Embed Size (px)
Citation preview
1
Introduction to Computer Systems
2
Outline
• Teaching staffs
• Textbook and Grading
• Course Schedule
• Motivation
• Suggested reading
– Preface xvii~xx
3
Instructor
• 路红
• Email: [email protected]
• Office phone: 65643922• Make Appointment or Open Door
Policy
5
Text Book
• Randy Bryant and David O’Hallaron,– Computer Systems: A Programmer’s
Perspective– Prentice Hall, August 12, 2002.– 电子工业出版社， 2006.
• Brian Kernighan and Dennis Ritchie,– The C Programming Language, Second Edition– Prentice Hall, 1988
6
Teaching Notes
• 10.11.4.101• User: ics• Pwd: ics• \ 课件• Right: can read/write and cannot delete
7
Grading
• Exams(50%)– Three in class exams (10% each)– Final (20%)– All exams are open books/open notes.
• Labs (40%)– 5~6 labs, (2-10% each)
• Home work(10%)
8
Grading
• Lab deadline & Late Submission– Due at 11:59pm of the specific due date– Give 5 late days– Lose 1/5 of points for each other late day
9
Course Schedule -1
• Mainly introduce the content of Chap 1 ~
Chap 6. Some content in Chap 10, if time
permitted.
10
Course Schedule -2
• 2006 ICS 课程 PPT 安排表 _Chap 1~Chap 6,
Chap 10.doc
11
Why are we here?
• From abstractions to details (realities)
• From application level to system level
• From Java to C
12
Features of this course
• Enduring Concepts
• From programmer’s perspective
• Actively study
• Becoming the rare “power programmer”
Enduring: 持久的
13
Enduring concepts
• Computer systems consists hardware and systems software that work together to run programs
• Specific implementations of systems change over time
• But the underlying concepts do not• All computer systems have similar
hardware and software components that perform similar functions
14
From programmer’s perspective
• Written for programmers instead of system builders– Few students would have the opportunity to
build a computer system– Even the computer engineers would be required
to use and program computers on a daily basis
• It covers a topic only if it affected– correctness, performance or utility of user-level
C programs
15
From programmer’s perspective
• Topics on hardware adder and bus designs were out
• Introduce assembly in a different way– How C constructs are translated by the compiler
• Pointers
• Loops
• Procedure calls and returns
• Switch statements
16
From programmer’s perspective
• Take a broader and more realistic view of the system – Linking and loading
– Process, signals
– Performance optimization
– I/O and network and concurrent programming （ Not introduced here, can read if you are interested in. ）
17
Actively study
• New concepts are followed by practical problems
• Homework problems and labs are also real• Learning by doing
– Working concrete problems– Writing and running programs on real systems
• Practical, concrete, hands-on and exciting
18
Becoming the rare “power programmer”
• Enlightened by an understanding of – the underlying computer system – and its impact on your application programs
• You know– How things work and – How to fix them when they break
19
Examples that we are going to learn
• How to avoid strange numerical errors – caused by the way that computers represent
numbers
• How to optimize the C code by using– Clever tricks that exploit the designs of modern
processors and memory systems
20
Examples that we are going to learn
• How the compiler implements procedure call
• How to use above knowledge to avoid – The security holes from buffer overflow bugs that
• Plague network and Internet software
• How to recognize and avoid the nasty errors during linking– That confound the average programmer
Plague: 引起麻烦Nasty: 危险的Confound: 混淆
21
Examples that we are going to learn
• How to write our own (*Optional) – Unix shell
– Dynamic storage allocation
– Web server
22
Fundamental course for systems
• Compilers
• Operating Systems
• Networking
• Architectures (with digital component design)
23
Platforms
• Hardware platform– Intel IA-32
• Operating system– Linux
• Programming language– ANSI C
• Compiler– GNU-gcc
24
The C Programming Language
• C was developed – in 1969 to 1973 – by Dennis Ritchie of Bell Laboratories.
• The American National Standards Institute (ANSI)– ratified the ANSI C standard in 1989.
• The standard defines – the C language – and a set of library functions known as the C standard
library.
Ratify: 批准 , 认可
25
The C Programming Language
• Kernighan and Ritchie describe ANSI C in their classic book– which is known affectionately as “K&R” .
• In Ritchie’s words [60], C is – quirky, – flawed, – and an enormous success.
• Why the success?
Quirky: 离奇的Flawed: 有缺陷的
26
The C Programming Language
• C was closely tied with the Unix operating system. – C was developed from the beginning as the system
programming language for Unix. – Most of the Unix kernel, and all of its supporting tools and
libraries, were written in C. – As Unix became popular in universities in the late 1970s
and early 1980s, many people were exposed to C and found that they liked it.
– Since Unix was written almost entirely in C, it could be easily ported to new machines, which created an even wider audience for both C and Unix.
27
The C Programming Language
• C is a small, simple language. – The design was controlled by a single person,
rather than a committee, and the result was a clean, consistent design with little baggage.
– The K&R book describes the complete language and standard library, with numerous examples and exercises, in only 261 pages.
– The simplicity of C made it relatively easy to learn and to port to different computers.
28
The C Programming Language
• C was designed for a practical purpose. – C was designed to implement the Unix operating
system. – Later, other people found that they could write
the programs they wanted, without the language getting in the way.
29
The C Programming Language
• C is the language of choice for system-level programming
• There is a huge installed based of application-level programs as well.
30
The C Programming Language
• However, it is not perfect for all programmers and all situations– C pointers are a common source of confusion
and programming errors – C also lacks explicit support for useful
abstractions such as classes and objects– Newer languages such as C++ and Java address
these issues for application-level programs
31
How do we start
• From a very simple program “Hello”
• To run and completion this simple program– Every major part of the system must work in
concert
• This course is to help you understand – what happens and why
– When you run hello on your system
32
“Hello world” example
1 #include <stdio.h>
2
3 int main()
4 {
5 printf("hello, world\n");
6 }
33
How do we start
• We begin our study of systems by– Tracing the lifetime of the hello program
– From it is created by a programmer
– To it runs on a system, prints its result, and terminates
34
Outline
• Bit and Byte
• Context is very important
• Understand machine representations of numbers
• Information storage
• Bit level manipulation
• Suggested reading– Chap 1.1, 2.1
35
“Hello world” example
1 #include <stdio.h>
2
3 int main()
4 {
5 printf("hello, world\n");
6 }
• Source program– Created by editor and saved as a text file
36
“Hello world” example
# i n c l u d e <sp> < s t d i o .
35 105 110 99 108 117 100 101 32 60 115 116 100 105 111 46
h > \n \n i n t <sp> m a i n ( ) \n {
104 62 10 10 105 110 116 32 109 97 105 110 40 41 10 123
\n <sp> <sp> <sp> <sp> p r i n t f ( " h e
10 32 32 32 32 112 114 105 110 116 102 40 34 104 101
l l o , <sp> w o r l d \ n " ) ; \n }
108 108 111 44 32 119 111 114 108 100 92 110 34 41 59 10 125
37
Why Bit?
• The source program is a sequence of bits
• Modern computers store and process
– Information represented as two-valued signals
– These lowly binary digits are bits
• Bits form the basis of the digital revolution
38
The Decimal Representation
• Base-10• Has been in use for over 1000 years• Developed in India• Improved by Arab mathematicians in the 12th
century• Brought to the West in the 13th century by
– the Italian mathematician Leonardo Pisano, • better known as Fibonacci.
* Fibonacci: 斐波纳契数列 ( 一种整数数列 , 其中每数等于前面两数之和 )
39
Why Bit?
• Using decimal notation is natural for ten-fingered humans
• But binary values work better when building machines – that store and process information
40
Why Bit?
• Two-valued signals can readily be – represented, stored, and transmitted,
• Examples– The presence or absence of a hole in a punched
card
– A high or low voltage on a wire
– A magnetic domain oriented clockwise or counterclockwise.
41
Why Bit?
• The electronic circuitry is very simple and reliable for – storing and performing computations on two-
valued signals
• This enabling manufacturers to integrate– millions of such circuits on a single silicon chip
42
Group Bits
• In isolation, a single bit is not very useful• However, we are able to represent the
elements of any finite set by using bits• To do this, we
– first group bits together – then apply some interpretation to the different
possible bit patterns• that gives meaning to each patterns
Interpretation: 解释
43
ASCII standard
• 8-bit chunks are organized as a byte
• Each byte represents some text character in the program
• Most modern systems represent text characters – using the ASCII standard
• ASCII standard represents – each character with a unique byte-sized integer
value
44
“Hello world” example
# i n c l u d e <sp> < s t d i o .
35 105 110 99 108 117 100 101 32 60 115 116 100 105 111 46
h > \n \n i n t <sp> m a i n ( ) \n {
104 62 10 10 105 110 116 32 109 97 105 110 40 41 10 123
\n <sp> <sp> <sp> <sp> p r i n t f ( " h e
10 32 32 32 32 112 114 105 110 116 102 40 34 104 101
l l o , <sp> w o r l d \ n " ) ; \n }
108 108 111 44 32 119 111 114 108 100 92 110 34 41 59 10 125
45
Text file
• Source program is stored in a file– As a sequence of bytes– Each byte has an integer value that corresponds
to some character
• Text files– Files that consist exclusively of ASCII characters
• Binary files– Files other than text files
46
Information is Bits+Context
• All information in a system is represented – as a bunch of bits– Such as
• Disk files• Programs stored in memory• User data stored in memory• Data transferred across a network
47
Information is Bits+Context
• The only thing that distinguishes different data objects is – the context in which we view them– In different contexts, the same sequence of bytes
might represent• A number (integer or floating point number)• A character string• A machine instruction
• Context is very important in interpreting bits!
48
Three number encodings
• Unsigned encoding– Representing numbers greater than or equal to 0– Using traditional binary representation
• Two’s-complement encoding– Most common way to represent either positive or
negative numbers
• Floating point encoding– Base-two version of scientific notation for
representing real numbers
49
Understanding numbers
• Machine representation of numbers are not same as – Integers and real numbers
• They are finite approximations to integers and real numbers– Sometimes, they can behave in unexpected way
50
‘ int’ is not integer
• Overflow– 200*300*400*500 = -884,901,888– Product of a set of positive numbers yielded a
negative result
• Commutativity & Associativity remain– (500 * 400) * (300 * 200)– ((500 * 400) * 300) * 200– ((200 * 500) * 300) * 400– 400 * (200 * (300 * 500))*Commutativity: 交换律Associativity: 结合律
51
‘float’ is not real number
• Product of a set of positive numbers is positive
• Overflow and Underflow
• Associativity does not hold
– (3.14+1e20)-1e20 = 0.0
– 3.14+(1e20-1e20) = 3.14
*Overflow: 上溢Underflow: 下溢
52
Ranges of Values that can be Represented
• Critical to writing programs – that work correctly over the full range of
numeric values – that are portable across different combinations
of • Machine （机器）• operating system （操作系统）• and compiler （编译器）
53
Properties of Arithmetic Operations
• Several ways are designed – to perform arithmetic operations
• by directly manipulating the bit-level representations of numbers
• It is important for understanding – the machine-level code generated
• when compiling arithmetic expressions.
54
Hexadecimal
• Base 16 number representation
• Use characters ‘0’ to ‘9’ and ‘A’ to ‘F’
• Write FA1D37B16 in C as
– 0xFA1D37B or
– 0xfa1d37b
55
Hexadecimal vs. Binary
0x173A4C
Hexadecimal 1 7 3 A 4 C
Binary 0001 0111 0011 1010 0100 1100
1111001010110110110011
Binary 11 1100 1010 1101 1011 0011
Hexadecimal 3 C A D B 3
0x3CADB3
56
Hexadecimal vs. Decimal
Hexadecimal 0xA7
Decimal 10*16+7 = 167
Decimal 314156 = 19634*16 + 12 (C)
19634 = 1227*16 + 2 (2)
1227 = 76*16 + 11 (B)
76 = 4*16 + 12 (C)
4 = 0*16 + 4 (4)
Hexadecimal 0x4CB2C
57
Hexadecimal
• Byte = 8 bits– Binary 000000002 to
111111112
– Decimal: 010 to 25510
– Hexadecimal 0016 to FF16
0 0 00001 1 00012 2 00103 3 00114 4 01005 5 01016 6 01107 7 01118 8 10009 9 1001A 10 1010B 11 1011C 12 1100D 13 1101E 14 1110F 15 1111
HexDecim
al
Binary
58
Virtual Memory (虚拟内存 )
• Most computers cannot access individual bits in a memory directly
• Instead, they use bytes as the smallest addressable unit of memory, that is– Computers can access each byte in a memory
directly
59
000000010002000300040005000600070008000900100011
Bytes Addr.
001200130014
Virtual Memory
60
Virtual Memory
• Every byte of memory is identified by a unique number– its address
• The set of all possible addresses is known as – the virtual address space ( 虚拟地址空间 ).
• This virtual address space is just – a conceptual image presented to the machine-
level program
61
Virtual Memory
• The actual implementation uses a combination of – random-access memory (RAM)– disk storage– special hardware– and operating system software
• These provide the program with what appears to be a monolithic* byte array
*monolithic: 单片集成电路
62
Subdivide Virtual Memory into More Manageable Units
• One task of – a compiler and – the run-time system
• To store the different program objects– Program data– Instructions– Control information
63
Word Size
• Indicating the nominal size of – integer and – pointer data
• A virtual address is encoded by – such a word
• The maximum size of the virtual address space– the most important system parameter
determined by the word size
64
Word Size
• For machine with n-bit word size– Virtual address can range from 0 to 2n-1
• Most current machines are 32 bits (4 bytes)– Limits addresses to 4GB– Becoming too small for memory-intensive
applications
• High-end systems are 64 bits (8 bytes)– Potentially address 1.8 X 1019 bytes
• Machines support multiple data formats– Always integral number of bytes
65
Sizes of C Objects (in Bytes)
C Declaration Typical 32-bit Compaq Alpha
char 1 1
short int 2 2
int 4 4
long int 4 8
char * 4 8
float 4 4
double 8 8
66
Pointer Declaration
• For a type T, the declaration – T *p ;– defines a pointer variable p– P is pointing to an object of type T
• For example: char *p ;
67
Data Size
• Difficulty to make programs portable across different machines and compilers– The program is sensitive to the exact sizes of the
different data types– The C standard sets lower bounds on the
numeric ranges of the different data types– but there are no upper bounds
68
Data Size
• 32-bit machines have been the standard for the last 20 years
• Many programs have been written – assuming the allocations listed as “typical 32-bit”
in the table
• With the increasing of 64-bit machines – many hidden word size dependencies show up as
• bugs in migrating these programs to new machines
69
Example
• Many programmers assume that
– a program object declared as type int can be
used to store a pointer
• This works fine for most 32-bit machines
• But leads to problems on an Alpha.
70
How to Access an Object
• In C, an object may be– an integer– a structure or – some other program unit
• In C, the value of a pointer in C is – the virtual address of the first byte of some block
of storage
71
How to Access an Object
• The C compiler also associates – type information with each pointer
• It can generate different machine-level code to access the value– stored at the location designated by the pointer– depending on the type of that value.
Designated: 指定的
72
How to Access an Object
• The actual machine-level program generated by C compiler – has no information about data types – simply treats each program object as a block of
bytes
73
Byte Ordering
• How should bytes within multi-byte object be ordered in memory
• Little Endian– Least significant byte has lowest address– Alpha, PC
• Big Endian– Least significant byte has highest address– Sun, Mac
• Example: 0x1234567
74
Big Endian P34
0x100 0x101 0x102 0x103
01 23 45 67
75
Little Endian P34
0x100 0x101 0x102 0x103
67 45 23 01
76
Byte Ordering Becomes Visible P36
• Binary data is communicated over a network between different machines
• Reading machine level programs– 80483bd: 01 05 64 94 04 08– add %eax, 0x8049464
• Circumvent the normal type system
77
Byte Ordering Becomes Visible
• Circumvent the normal type system– Casting– Reference an object according to a different data
type from which it was created– Strongly discouraged for most application
programming– Quite useful and even necessary for system-level
programming
78
Code to Print Byte Representation P37
typedef unsigned char *pointer;
void show_bytes(pointer start, int len){ int i; for (i = 0; i < len; i++) printf("0x%p\t0x%.2x\n", start+i, start[i]); printf("\n");}
79
int a = 12345;printf("int a = 12345;\n");show_bytes((pointer) &a, sizeof(int));
Example
80
Code to Print Byte Representation
• typedef– Giving a name of type– Syntax is exactly like that of declaring a variable
• printf– Format string– %d, %c, %x, %f
* Syntax: 语法
81
Code to Print Byte Representation
• Pointers and arrays– start is declared as a pointer– It is referenced as an array start[i]
• Pointer creation and dereferencing– Address of &a
• Sizeof– Sizeof(T) returns the number of bytes required to
store an object of type T– One step toward writing code that is portable
across different machine types
82
int a = 12345;printf("int a = 12345;\n");show_bytes((pointer) &a, sizeof(int));
Example
83
Result:
int a = 12345;0x11ffffcb80x390x11ffffcb90x300x11ffffcba0x000x11ffffcbb0x00
Example P39
84
int A = 12345;
long int C = 12345;
Decimal: 12345
Binary: 0011 0000 0011 1001
Hex: 3 0 3 9
Example
85
39
30
00
00
Linux/Alpha A
30
39
00
00
Sun A
00
00
00
00
39
30
00
00
Alpha C
30
39
00
00
Sun C
39
30
00
00
Linux C
Example P39
86
Float F = 12345.0;
IEEE Single Precision Floating Point Representation
Hex: 4 6 4 0 E 4 0 0 Binary: 0100 0110 1000 0000 1110 0100 0000 0000
00e44046
Linux/Alpha F
e400
4640
Sun F
Representing Floats
87
char S[6] = "12345";• Strings in C– Represented by array of characters
– Each character encoded in ASCII format• Standard 7-bit encoding of character set
• Character “0” has code 0x30– Digit i has code 0x30+i
– String should be null-terminated• Final character = 0
Linux/Alpha S Sun S
3334
3132
3500
3334
3132
3500
Representing Strings
88
char S[6] = "12345";• Compatibility (兼容性 )– Byte ordering not an issue
• Data are single byte quantities
– Text files generally platform independent
• Except for different conventions of line termination character!
Linux/Alpha S Sun S
3334
3132
3500
3334
3132
3500
Representing Strings
89
Machine-Level Code Representation
• Encode Program as Sequence of Instructions
• Each instruction encoded as bytes– Alpha’s, Sun’s use 4 byte instructions (IA64 use 41bits)
• Reduced Instruction Set Computer (RISC)
– IA32’s use variable length instructions
• Complex Instruction Set Computer (CISC)
• RISC: 精简指令集计算机• CISC: 复杂指令集计算机
90
Machine-Level Code Representation
• Different instruction types and encodings for different machines– Most code not binary compatible
• Programs are Byte Sequences Too !
91
Representing Instructions P41
int sum(int x, int y)
{
return x+y;
}
00003042
Alpha sum
0180FA6B
E008
81C3
Sun sum
90020009
E58B
5589
PC sum
450C03450889EC5DC3
92
Boolean Algebra
• Developed by George Boole in 19th Century– Algebraic representation of logic
• Encode “True” as 1 • Encode “False” as 0
93
Boolean Algebra P42
AndA&B = 1 when both A=1 and B=1
Not~A = 1 when A=0
OrA|B = 1 when either A=1 or B=1
Exclusive-Or (Xor)A^B = 1 when either A=1 or B=1, but
not both
94
Integer Ring P43
• Integer Arithmetic Z, +, *, –, 0, 1 forms a “ring”– Addition is “sum” operation– Multiplication is “product” operation– – is additive inverse– 0 is identity for sum– 1 is identity for product
95
Boolean Algebra
• Boolean Algebra {0,1}, |, &, ~, 0, 1 forms a “Boolean algebra”– Or is “sum” operation– And is “product” operation– ~ is “complement” operation (not additive
inverse)– 0 is identity for sum– 1 is identity for product
96
Integer Ring & Boolean Algebra P43
Boolean Algebra Integer Ring
Commutativity ( 交换律 ) A | B = B | A A + B = B + A
A & B = B & A A * B = B * A
Associativity ( 结合律 ) (A | B) | C = A | (B | C) (A + B) + C = A + (B + C)
(A & B) & C = A & (B & C) (A * B) * C = A * (B * C)
Distributivity ( 分配律 ) A & (B | C) = (A & B) | (A & C) A * (B + C) = A * B + B * C
97
Integer Ring & Boolean Algebra
Boolean Algebra Integer RingIdentities ( 同一性 ) A | 0 = A A + 0 = A A & 1 = A A * 1 = A Annihilator ( 零化子 ) A & 0 = 0 A * 0 = 0Cancellation of negation （去否定） ~ (~ A) = A – (– A) = A
98
Ring Boolean Algebra
Boolean Algebra Integer Ring
Distribuitivity ( 分配律 )
A | (B & C) = (A | B) & (A | C) A + (B * C) (A + B) *
(B + C)
Idempotency ( 幂等性 )
A | A = A A + A A
“A is true” or “A is true” = “A is true”
A & A = A A * A A
99
Ring Boolean Algebra
Boolean Algebra Integer RingAbsorption ( 吸收律 ) A | (A & B) = A A + (A * B) A “A is true” or “A is true and B is true” = “A is true”
A & (A | B) = A A * (A + B) ALaws of Complements （补集定律） A | ~A = 1 A + –A 1 “A is true” or “A is false”
Every element has additive inverse A | ~A 0 A + –A = 0
100
Boolean Ring
• Boolean Ring {0,1}, ^, &, , 0, 1 – Identical to integers mod 2– is identity operation: (A) = A
A ^ A = 0
101
Boolean Ring
• Property Boolean Ring– Commutative sum A ^ B = B ^ A– Commutative product A & B = B & A– Associative sum (A ^ B) ^ C = A ^ (B ^ C)– Associative product (A & B) & C = A & (B & C)– Prod. over sum A & (B ^ C) = (A & B) ^ (B &
C)– 0 is sum identity A ^ 0 = A– 1 is prod. identity A & 1 = A– 0 is product annihilator A & 0 = 0– Additive inverse A ^ A = 0
102
Relations Between Operations P43
• DeMorgan’s Laws– Express & in terms of |, and vice-versa
A & B = ~(~A | ~B)– A and B are true if and only if neither A nor B is false
A | B = ~(~A & ~B)– A or B are true if and only if A and B are not both
false
103
Relations Between Operations
• Exclusive-Or using Inclusive OrA ^ B = (~A & B) | (A & ~B)
– Exactly one of A and B is trueA ^ B = (A | B) & ~(A & B)
– Either A is true, or B is true, but not both
*exclusive: 互斥性
104
General Boolean Algebras P45 Practice Problem 2.8 [Solution P110]
• Operate on Bit Vectors– Operations applied bitwise
01101001& 01010101 01000001
01101001| 01010101 01111101
01101001^ 01010101 00111100
~ 01010101 10101010
105
General Boolean Algebras P45
• Representation of Sets– Width w bit vector represents subsets of {0, …, w–
1}
– aj = 1 if j A• 01101001 { 0, 3, 5, 6 }• 01010101 { 0, 2, 4, 6 }
– & Intersection 01000001 { 0, 6 }– | Union 01111101 { 0, 2, 3, 4, 5,
6 }– ^ Symmetric difference 00111100 { 2, 3,
4, 5 }– ~ Complement 10101010 { 1, 3,
5, 7 }
106
Logical Operations P46
• Logical Operators– &&, ||, !
• View 0 as “False”• Anything nonzero as “True”• Always return 0 or 1• Early termination (short cut)
107
Logical Operations P49
• Examples (char data type)– !0x41 --> 0x00– !0x00 --> 0x01– !!0x41 --> 0x01– 0x69 && 0x55 --> 0x01– 0x69 || 0x55 --> 0x01– p && *p (avoid null pointer access)– a && 5/a (avoid division by zero)
108
Shift Operations
• Left Shift: x << y– Shift bit-vector x left y positions
• Throw away extra bits on left• Fill with 0’s on right 01100010Argument x
00010000<< 3
10100010Argument x
00010000<< 3
109
Shift Operations P50
• Right Shift: x >> y– Shift bit-vector x right y
positions• Throw away extra bits on right
– Logical shift• Fill with 0’s on left
– Arithmetic shift• Replicate most significant bit on
right• Useful with two’s complement
integer representation
01100010Argument x
00011000Log. >> 2
00011000Arith. >> 2
10100010Argument x
00101000Log. >> 2
11101000Arith. >> 2
110
Bit-Level Operations in C
• Operations &, |, ~, ^ Available in C
– Apply to any “integral” data type
• long, int, short, char
– View arguments as bit vectors
– Arguments applied bit-wise
111
Bit-Level Operations in C P49
• Examples (Char data type)– ~0x41 --> 0xBE– ~010000012 --> 101111102
– ~0x00 --> 0xFF– ~000000002 --> 111111112
– 0x69 & 0x55 --> 0x41– 011010012 & 010101012 --> 010000012
– 0x69 | 0x55 --> 0x7D– 011010012 | 010101012 --> 011111012
112
Cool Stuff with Xor
• Bitwise Xor is form of addition• With extra property that every value is its
own additive inverse– A ^ A = 0
113
Cool Stuff with Xor
void funny(int *x, int *y)
{
*x = *x ^ *y; /* #1 */
*y = *x ^ *y; /* #2 */
*x = *x ^ *y; /* #3 */
}
Step *x *yBegin A B
1 A^B B2 A^B (A^B)^B = A^(B^B) =
A^0 = A3 (A^B)^A = (B^A)^A =
B^(A^A) = B^0 = BA
End B A
