Tutorial for Chapter 3, 4

Transcription

1 Eastern Mediterranean University School of Computing and Technology ITEC2 Computer Organization & Architecture Tutorial for Chapter 3, 4 Number Systems Binary Number Systems o Base = 2 o A single bit can represent two states: 0 or o Examples: 000, 00, 000 o When converting to decimal, notice that each digit corresponds to 2 x, where x 0 starting from the rightmost bit Hexadecimal Number Systems o Base = 6 o 6 symbols = {0,, 2, 3, 4,, 6, 7, 8, 9, A, B, C, D, E, F} { 0=A, =B, 2=C, 3=D, 4=E, = F} o Examples: AB2, 876F, FFFF o When converting to decimal, notice that each digit corresponds to 6 x, where x 0 starting from the rightmost bit 2

2 Decimal to Binary Conversion Repeated division by 2 until quotient is 0. Example 23 0 =? 2 Divide by 2 Quotient Remainder Binary digit 23 / 2 / 2 / 2 2 / 2 / Answer = Binary to Decimal Conversion Each digit corresponds to power of 2. Digit 8 Digit 7 Digit 6 Digit Digit 4 Digit 3 Digit 2 Digit Example: Convert 00 2 to decimal x x x2 + x2 0 = = 9 4 2

3 Decimal to Hexadecimal Conversion Repeated division by 6 until quotient is 0. Example 23 0 =? 6 Divide by 6 Quotient Remainder Hex digit 23 / 6 3 / D Answer = D 6 Hexadecimal to Decimal Conversion Each digit corresponds to power of 6. Digit 8 Digit 7 Digit 6 Digit Digit 4 Digit 3 Digit 2 Digit Example: Convert D 6 to decimal Dx6 + x6 0 = 3x6 + x = =

4 Binary to Decimal/Hexadecimal Conversion For binary to decimal/hexadecimal conversion, each digit, starting from the least significant bit, should be multiplied with: where x is the digit number. Example: 2 x, where x 0 Binary Value Decimal Value Hexadecimal Value A 0 B 00 2 C 0 3 D 0 4 E F 7 Exercise Consider a hypothetical machine that is shown in the figure below. Show the program execution for the following program:. Load AC from memory location Subtract content of memory location from AC. 3. Store AC to memory location 600. Assume that the values retrieved from memory location 0 and are 0009 and 0006, respectively Opcode Address (a) Instruction format 0 S Magnitude (b) Integer format Program counter (PC) Instruction register (IR) Accumulator (AC) (c) Internal CPU registers 000 = Load AC from memory 000 = Store AC to memory 00 = Add to AC from memory 00 = Subtract memory from AC (d) Partial list of opcodes 8 4

5 Exercise - Solution 9 Exercise 2 Consider a system with three I/O devices: Printer (priority = 2) Disk (priority = 4) Communication line (priority = ) Suppose that a user program (priority = 0) begins and a disk interrupt occurs at time t=. While disk interrupt carries on, a communication line interrupt occurs at t=0. Then while communication interrupt carries on, a printer interrupt occurs at time=. After completing all of interrupts, control returns to user program. Assume that the duration for job completion in each device is 0s. Draw the timeline diagram for each of the following: a) sequential interrupt processing b) nested interrupt processing 0

6 Exercise 2 - Solution a) Sequential Interrupt Processing User Program Disk Interrupt Communication line interrupt 0 Printer interrupt Communication Interrupt 2 Printer Interrupt 2 3 Exercise 2 - Solution b) Nested Interrupt Processing User Program Disk Interrupt Communication Interrupt Printer Interrupt 2 Printer interrupt 3 2 6

7 Exercise 3 For the hexadecimal main memory addresses EFA3C and 0BB2D, find: a) Tag, line and word values for a direct-mapped cache. b) Tag and word values for an associative cache. c) Tag, set and word values for a two-way set associative cache. Direct-Mapped Cache Tag Line Word Main memory address = Associative Cache Tag Word Main memory address = 22 2 Two-way set associative cache Tag Set Word Main memory address = Exercise 3 - Solution a) Direct-mapped cache Direct-Mapped Cache Tag Line Word Main memory address = E F A 3 C Tag = = E Line = = 3E8F Word = 00 = 0 0 B B 2 D Tag = = 0 Line = = 2ECB Word = 0 = 4 7

8 Exercise 3 - Solution b) Associative cache Associative Cache Tag Word Main memory address = 22 2 E F A 3 C Tag = = 07BE8F Word = 00 = 0 0 B B 2 D Tag = = 006ECB Word = 0 = Exercise 3 - Solution c) Two-way set associative cache Two-way set associative cache Tag Set Word Main memory address = E F A 3 C Tag = = 03D Set = = E8F Word = 00 = 0 0 B B 2 D Tag = = 003 Set = = 0ECB Word = 0 = 6 8

9 Exercise 4 According to the table given below, decide which line number should be selected for replacement with least recently used (LRU), least frequently used (LFU) and first in first out (FIFO) algorithms. Line Number Content Time Last Accessed Time Arrived to Memory Number of hits Block 3 32 ms ago 60 ms ago 2 Block 8 6 ms ago 72 ms ago 6 3 Block 2 2 ms ago 77 ms ago 4 Block 4 ms ago 20 ms ago 3 Block 9 0 ms ago 0 ms ago 7 Exercise 4 - Solution Algorithm Line Number to be selected LRU LFU 3 FIFO 4 Line Number Content Time Last Accessed Time Arrived to Memory Number of hits Block 3 32 ms ago 60 ms ago 2 Block 8 6 ms ago 72 ms ago 6 3 Block 2 2 ms ago 77 ms ago 4 Block 4 ms ago 20 ms ago 3 Block 9 0 ms ago 0 ms ago 8 9