Chapter 2. Machine  Instructions and         Programs   Computer Organization               Lecture 6
Objectives   Machine instructions and program execution,    including branching and subroutine call and return    operati...
Number, Arithmetic  Operations, and       Characters
Unsigned Integer   Consider a n-bit vector of the form:           A = an −1an − 2 an − 3  a0    where ai=0 or 1 for i in...
Signed Integer3   major representations:      Sign and magnitude      One’s complement      Two’s complement Assumptions...
Sign and MagnitudeRepresentation                         -7       +0                -6       1111   0000          +1      ...
One’s ComplementRepresentation                           -0       +0                  -1       1111   0000          +1    ...
Two’s ComplementRepresentation                                     -1       +0                            -2       1111   ...
Binary, Signed-IntegerRepresentations         B                             V alues represented                           ...
Comparison Sign   and Magnitude   Cumbersome addition/subtraction   Must compare magnitudes to determine sign of    res...
Addition of Positive Numbers    0              1               0                   1+   0          +   0           +   1  ...
Addition and Subtraction – SignMagnitude                           4   0100      -4    1100 result sign bit is the same as...
Addition and Subtraction – 1’sComplement 4   0100          -4        1011+3   0011       + (-3)       1100 7   0111       ...
Addition and Subtraction – 1’sComplement Why does end-around carry work?                                  n   Its equivale...
Addition and Subtraction – 2’sComplement                              4   0100           -4     1100                      ...
Addition and Subtraction – 2’sComplement   Why can the carry-out be ignored?   -M + N when N > M:                   n     ...
2’s-Complement Add andSubtract Operations   (a)     0010       ( + 2)          (b)         0100        ( + 4)         + 00...
Overflow - Add two positive numbers to get anegative number or two negative numbers toget a positive number               ...
Overflow Conditions              0111                               1000    5          0101                   -7          ...
Sign Extension   Task:     Given w-bit signed integer x     Convert it to w+k-bit integer with same value   Rule:    ...
Sign Extension Example              short int x = 15213;              int      ix = (int) x;              short int y = -1...
Memory Locations,  Addresses, and      Operations
Memory Location, Addresses,and Operation                          n bits                                                  ...
Memory Location, Addresses,and Operation 32-bit   word length example                                      32 bits      b...
Memory Location, Addresses,and Operation   To retrieve information from memory, either for one    word or one byte (8-bit...
Memory Location, Addresses,and Operation Itis impractical to assign distinct addresses  to individual bit locations in th...
Big-Endian and Little-EndianAssignments  Word  address           Byte address                                   Byte addre...
Memory Location, Addresses,and Operation Address  ordering of bytes Word alignment Access numbers, characters, and char...
Memory Operation Load    (or Read or Fetch)   Copy the content. The memory content doesn’t change.   Address – Load   ...
Instruction andInstruction Sequencing
“Must-Perform” Operations Data  transfers between the memory and the  processor registers Arithmetic and logic operation...
Register Transfer Notation Identifya location by a symbolic name  standing for its hardware binary address  (LOC, R0,…) ...
Assembly Language Notation Represent   machine instructions and  programs. Move LOC, R1 = R1←[LOC] Add R1, R2, R3 = R3 ...
Basic Instruction Types High-levellanguage: C = A + B Action: C ← [A] + [B] Assembly: Add A, B, C Three-address instru...
Basic Instruction Types   Need to add something to the above two-address    instruction to finish:    Move B, C = C ← [B]...
Using Registers Registers  are faster The number of registers is smaller Shorter instructions Potential speedup Minim...
Using Registers Load    A, Ri Store   Ri, A Add   A, Ri Add   Ri, Rj Add   Ri, Rj, Rk Move Source, Destination Move...
Using Registers   In the processors where arithmetic operations are    allowed only on operands in register    Move A, Ri...
Instruction Execution and   Straight-Line Sequencing                         Address          Contents                    ...
i              Move    NUM1,R0               i+4            Add     NUM2,R0Branching      i+8            Add     NUM3,R0  ...
Move         N,R1                                                      Clear        R0 Branching                          ...
Condition Codes Condition  code flags Condition code register / status register N (negative) Z (zero) V (overflow) C...
Generating Memory Addresses How   to specify the address of branch target? Can we give the memory operand address  direc...
Stacks and Queues
StacksA  list of data elements, usually words or  bytes, with the accessing restriction that  elements can be added or re...
Stacks                            0             Stack                            •            pointer                     ...
Stacks   Stack Pointer (SP)   Push    Subtract #4, SP    Move NEWITEM, (SP)    Move NEWITEM, -(SP)   Pop    Move (SP), ...
Stacks   SP                19                    - 28                                           - 28                     1...
Stacks The  size of stack in a program is fixed in  memory. Need to avoid pushing if the maximum size is  reached Need ...
Stacks   SAFEPOP    Compare     #2000,SP           Chec to seeif the stac pointer contains                                ...
Queues Data are stored in and retrieved from a queue  on a First-In-First-Out (FIFO) basis. New data are added at the ba...
Subroutines
Subroutines   It is often necessary to perform a particular subtask    (subroutine) many times on different data values....
Subroutines   Since the subroutine may be called from different    places in a calling program, provision must be made   ...
Subroutines   Memory                                               Memory   location      Calling program                 ...
Subroutine Nesting and TheProcessor Stack If a subroutine calls another subroutine, the  contents in the link register wi...
Parameter Passing Exchange  of information between a calling  program and a subroutine. Several ways:   Through registe...
Passing Parameters throughProcessor Registers                 Calling   program                              Move         ...
Passing Parameters through   StackAssumetop of stac is atlevel 1 below.                k                                  ...
The Stack Frame Some   stack locations constitute a private  work space for a subroutine, created at the  time the subrou...
The Stack Frame         SP                           saved [R1]    (stack pointer)                                      sa...
SP and FP   Move FP, -(SP)   Move SP, FP   Subtract #12, SP   Push R0 and R1   …   Pop R0 and R1   Add #12, SP   P...
Stack Frames for NestedSubroutines     Memory     location                    Instructions            Commen              ...
Stack Frames for NestedSubroutines                   [R1] from SUB1                   [R0] from SUB1              Stack   ...
AdditionalInstructions
Logic Instructions   AND   OR   NOT (what’s the purpose of the following)    Not R0    Add #1, R0   Determine if the l...
Logical Shifts   Logical shift – shifting left (LShiftL) and shifting right    (LShiftR)                       C         ...
Logical Shifts   Two decimal digits represented in ASCII code are    located at LOC and LOC+1. Pack these two digits in  ...
Arithmetic Shifts                                             R0                         C       before:         1   0   0...
C                                 R0         before:                 0   1   1   1     0    . . .        0    1   1Rotate ...
Multiplication and Division Not very popular (especially division) Multiply R , R             i   j  Rj ← [Ri] х [Rj] A...
Example Programs
Vector Dot Product Program                                           n −1                    Dot Product = ∑ A(i ) × B (i ...
Byte-Sorting Program Sort  a list of bytes stored in memory into  ascending alphabetic order. The list consists of n byt...
Byte-Sorting Program                 for    (j = n – 1; j > 0; j = j – 1)                        { for ( k = j – 1; k > = ...
Byte-Sorting Program The   list must have at least two elements  because the check for loop termination is  done at the e...
Linked List Many   nonnumeric application programs  require that an ordered list of information  items be represented and...
Problem Illustration                             N               n   Maintain this list of                Student ID     ...
Linked List   Each record still occupies a consecutive four-word block in the memory.   But successive records in the or...
List in Memory                 Memory     Key        Link                  Data                               address    f...
Insertion of a New Record   Suppose that the                         INSERTION    Compare    #0, RHEAD    ID number of th...
Deletion of a Record                       DELETION         Compare            (RHEAD), RIDNUM                            ...
Encoding of Machine        Instructions
Encoding of MachineInstructions   Assembly language program needs to be converted into machine    instructions. (ADD = 01...
Encoding of MachineInstructions   What happens if we want to specify a memory    operand using the Absolute addressing mo...
Encoding of MachineInstructions   Then what if an instruction in which two operands    can be specified using the Absolut...
Encoding of MachineInstructions   If we insist that all instructions must fit into a single    32-bit word, it is not pos...
Encoding of MachineInstructions   How to load a 32-bit address into a register that    serves as a pointer to memory loca...
Encoding of MachineInstructions An instruction must occupy only one word –  Reduced Instruction Set Computer (RISC) Othe...
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comp.org Chapter 2

  1. 1. Chapter 2. Machine Instructions and Programs Computer Organization Lecture 6
  2. 2. Objectives Machine instructions and program execution, including branching and subroutine call and return operations. Number representation and addition/subtraction in the 2’s-complement system. Addressing methods for accessing register and memory operands. Assembly language for representing machine instructions, data, and programs. Program-controlled Input/Output operations. Operations on stack, queue, list, linked-list, and array data structures.
  3. 3. Number, Arithmetic Operations, and Characters
  4. 4. Unsigned Integer Consider a n-bit vector of the form: A = an −1an − 2 an − 3  a0 where ai=0 or 1 for i in [0, n-1]. This vector can represent positive integer values V = A in the range 0 to 2n-1, where n −1 n−2 A=2 an −1 + 2 an − 2 +  + 2 a1 + 2 a0 1 0
  5. 5. Signed Integer3 major representations: Sign and magnitude One’s complement Two’s complement Assumptions: 4-bit machine word 16 different values can be represented Roughly half are positive, half are negative
  6. 6. Sign and MagnitudeRepresentation -7 +0 -6 1111 0000 +1 1110 0001 -5 +2 + 1101 0010 -4 1100 0011 +3 0 100 = + 4 -3 1011 0100 +4 1 100 = - 4 1010 0101 -2 +5 - 1001 0110 -1 1000 0111 +6 -0 +7 High order bit is sign: 0 = positive (or zero), 1 = negative Three low order bits is the magnitude: 0 (000) thru 7 (111) Number range for n bits = +/-2n-1 -1 Two representations for 0
  7. 7. One’s ComplementRepresentation -0 +0 -1 1111 0000 +1 1110 0001 -2 +2 + 1101 0010 -3 1100 0011 +3 0 100 = + 4 -4 1011 0100 +4 1 011 = - 4 1010 0101 -5 +5 - 1001 0110 -6 1000 0111 +6 -7 +7  Subtraction implemented by addition & 1s complement  Still two representations of 0! This causes some problems  Some complexities in addition
  8. 8. Two’s ComplementRepresentation -1 +0 -2 1111 0000 +1 1110 0001 -3 +2 + 1101 0010 like 1s comp except shifted -4 1100 0011 +3 0 100 = + 4 one position clockwise -5 1011 0100 +4 1 100 = - 4 1010 0101 -6 +5 - 1001 0110 -7 1000 0111 +6 -8 +7  Only one representation for 0  One more negative number than positive number
  9. 9. Binary, Signed-IntegerRepresentations B V alues represented Sign and b3 b2b1b0 magnitude 1 s complement 2 s complement 0 1 1 1 +7 +7 + 7 0 1 1 0 +6 +6 + 6 0 1 0 1 +5 +5 + 5 0 1 0 0 +4 +4 + 4 0 0 1 1 +3 +3 + 3 0 0 1 0 +2 +2 + 2 0 0 0 1 +1 +1 + 1 0 0 0 0 +0 +0 + 0 1 0 0 0 - 0 -7 - 8 1 0 0 1 - 1 -6 - 7 1 0 1 0 - 2 -5 - 6 1 0 1 1 - 3 -4 - 5 1 1 0 0 - 4 -3 - 4 1 1 0 1 - 5 -2 - 3 1 1 1 0 - 6 - 1 - 2 1 1 1 1 - 7 -0 - 1 Figure 2.1. Binary, signed-integer representations.
  10. 10. Comparison Sign and Magnitude Cumbersome addition/subtraction Must compare magnitudes to determine sign of result One’s Complement Simply bit-wise complement Two’s Complement Simply bit-wise complement + 1
  11. 11. Addition of Positive Numbers 0 1 0 1+ 0 + 0 + 1 + 1 0 1 1 10 Carry-out Figure 2.2. Addition of 1-bit numbers.
  12. 12. Addition and Subtraction – SignMagnitude 4 0100 -4 1100 result sign bit is the same as the operands +3 0011 + (-3) 1011 sign 7 0111 -7 1001 when signs differ, 4 0100 -4 1100 operation is subtract, sign of result depends -3 1011 +3 0011 on sign of number with the larger magnitude 1 0001 -1 1111 `
  13. 13. Addition and Subtraction – 1’sComplement 4 0100 -4 1011+3 0011 + (-3) 1100 7 0111 -7 10111 End around carry 1 1000 4 0100 -4 1011 -3 1100 +3 0011 1 10000 -1 1110 End around carry 1 0001
  14. 14. Addition and Subtraction – 1’sComplement Why does end-around carry work? n Its equivalent to subtracting 2 and adding 1 n n M - N = M + N = M + (2 - 1 - N) = (M - N) + 2 - 1 (M > N) n n -M + (-N) = M + N = (2 - M - 1) + (2 - N - 1) n-1 M+N<2 n n = 2 + [2 - 1 - (M + N)] - 1 after end around carry: n = 2 - 1 - (M + N) this is the correct form for representing -(M + N) in 1s comp!
  15. 15. Addition and Subtraction – 2’sComplement 4 0100 -4 1100 +3 0011 + (-3) 1101If carry-in to the highorder bit = 7 0111 -7 11001carry-out then ignorecarryif carry-in differs from 4 0100 -4 1100carry-out then overflow -3 1101 +3 0011 1 10001 -1 1111 Simpler addition scheme makes twos complement the most common choice for integer number systems within digital systems
  16. 16. Addition and Subtraction – 2’sComplement Why can the carry-out be ignored? -M + N when N > M: n n M* + N = (2 - M) + N = 2 + (N - M) n Ignoring carry-out is just like subtracting 2 -M + -N where N + M < = 2n-1 n n -M + (-N) = M* + N* = (2 - M) + (2 - N) n n = 2 - (M + N) + 2 After ignoring the carry, this is just the right two’s complement representation for -(M + N)!
  17. 17. 2’s-Complement Add andSubtract Operations (a) 0010 ( + 2) (b) 0100 ( + 4) + 0011 ( + 3) + 1010 (- 6) 0101 ( + 5) 1110 (- 2) (c) 1011 (- 5) (d) 0111 ( + 7) + 1110 (- 2) + 1101 ( - 3) 1001 (- 7) 0100 ( + 4) (e) 1101 (- 3) 1101 - 1001 (- 7) + 0111 0100 ( + 4) (f) 0010 ( + 2) 0010 - 0100 ( + 4) + 1100 1110 ( - 2) (g) 0110 ( + 6) 0110 - 0011 ( + 3) + 1101 0011 ( + 3) (h) 1001 ( - 7) 1001 - 1011 (- 5) + 0101 1110 ( - 2) (i) 1001 (- 7) 1001 - 0001 ( + 1) + 1111 1000 ( - 8) (j) 0010 ( + 2) 0010 - 1101 ( - 3) + 0011 0101 ( + 5) Figure 2.4. 2s-complement Add and Subtract operations.
  18. 18. Overflow - Add two positive numbers to get anegative number or two negative numbers toget a positive number -1 +0 -1 +0 -2 1111 0000 +1 -2 1111 0000 +1 1110 0001 1110 0001 -3 +2 -3 1101 1101 +2 0010 0010-4 -4 1100 0011 +3 1100 0011 +3-5 1011 -5 1011 0100 +4 0100 +4 1010 1010 -6 0101 -6 0101 1001 +5 +5 0110 1001 0110 -7 1000 0111 +6 -7 1000 +6 0111 -8 +7 -8 +7 5 + 3 = -8 -7 - 2 = +7
  19. 19. Overflow Conditions 0111 1000 5 0101 -7 1001 3 0011 -2 1100 -8 1000 7 10111 Overflow Overflow 0000 1111 5 0101 -3 1101 2 0010 -5 1011 7 0111 -8 11000 No overflow No overflow Overflow when carry-in to the high-order bit does not equal carry out
  20. 20. Sign Extension Task:  Given w-bit signed integer x  Convert it to w+k-bit integer with same value Rule:  Make k copies of sign bit:  X′= x w–1 ,…, xw–1 , xw–1 , xw–2 ,…, x0 w X • • • k copies of MSB • • • X′ • • • • • • k w
  21. 21. Sign Extension Example short int x = 15213; int ix = (int) x; short int y = -15213; int iy = (int) y; Decimal Hex Binaryx 15213 3B 6D 00111011 01101101ix 15213 00 00 C4 92 00000000 00000000 00111011 01101101y -15213 C4 93 11000100 10010011iy -15213 FF FF C4 93 11111111 11111111 11000100 10010011
  22. 22. Memory Locations, Addresses, and Operations
  23. 23. Memory Location, Addresses,and Operation n bits first word Memory consists second word of many millions of storage cells, • each of which can • • store 1 bit. Data is usually i th word accessed in n-bit groups. n is called • word length. • • last word Figure 2.5. Memory words.
  24. 24. Memory Location, Addresses,and Operation 32-bit word length example 32 bits b 31 b 30 b1 b0 • • • Sign bit: b 31= 0 for positive numbers b 31= 1 for negative numbers (a) A signed integer 8 bits 8 bits 8 bits 8 bits ASCII ASCII ASCII ASCII character character character character (b) Four characters
  25. 25. Memory Location, Addresses,and Operation To retrieve information from memory, either for one word or one byte (8-bit), addresses for each location are needed. A k-bit address memory has 2k memory locations, namely 0 – 2k-1, called memory space. 24-bit memory: 224 = 16,777,216 = 16M (1M=220) 32-bit memory: 232 = 4G (1G=230) 1K=210 1T=240
  26. 26. Memory Location, Addresses,and Operation Itis impractical to assign distinct addresses to individual bit locations in the memory. The most practical assignment is to have successive addresses refer to successive byte locations in the memory – byte- addressable memory. Byte locations have addresses 0, 1, 2, … If word length is 32 bits, they successive words are located at addresses 0, 4, 8,…
  27. 27. Big-Endian and Little-EndianAssignments Word address Byte address Byte address 0 0 1 2 3 0 3 2 1 0 4 4 5 6 7 4 7 6 5 4 • • • • • • k k k k k k k k k k 2 -4 2 -4 2 -3 2- 2 2 - 1 2 - 4 2- 1 2 - 2 2 -3 2 -4 (a) Big-endian assignment (b) Little-endian assignment Figure 2.7. Byte and word addressing.
  28. 28. Memory Location, Addresses,and Operation Address ordering of bytes Word alignment Access numbers, characters, and character strings
  29. 29. Memory Operation Load (or Read or Fetch) Copy the content. The memory content doesn’t change. Address – Load Registers can be used Store (or Write) Overwrite the content in memory Address and Data – Store Registers can be used
  30. 30. Instruction andInstruction Sequencing
  31. 31. “Must-Perform” Operations Data transfers between the memory and the processor registers Arithmetic and logic operations on data Program sequencing and control I/O transfers
  32. 32. Register Transfer Notation Identifya location by a symbolic name standing for its hardware binary address (LOC, R0,…) Contents of a location are denoted by placing square brackets around the name of the location (R1←[LOC], R3 ←[R1]+[R2]) Register Transfer Notation (RTN)
  33. 33. Assembly Language Notation Represent machine instructions and programs. Move LOC, R1 = R1←[LOC] Add R1, R2, R3 = R3 ←[R1]+[R2]
  34. 34. Basic Instruction Types High-levellanguage: C = A + B Action: C ← [A] + [B] Assembly: Add A, B, C Three-address instruction: Operation Source1, Source2, Destination Two-address instruction: Operation Source, Destination Add A, B = B ←[A] + [B]
  35. 35. Basic Instruction Types Need to add something to the above two-address instruction to finish: Move B, C = C ← [B] One-address instruction (to fit in one word length) Accumulator: Add A Load A Add B Store C Zero-address instructions (stack operation)
  36. 36. Using Registers Registers are faster The number of registers is smaller Shorter instructions Potential speedup Minimize the frequency with which data is moved back and forth between the memory and processor registers.
  37. 37. Using Registers Load A, Ri Store Ri, A Add A, Ri Add Ri, Rj Add Ri, Rj, Rk Move Source, Destination Move A, R = Load A, R i i Move Ri, A = Store Ri, A
  38. 38. Using Registers In the processors where arithmetic operations are allowed only on operands in register Move A, Ri Move B, Rj Add Ri, Rj Move Rj, C In the processors where one operand may be in the memory but the other one must be in registers Move A, Ri Add B, Ri Move Ri, C
  39. 39. Instruction Execution and Straight-Line Sequencing Address Contents i Assumptions:Begin execution here Move A,R0 i +4 3-instruction program - One memory operand Add B,R0 segment per instruction i +8 Move R0,C - 32-bit word length - Memory is byte addressable A - Full memory address can be directly specified in a single-word instruction B Data for the program Two-phase procedure C Figure 2.8. A program for C ← [Α] + [Β].
  40. 40. i Move NUM1,R0 i+4 Add NUM2,R0Branching i+8 Add NUM3,R0 • • • i + 4n - 4 Add NUMn,R0 i + 4n Move R0,SUM • • • SUM NUM1 NUM2 • • • NUMn Figure 2.9. A straight-line program for adding n numbers.
  41. 41. Move N,R1 Clear R0 Branching LOOP Determine address of "Next" number and add Program "Next" number to R0 loop Decrement R1 Branch>0 LOOP Branch target Move R0,SUM Conditional branch • • • SUM N n NUM1Figure 2.10. Using a loop to add n numbers. NUM2 • • • NUMn
  42. 42. Condition Codes Condition code flags Condition code register / status register N (negative) Z (zero) V (overflow) C (carry) Different instructions affect different flags
  43. 43. Generating Memory Addresses How to specify the address of branch target? Can we give the memory operand address directly in a single Add instruction in the loop? Use a register to hold the address of NUM1; then increment by 4 on each pass through the loop.
  44. 44. Stacks and Queues
  45. 45. StacksA list of data elements, usually words or bytes, with the accessing restriction that elements can be added or removed at one end of the list only. Top / Bottom / Pushdown Stack Last-In-First-Out (LIFO) Push / Pop
  46. 46. Stacks 0 Stack • pointer • register • Current SP - 28 top element 17 739 Stack • • • Bottom BOTTOM 43 element • • • k 2 - 1 Figure 2.21. A stack of words in the memory.
  47. 47. Stacks Stack Pointer (SP) Push Subtract #4, SP Move NEWITEM, (SP) Move NEWITEM, -(SP) Pop Move (SP), ITEM Add #4, SP Move (SP)+, ITEM
  48. 48. Stacks SP 19 - 28 - 28 17 SP 17 739 739 Stack • • • • • • 43 43 NEWITEM 19 ITEM - 28 (a) After push from NEWITEM (b) After pop into ITEM Figure 2.22. Effect of stack operations on the stack in Figure 2.21.
  49. 49. Stacks The size of stack in a program is fixed in memory. Need to avoid pushing if the maximum size is reached Need to avoid popping if stack is empty Compare instruction Compare src, dst [dst] – [src] Will not change the values of src and dst.
  50. 50. Stacks SAFEPOP Compare #2000,SP Chec to seeif the stac pointer contains k k Branc 0 h> EMPTYERR OR an addressvaluegreaterthan 2000. If it does,the stac is empt . Branc to the k y h routine EMPTYERROR for appropriate action. Move (SP)+,ITEM Otherwise,pop the top of the stac into k memory location ITEM. (a) Routine for a safe pop operation SAFEPUSH Compare #1500,SP Chec to seeif the stac pointer k k Branc ≤ 0 h FULLERR OR contains an addressvalueequal to or less than 1500. If it does, the stac is full. Branc to the routine k h FULLERR OR for appropriate action. Move NEWITEM, – (SP) Otherwise,push the elemen in memory t location NEWITEM onto the stac k. (b) Routine for a safe push operation Figure 2.23. Checking for empty and full errors in pop and push operations.
  51. 51. Queues Data are stored in and retrieved from a queue on a First-In-First-Out (FIFO) basis. New data are added at the back (high- address end) and retrieved from the front (low-address end). How many pointers are needed for stack and queue, respectively? Circular buffer
  52. 52. Subroutines
  53. 53. Subroutines It is often necessary to perform a particular subtask (subroutine) many times on different data values. To save space, only one copy of the instructions that constitute the subroutine is placed in the memory. Any program that requires the use of the subroutine simply branches to its starting location (Call). After a subroutine has been executed, it is said to return to the program that called the subroutine, and the program resumes execution. (Return)
  54. 54. Subroutines Since the subroutine may be called from different places in a calling program, provision must be made for returning to the appropriate location. Subroutine Linkage method: use link register to store the PC. Call instruction Store the contents of the PC in the link register Branch to the target address specified by the instruction Return instruction Branch to the address contained in the link register
  55. 55. Subroutines Memory Memory location Calling program location Subroutine SUB 200 Call SUB 1000 first instruction 204 next instruction Return 1000 PC 204 Link 204 Call Return Figure 2.24. Subroutine linkage using a link register.
  56. 56. Subroutine Nesting and TheProcessor Stack If a subroutine calls another subroutine, the contents in the link register will be destroyed. If subroutine A calls B, B calls C, after C has been executed, the PC should return to B, then A LIFO – Stack Automatic process by the Call instruction Processor stack
  57. 57. Parameter Passing Exchange of information between a calling program and a subroutine. Several ways: Through registers Through memory locations Through stack
  58. 58. Passing Parameters throughProcessor Registers Calling program Move N,R1 R1 servesas a coun ter. Move #NUM1,R2 R2 pointsto thelist. Call LISTADD Call subroutine. Move R0,SUM Sa result. ve . . . Subroutine LISTADD Clear R0 Initialize sumto 0. LOOP Add (R2)+,R0 Add entry from list. Decremen t R1 Branc >0 h LOOP Return Return to calling program. Figure 2.25. Program of Figure 2.16 written as a subroutine; parameters passed through registers.
  59. 59. Passing Parameters through StackAssumetop of stac is atlevel 1 below. k - Passing by reference Move #NUM1, – (SP) Pushparameters onto stac k. - Passing by value Move N, – (SP) Call LISTADD Call subroutine (top of stac at level 2). k Move 4(SP),SUM Sa result. ve Add #8,SP Restoretop of stack (top of stac at level 1). k Level 3 → [R2] . . . [R1] [R0]LISTADD MoveMultiple R0– R2,– (SP) Sa registers ve (top of stac at level 3). k Level 2 → Return address Move 16(SP),R1 Initialize coun to n. ter n Move 20(SP),R2 Initialize pointer to the list. Clear R0 Initialize sum to 0. NUM1LOOP Add (R2)+,R0 Add entry from list. Level 1 → Decremen t R1 Branch>0 LOOP Move R0,20(SP) Put result on the stac k. MoveMultiple (SP)+,R0 R2 – Restoreregisters. (b) Top of stack at various times Return Return to calling program. (a) Calling program and subroutine Figure 2.26. Program of Figure 2.16 written as a subroutine; parameters passed on the stack.
  60. 60. The Stack Frame Some stack locations constitute a private work space for a subroutine, created at the time the subroutine is entered and freed up when the subroutine returns control to the calling program. Such space is called a stack frame. Frame pointer (FP) Index addressing to access data inside frame -4(FP), 8(FP), …
  61. 61. The Stack Frame SP saved [R1] (stack pointer) saved [R0] localvar3 localvar2 localvar1 Stack frame FP for (frame pointer) saved [FP] called Return address subroutine param1 param2 param3 param4 Old TOS (top-of-stack) Figure 2.27. A subroutine stack frame example.
  62. 62. SP and FP Move FP, -(SP) Move SP, FP Subtract #12, SP Push R0 and R1 … Pop R0 and R1 Add #12, SP Pop FP Return
  63. 63. Stack Frames for NestedSubroutines Memory location Instructions Commen ts Main program . . . 2000 Move PARAM2, – (SP) Placeparameters stack. on 2004 Move PARAM1, – (SP) 2008 Call SUB1 2012 Move (SP),RESULT Store result. 2016 Add #8,SP Restorestack level. 2020 next instruction . . . First subroutine 2100 SUB1 Move FP, – (SP) Sa frame pointer register. ve 2104 Move SP,FP Load the frame pointer. 2108 MoveMultiple R0– R3,– (SP) Sa registers. ve 2112 Move 8(FP),R0 Get first parameter. Move 12(FP),R1 Get secondparameter. . . . Move PARAM3, – (SP) Placea parameter n stack. o 2160 Call SUB2 2164 Move (SP)+,R2 Pop SUB2 result into R2. . . . Move R3,8(FP) Placeansw on stack. er MoveMultiple (SP)+,R0– R3 Restoreregisters. Move (SP)+,FP Restoreframe pointer register. Return Return to Main program. Second subroutine 3000 SUB2 Move FP, – (SP) Sa frame pointer register. ve Move SP,FP Load the frame pointer. MoveMultiple R0– R1,– (SP) Sa registers R0 and R1. ve Move 8(FP),R0 Get the parameter. . . . Move R1,8(FP) Place SUB2 result on stack. MoveMultiple (SP)+,R0– R1 Restoreregisters R0 and R1. Move (SP)+,FP Restoreframe pointer register. Return Return to Subroutine 1. Figure 2.28. Nested subroutines.
  64. 64. Stack Frames for NestedSubroutines [R1] from SUB1 [R0] from SUB1 Stack frame FP [FP] from SUB1 for second 2164 subroutine param3 [R3] from Main [R2] from Main [R1] from Main Stack [R0] from Main frame for FP [FP] from Main first subroutine 2012 param1 param2 Old TOS Figure 2.29. Stack frames for Figure 2.28.
  65. 65. AdditionalInstructions
  66. 66. Logic Instructions AND OR NOT (what’s the purpose of the following) Not R0 Add #1, R0 Determine if the leftmost character of the four ASCII characters stored in the 32-bit register R0 is Z (01011010) And #$FF000000, R0 Compare #$5A000000, R0 Branch=0 YES
  67. 67. Logical Shifts Logical shift – shifting left (LShiftL) and shifting right (LShiftR) C R0 0 before: 0 0 1 1 1 0 . . . 0 1 1 after: 1 1 1 0 . . . 0 1 1 0 0 (a) Logical shift left LShiftL #2,R0 0 R0 C before: 0 1 1 1 0 . . . 0 1 1 0 after: 0 0 0 1 1 1 0 . . . 0 1 (b) Logical shift irght LShiftR #2,R0
  68. 68. Logical Shifts Two decimal digits represented in ASCII code are located at LOC and LOC+1. Pack these two digits in a single byte location PACKED. Move #LOC,R0 R0 points to data. MoveByte (R0)+,R1 Load first byte into R1. LShiftL #4,R1 Shift left by 4 bit positions. MoveByte (R0),R2 Load secondbyte into R2. And #$F,R2 Eliminate high-order bits. Or R1,R2 ConcatenateheBCD digits. t MoveByte R2,PACKED Store the result. Figure 2.31. A routine that packs two BCD digits.
  69. 69. Arithmetic Shifts R0 C before: 1 0 0 1 1 . . . 0 1 0 0 after: 1 1 1 0 0 1 1 . . . 0 1 (c) Arithmetic shift rght i AShiftR #2,R0
  70. 70. C R0 before: 0 1 1 1 0 . . . 0 1 1Rotate 0 after: 1 1 1 0 . . . 0 1 1 0 1 (a) Rotate left without carr y RotateL #2,R0 C R0 before: 0 0 1 1 1 0 . . . 0 1 1 after: 1 1 1 0 . . . 0 1 1 0 0 (b) Rotate left with carr y RotateLC #2,R0 R0 C before: 0 1 1 1 0 . . . 0 1 1 0 after: 1 1 0 1 1 1 0 . . . 0 1 (c) Rotate ight without carr r y RotateR #2,R0 R0 C before: 0 1 1 1 0 . . . 0 1 1 0 after: 1 0 0 1 1 1 0 . . . 0 1 (d) Rotate ir with carr ght y RotateRC #2,R0 Figure 2.32. Rotate instructions.
  71. 71. Multiplication and Division Not very popular (especially division) Multiply R , R i j Rj ← [Ri] х [Rj] Any problem? Divide R , R i j Rj ← [Ri] / [Rj]
  72. 72. Example Programs
  73. 73. Vector Dot Product Program n −1 Dot Product = ∑ A(i ) × B (i ) i =0 Move #AVEC,R1 R1 points to vector A. Move #BVEC,R2 R2 points to vector B. Move N,R3 R3 serv as a coun es ter. Clear R0 R0 accum ulates the dot product. LOOP Move (R1)+,R4 Computethe productof Multiply (R2)+,R4 nextcomponen ts. Add R4,R0 Add to previoussum. Decrement R3 Decrement thecounter. Branch > 0 LOOP Loop again if not done. Move R0,DOTPR OD Storedot product in memory. Figure 2.33. A program for computing the dot product of two vectors.
  74. 74. Byte-Sorting Program Sort a list of bytes stored in memory into ascending alphabetic order. The list consists of n bytes, not necessarily distinct, stored from memory location LIST to LIST+n-1. Each byte contains the ASCII code for a character from A to Z. The first bit is 0. Straight-selection algorithm (compare and swap)
  75. 75. Byte-Sorting Program for (j = n – 1; j > 0; j = j – 1) { for ( k = j – 1; k > = 0; k = k – 1 ) { if (LIST[k] > LIST[ j]) { TEMP = LIST[k]; LIST[k] = LIST[ j ]; LIST[ j] = TEMP; } } } (a) C-language program for sorting Move #LIST,R0 Load LIST into baseregister R0. Move N,R1 Initialize outer loop index Subtract #1,R1 register R1 to j = n – 1. OUTER Move R1,R2 Initialize inner loop index Subtract #1,R1 register R2 to k = j – 1. MoveByte (R0,R1),R3 Load LIST( j ) into R3, which holds current maximum in sublist. INNER CompareByte R3,(R0,R2) If LIST( k) ≤ [R3], Branc ≤ 0 h NEXT do not exhange. MoveByte (R0,R2),R4 Otherwise,exchange LIST(k) MoveByte R3,(R0,R2) with LIST(j ) and load MoveByte R4,(R0,R1) new maximum into R3. MoveByte R4,R3 RegisterR4 serv esas TEMP. NEXT Decremen t R2 Decremen index registersR2 and t Branc ≥ 0 h INNER R1, which alsoserv e Decremen t R1 as loop counters, and branc h Branc 0 h> OUTER back if loopsnot finished. (b) Assembly language program for sorting
  76. 76. Byte-Sorting Program The list must have at least two elements because the check for loop termination is done at the end of each loop. If the machine instruction set allows a move operation from one memory location directly to another memory location: MoveByte (R0, R2), (R0, R1) MoveByte R3, (R0, R2) MoveByte (R0, R1), R3
  77. 77. Linked List Many nonnumeric application programs require that an ordered list of information items be represented and stored in memory in such a way that it is easy to add items to the list or to delete items from the list at ANY position while maintaining the desired order of items. Different from Stacks or Queues.
  78. 78. Problem Illustration N n Maintain this list of Student ID LIST records in consecutive memory locations in LIST + 4 Test 1 some contiguous Student 1 LIST + 8 Test 2 block of memory in increasing order of LIST + 12 Test 3 student ID numbers. LIST + 16 Student ID What if a student withdraws from the Test 1 course so that an Student 2 Test 2 empty record slot is created? Test 3 What if another student registers in • the course? • •
  79. 79. Linked List Each record still occupies a consecutive four-word block in the memory. But successive records in the order do not necessarily occupy consecutive blocks in the memory address space. Each record contains an address value in a one-word link field that specifies the location of the next record in order to enable connecting the blocks together to form the ordered list. Link address Record 1 Record 2 Record k 0 Head Tail (a) Linking structure Record 1 Record 2 New record (b) Inserting a new record between Record 1 and Record 2
  80. 80. List in Memory Memory Key Link Data address field field field (ID) (Test scores) 1 word 1 word 3 words First record 2320 27243 1040 HeadHead pointer Second record 1040 28106 1200 Third record 1200 28370 2880 • • • Second last record 2720 40632 1280 Last 1280 47871 0 Tail record Figure 2.36. A list of student test scores organized as a linked list in memory.
  81. 81. Insertion of a New Record Suppose that the INSERTION Compare #0, RHEAD ID number of the new record is Branch>0 HEAD new record Move RNEWREC, RHEAD becomes a 28241, and the not empty one-entry list Return next available free record block HEAD Compare (RHEAD), (RNEWREC) is at address Branch>0 SEARCH new record 2960. insert new record Move RHEAD, 4(RNEWREC) becomes somewhere after Move RNEWREC, RHEAD What are the current head new head Return possibilities of the SEARCH Move RHEAD, RCURRENT new record’s Move 4(RCURRENT), RNEXT position in the list. LOOP Compare #0, RNEXT Branch=0 TAIL ne w record becomes ne tail w Compare (RNEXT), (RNEWREC) Branch<0 INSERT insert new record in Move RNEXT, RCURRENT an interior position Branch LOOP INSERT Move RNEXT, 4(RNEWREC) TAIL Move RNEWREC, 4(RCURRENT) Return
  82. 82. Deletion of a Record DELETION Compare (RHEAD), RIDNUM Branch>0 SEARCH Move 4(RHEAD), RHEAD not the head record Return SEARCH Move RHEAD, RCURRENT LOOP Move 4(RCURRENT), RNEXT Compare (RNEXT), RIDNUM Branch=0 DELETE Move RNEXT , RCURRENT Branch LOOP DELETE Move 4(RNEXT), RTEMP Move RTEMP , 4(RCURRENT) Return Figure 2.38. A subroutine for deleting a record from a linked list. Any problem?
  83. 83. Encoding of Machine Instructions
  84. 84. Encoding of MachineInstructions Assembly language program needs to be converted into machine instructions. (ADD = 0100 in ARM instruction set) In the previous section, an assumption was made that all instructions are one word in length. Suppose 32-bit word length, 8-bit OP code (how many instructions can we have?), 16 registers in total (how many bits?), 3-bit addressing mode indicator. Add R1, R2 8 7 7 10 Move 24(R0), R5 LshiftR #2, R0 OP code Source Dest Other info Move #$3A, R1 Branch>0 LOOP (a) One-word instruction
  85. 85. Encoding of MachineInstructions What happens if we want to specify a memory operand using the Absolute addressing mode? Move R2, LOC 14-bit for LOC – insufficient Solution – use two words OP code Source Dest Other info Memory address/Immediate operand (b) Two-word instruction
  86. 86. Encoding of MachineInstructions Then what if an instruction in which two operands can be specified using the Absolute addressing mode? Move LOC1, LOC2 Solution – use two additional words This approach results in instructions of variable length. Complex instructions can be implemented, closely resembling operations in high-level programming languages – Complex Instruction Set Computer (CISC)
  87. 87. Encoding of MachineInstructions If we insist that all instructions must fit into a single 32-bit word, it is not possible to provide a 32-bit address or a 32-bit immediate operand within the instruction. It is still possible to define a highly functional instruction set, which makes extensive use of the processor registers. Add R1, R2 ----- yes Add LOC, R2 ----- no Add (R3), R2 ----- yes
  88. 88. Encoding of MachineInstructions How to load a 32-bit address into a register that serves as a pointer to memory locations? Solution #1 – direct the assembler to place the desired address in a word location in a data area close to the program, so that the Relative addressing mode can be used to load the address. Solution #2 – use logical and shift instructions to construct the desired 32-bit address by giving it in parts that are small enough to be specifiable using the Immediate addressing mode.
  89. 89. Encoding of MachineInstructions An instruction must occupy only one word – Reduced Instruction Set Computer (RISC) Other restrictions OP code Ri Rj Rk Other info (c) Three-operand instruction
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