mith College Computer Science CSC231 - Assembly Week #7 Dominique Thiébaut

Transcription

1 mith College Computer Science CSC231 - Assembly Week #7 Dominique Thiébaut dthiebaut@smith.edu

2 public class JavaLimits { public static void main(string[] args) { // // a multiplication of ints int x = 0x ; int y = 0x ; System.out.println( "x = " + x ); System.out.println( "y = " + y ); int z = x * y; System.out.println( "z = " + z ); System.out.println(); } } x = y = z =

3 int x, y, z; x = y = z = x * y; Java's Attitude RAM Pentium x ALU mul y z

4 int x, y, z; x = y = z = x * y; Java's Attitude RAM Pentium x ALU mul eax y edx eax z

5 int x, y, z; x = y = z = x * y; Java's Attitude RAM Pentium x ALU mul eax y edx eax z

6 int x, y, z; x = y = z = x * y; Java's Attitude RAM Pentium x ALU mul eax y edx eax z

7 Same Computation in Python

8 Same Computation in Python Interpreted vs. Compiled Languages

9 How big is a 32-bit int?

10 Ranges (Unsigned Integers) 8 bits bits 0-65, bits 0-4,294,967,295

11 Puzzling Behavior What is the output? int x = 1; for (int i=0; i<40; i++ ) { System.out.println( x ); x = x * 2; } JavaMulBy2.java

12 mul mul operand edx:eax < operand32 * eax dx:ax < operand16 * ax ax < operand8 * al alpha db 3 beta dw 4 x dd 6 mul mul mul mul mul mul mul reg8 reg16 reg32 mem8 mem16 mem32 REVIEW byte[alpha] ;ax <- al*alpha mul ebx ;edx:eax <- ; ebx*eax

13 div R : Q div operand div div div div div div reg8 reg16 reg32 mem8 mem16 mem32 edx:eax < edx:eax / operand32 dx:ax < dx:ax / operand16 ah:al < ax / operand8 alpha db 3 beta dw 4 x dd 6 ;compute beta/alpha mov ax, word[beta] div byte[alpha] ;quotient in al ;remainder in ah

14 Exercise Compute x = 2*alpha +3*beta + x - 1 alpha db 3 beta dw 4 x dd 6

15

16 Logical Instructions AND, OR, NOT, XOR

17 Is (x,y) inside Rectangle? x1,y1 x2,y2

18 a b a and b F F F F T F T F F T T T Truth Table

19 a b a and b F F F F T F T F F T T T a b a and b

20 a b a and b F F F F T F T F F T T T a b a and b a b a or b

21 a b a and b F F F F T F T F F T T T a b a and b a b a or b a b a xor b

22 a b a and b F F F F T F T F F T T T a b a and b a b a or b a b a xor b a not a

23 10010 and or xor not 11100

24 Instruction Feature AND Good for setting bits to 0 OR Good for setting bits to 1 XOR Good for flipping bits NOT Good for complementing all the bits Image from

25 and and dest, src and op8,op8 and op16,op16 and op32,op32 op: mem, reg, imm alpha db 0xf3 beta dw 4 x dd 6 and mov and byte[alpha],7 ax,0x1234 ax,0xff00 and dword[x], 2

26 or or dest, src or op8,op8 or op16,op16 or op32,op32 op: mem, reg, imm alpha db 3 beta dw 4 x dw 0x0F06 or mov or byte[alpha],4 ax,0x1234 ax,0xff00 or word[x], 15

27 xor xor dest, src xor op8,op8 xor op16,op16 xor op32,op32 op: mem, reg, imm alpha db 3 beta dw 4 x dd 0xF06 xor mov xor byte[alpha],0x0f ax,0x1234 ax,0xff00 xor dword[x], 15

28 not not oprnd not op8 not op16 not op32 op: mem, reg alpha db 3 beta dw 4 x dd 0xF06 not mov not not byte[alpha] ax,0x1234 ax dword[x]

29 We Stopped Here Last Time

30 Exercises 1) Set top 16 bits of eax to 0 2) Set lower 8 bits of eax to 0 3) Set top 8 bits of eax to 1 4) Flip the lowest bit of eax 5) Read a 12-bit sensor value in ax. Set top 4 bits of ax to 0.

31 Logic Design

32 Logic Design

33 Image from Apple II Motherboard

34 A Bit of History Claude Shannon 21 years old 1937 MIT Master's Thesis All arithmetic operations on binary numbers can be performed using boolean logic operators

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36 Designing a 2-bit Adder with Logic

37

38 Processor CU ALU

39 xi yi ALU Compute add x, y carryi sumi

40 x y xn yn x3 y3 x2 y2 x1 y1 x0 y0 zn z3 z2 z1 z0 z

41 y0 x = 0 0 = 0 1 = 0 1 = 1 0 carry z0

42 x0 y0 Carry z

43 x0 y0 Carry z Carry = x0 and y0 z0 = x0 xor y

44 x0 y0 AND XOR carry z0

45 Moral of the Story: Addition is performed by logic operations using natural binary numbers (unsigned arithmetic)

46 NEGATIVE NUMBERS

47 How can we represent signed binary numbers when all we have are bits (0/1)? Whichever system we use should work with the binary adder in the ALU

48 4-bit Nybble Binary Hex Unsigned Decimal A B C D E F 15

49 Sign Bit 4-bit Nybble Binary Hex Unsigned Decimal A B C D E F 15

50 4-bit Nybble Binary Hex Unsigned Decimal A B C D E F 15 Positive Numbers Negative Numbers

51 Signed Magnitude Number System

52 Signed Magnitude Rule: To find the opposite of a number, just flip its MSB (+5) (-5) and vice versa

53 4-bit Nybble Binary Hex Unsigned Decimal Signed Magnitude A B C D E F 15-7

54 Does this System work With the ALU Adder? Binary Hex Unsigned Decimal Signed Magnitud e A B C D E F = = 3

55 1's Complement Number System

56 1's Complement Rule: To find the opposite of a number, just flip all its bits (+5) (-5) and vice versa

57 4-bit Nybble Binary Hex Unsigned Decimal 1's Complement A B C D E F 15-0

58 Does this System work With the ALU Adder? Binary Hex Unsigned Decimal 1's Complement A B C D E F = = = 3

59 2's Complement Number System

60 2's Complement Rule: To find the opposite of a number, just flip all its bits, and add (+5) (-5) and vice versa

61 4-bit Nybble Binary Hex Unsigned Decimal 2's Complement A B C D E F 15-1

62 Does this System work With the ALU Adder? Binary Hex Unsigned Decimal 2's Complement A B C D E F = = = 3

63 Interesting Property What is the binary representation of -1 as a byte? What is the binary representation of -1 as a word? What is the binary representation of -1 as a dword?

64 int x = 0x7fffffff - 5; for ( int i=0; i<10; i++ ) System.out.println( x++ ); getcopy Loop0x7fffffff.java

65 What did you just learn about Java ints?

66 neg neg oprnd neg op8 neg op16 neg op32 op: mem, reg alpha db 1 beta dw 4 x dd 0xF06 neg byte[alpha] mov ax,1234 neg ax To get the 2's complement of an int neg dword[x]

67 Range of 2's Comp't. ints Binary Hex Unsigned Decimal A B C D E F 15

68 Type Minimum Maximum unsigned byte signed byte unsigned short signed short unsigned int signed int # Bytes , ,768 32, ,294,967, ,147,483,648 2,147,483,647 4 signed long 9,223,372,036,854,775,808 9,223,372,036,854,775,807 8