Its average access time is

1ms. It has transfer rate of 100Mbps (mega-bits per second). Another computing system has  solid state disk (with random access technique) transfer data to main memory at minimum unit of 1KB of block of data.  It has access time of 50us per block of data transfer and refresh time of 250us. Both the system runs Linux operating system with initial size of 2MB to be loaded into main memory during boot time. Which system will boot faster and how much (ratio their performance)? [1pts]

 

4.   Your Project II processor is modified to hook into a cache memory system (i.e. states are introduced to handle cache miss ) and running on 1GHz clock. This system is connected to a memory system with separate instruction and data cache. Both these caches has access time 1ns and cache miss penalty of 150ns. However, miss rate for instruction cache is 5%  and miss rate for data cache is 10%.  If the following piece of code is executed in that processor and the 'loop' block (starting from 'loop' label to last 'jmp loop') has been executed 10,000 times what is the total execution time of this program so far in 'us' (microsecond) unit? [1pts]

 

addi r2, r2, 0x0001;

lui  r0, 0x0100;

sw  r1, r0, 0x0000; loop:   addi r0, r0, 0x0001; sw  r2, r0, 0x0000;

addi r3, r2, 0x0000;

add  r2, r2, r1;

addi r1, r3, 0x0000;

jmp  loop;

 

5.   A 32-bit computer system supports 4GB byte addressable memory. It's processor has cache with block size of 1KB.

Both the control and tag bits per cache line is 8 bits each. Assume that cache line is fully mapped from bits of the address A excluding block bits and tag bits in the address.

 

(a)  How much data is cached within this cache memory in MB unit.  [1pts] (b)  Also determine actual size of the cache memory in KB unit. [1pts]

(c)  Whole memory is divided into how many blocks? [0.5pts]

6.   Now, assume that the system in the #5 uses 8-way associative cache but cache same amount of information. (a)  Determine TAG, CACHE LINE INDEX and BLOCK INDEX of the address 0x30AB23F2. [0.5pts]

(b)  What is the actual size of the cache memory in this case in KB unit? [0.5pts]

 

7.   A 32-bit computer system uses virtual memory with 4K page size. It also uses a cache same as #6. For any memory access, both TLB and cache access time is 1ns each. TLB miss rate is 25% with 20us penalty. Cache miss rate is

10% with 150us penalty. Page fault rate is 0.01% with page service (bring back page from disk to memory) 1s.

 

(a)  How much time would be spent for one million (1,000,000) memory access in second unit?   [0.5pts]

(b)  Determine TAG, CACHE LINE INDEX and BLOCK INDEX for an virtual address 0x4CD67821 with TLB

entry for 0x4CD67 is 0x28701, if this system uses same cache as in #5. [0.5pts]