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Bits and Bytes Topics Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations » numbers » characters and strings » Instructions Bit-level manipulations – READ BOOK Boolean algebra Expressing in C CS 105 bits.ppt CS 105 “Tour of the Black Holes of Computing!”

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Page 1: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

Bits and BytesBits and BytesTopicsTopics

Why bits? Tell me Representing information as bits

Binary/HexadecimalByte representations

» numbers» characters and strings» Instructions

Bit-level manipulations – READ BOOKBoolean algebraExpressing in C

CS 105bits.ppt

CS 105“Tour of the Black Holes of Computing!”

Page 2: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 2 – CS 105

Binary RepresentationsBinary RepresentationsBase 2 Number RepresentationBase 2 Number Representation

Represent 1521310 as 111011011011012

Represent 1.2010 as 1.0011001100110011[0011]…2

Represent 1.5213 X 104 as 1.11011011011012 X 213

Electronic ImplementationElectronic Implementation Easy to store with bistable elements - relays Reliably transmitted on noisy and inaccurate wires (media)

Straightforward implementation of arithmetic functions

0.0V

0.5V

2.8V

3.3V

0 1 0

Page 3: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 3 – CS 105

Byte-Oriented Mem OrganizationByte-Oriented Mem Organization

Programs Refer to Virtual AddressesPrograms Refer to Virtual Addresses Conceptually very large array of bytes Actually implemented with hierarchy of different memory

types – SRAM, DRAM, Disk System provides address space private to particular

“process” Program being executed Program can clobber its own data, but not that of others

Compiler + Run-Time System Control AllocationCompiler + Run-Time System Control Allocation Where different program objects should be stored Multiple mechanisms: static, stack, heap, etc. All allocation within single virtual address space

• • •00

•••0

FF•••F

Page 4: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 4 – CS 105

Encoding Byte ValuesEncoding Byte Values

Byte = 8 bitsByte = 8 bits Binary 000000002 to 111111112

Decimal: 010 to 25510

Hexadecimal 0016 to FF16

Base 16 number representationUse characters ‘0’ to ‘9’ and ‘A’ to ‘F’Write FA1D37B16 in C as 0xFA1D37B

» Or 0xfa1d37b Internet used term ‘Octet’ Why?

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

Page 5: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 5 – CS 105

Word-Oriented Memory OrganizationWord-Oriented Memory Organization

Addresses Specify Byte Addresses Specify Byte LocationsLocations Address of first byte in

word Addresses of successive

words differ by 4 (32-bit) or 8 (64-bit)

000000010002000300040005000600070008000900100011

32-bitWords

Bytes Addr.

0012001300140015

64-bitWords

Addr =??

Addr =??

Addr =??

Addr =??

Addr =??

Addr =??

0000

0004

0008

0012

0000

0008

Page 6: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 6 – CS 105

Data RepresentationsData Representations

Sizes of C Objects (in Bytes)Sizes of C Objects (in Bytes) C Data Type Typical 32-bit Intel IA32

x86-64 char 1 1 1 short 2 2 2 int 4 4 4 long 4 4 8 long long 8 8 8 float 4 4 4 double 8 8 8 long double 8 10/12 10/16 char * 4 4 8

» Or any other pointer

Page 7: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 7 – CS 105

Examining Data RepresentationsExamining Data Representations

Code to Print Byte Representation of DataCode to Print Byte Representation of Data Casting pointer to unsigned char * creates byte array

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");}

Printf directives:%p: Print pointer%x: Print Hexadecimal

Page 8: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 8 – CS 105

show_bytes Execution Exampleshow_bytes Execution Example

int a = 15213;

printf("int a = 15213;\n");

show_bytes((pointer) &a, sizeof(int));

Result (Linux):

int a = 15213;

0x11ffffcb8 0x6d

0x11ffffcb9 0x3b

0x11ffffcba 0x00

0x11ffffcbb 0x00

Page 9: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 9 – CS 105

Representing IntegersRepresenting Integers

int A = 15213;int A = 15213;int B = -15213;int B = -15213;long int C = 15213;long int C = 15213;

Decimal: 15213

Binary: 0011 1011 0110 1101

Hex: 3 B 6 D

6D3B0000

IA32, x86-64 A

3B6D

0000

Sun A

93C4FFFF

IA32, x86-64 B

C493

FFFF

Sun B

Two’s complement representation(Covered later)

00000000

6D3B0000

x86-64 C

3B6D

0000

Sun C

6D3B0000

IA32 C

Page 10: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 10 – CS 105

Byte OrderingByte Ordering

How should bytes within multi-byte word be ordered in How should bytes within multi-byte word be ordered in memory? memory? Religious IssueReligious Issue

ConventionsConventions Suns, PowerPCs are “Big Endian” machines

Least significant data byte has highest addressMost significant data byte has lowest address

Alphas, PCs are “Little Endian” machinesLeast significant byte has lowest address

Page 11: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 11 – CS 105

Byte Ordering ExampleByte Ordering Example

Big EndianBig Endian Least significant byte has highest address

Little EndianLittle Endian Least significant byte has lowest address

ExampleExample Variable x has 4-byte representation 0x01234567 Address given by &x is 0x100

0x100 0x101 0x102 0x103

01 23 45 67

0x100 0x101 0x102 0x103

67 45 23 01

Big Endian

Little Endian

01 23 45 67

67 45 23 01

Page 12: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 12 – CS 105

Reading Byte-Reversed ListingsReading Byte-Reversed Listings

DisassemblyDisassembly Text representation of binary machine code Generated by program that reads the machine code

Example FragmentExample Fragment

Address Instruction Code Assembly Rendition 8048365: 5b pop %ebx 8048366: 81 c3 ab 12 00 00 add $0x12ab,%ebx 804836c: 83 bb 28 00 00 00 00 cmpl $0x0,0x28(%ebx)

Deciphering NumbersDeciphering Numbers Value: 0x12ab Pad to 4 bytes: 0x000012ab Split into bytes: 00 00 12 ab Reverse: ab 12 00 00

Page 13: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 13 – CS 105

Representing PointersRepresenting Pointersint B = -15213;int B = -15213;int *P = &B; // p is pointer, address values are int *P = &B; // p is pointer, address values are

different on different machines.different on different machines.

FF7F0000

0C89ECFF

x86-64 P

Different compilers & machines assign different locations to objects

FB2C

EFFF

Sun P

FFBF

D4F8

IA32 P

Page 14: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 14 – CS 105

Machine-Level Code RepresentationMachine-Level Code RepresentationEncode Program as Sequence of InstructionsEncode Program as Sequence of Instructions

Each simple operationArithmetic operationRead or write memoryConditional branch

Instructions encoded as bytesAlpha’s, Sun’s, Mac’s use 4 byte instructions

» Reduced Instruction Set Computer (RISC)PC’s use variable length instructions

» Complex Instruction Set Computer (CISC)

Different instruction types and encodings for different machines

Most code not binary compatible

Programs are Byte Sequences Too - von Neumman!Programs are Byte Sequences Too - von Neumman!

Page 15: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 15 – CS 105

Representing InstructionsRepresenting Instructions

int sum(int x, int y)int sum(int x, int y){{ return x+y;return x+y;}}

Different machines use totally different instructions and encodings

00003042

Alpha sum

0180FA6B

E008

81C3

Sun sum

90020009

For this example, Alpha & Sun use two 4-byte instructions

Use differing numbers of instructions in other cases

PC uses 7 instructions with lengths 1, 2, and 3 bytes

Same for NT and for LinuxNT / Linux not fully binary

compatible

E58B

5589

PC sum

450C03450889EC5DC3

Page 16: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 16 – CS 105

Boolean Algebra – a reviewBoolean Algebra – a reviewDeveloped by George Boole in 19th CenturyDeveloped by George Boole in 19th Century

Algebraic representation of logicEncode “True” as 1 and “False” as 0

AndAnd A&B = 1 when both A=1 and B=1

NotNot ~A = 1 when A=0

OrOr A|B = 1 when either A=1 or B=1

Exclusive-Or (Xor)Exclusive-Or (Xor) A^B = 1 when either A=1 or B=1, but

not both

Page 17: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 17 – CS 105

Bit-Level Operations in C follow Boolean AlgebraBit-Level Operations in C follow Boolean Algebra

Operations &, |, ~, ^ Available in COperations &, |, ~, ^ Available in C Apply to any “integral” data type

long, int, short, char View arguments as bit vectors Arguments applied bit-wise

Examples (Char data type)Examples (Char data type) ~0x41 --> 0xBE

~010000012 --> 101111102

~0x00 --> 0xFF~000000002 --> 111111112

0x69 & 0x55 --> 0x41011010012 & 010101012 --> 010000012

0x69 | 0x55 --> 0x7D011010012 | 010101012 --> 011111012

Page 18: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 18 – CS 105

Contrast: Logic Operations in CContrast: Logic Operations in C

Contrast to Logical OperatorsContrast to Logical Operators &&, ||, !

View 0 as “False” Anything nonzero as “True” -- key point Always return 0 or 1 Early termination

Examples (char data type)Examples (char data type) !0x41 --> 0x00 !0x00 --> 0x01 !!0x41 --> 0x01

0x69 && 0x55 --> 0x01 0x69 || 0x55 --> 0x01 p && *p (avoids null pointer

access) ??

Page 19: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 19 – CS 105

Shift OperationsShift Operations

Left Shift: Left Shift: x << yx << y Shift bit-vector x left y positions

Throw away extra bits on leftFill with 0’s on right

Right Shift: Right Shift: x >> yx >> y Shift bit-vector x right y

positionsThrow away extra bits on right

Logical shiftFill with 0’s on left

Arithmetic shiftReplicate most significant bit Useful with two’s complement

integer representation

01100010Argument x

00010000<< 3

00011000Log. >> 2

00011000Arith. >> 2

10100010Argument x

00010000<< 3

00101000Log. >> 2

11101000Arith. >> 2

0001000000010000

0001100000011000

0001100000011000

00010000

00101000

11101000

00010000

00101000

11101000

Page 20: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 20 – CS 105

Cool Stuff with XorCool Stuff with Xor

void funny(int *x, int *y)void funny(int *x, int *y){{ *x = *x ^ *y; /* #1 */*x = *x ^ *y; /* #1 */ *y = *x ^ *y; /* #2 */*y = *x ^ *y; /* #2 */ *x = *x ^ *y; /* #3 */*x = *x ^ *y; /* #3 */}}// x, y not equal// x, y not equal

Bitwise XOR is form of addition

With extra property that every value is its own additive inverse

A ^ A = 0

BABegin

BA^B1

(A^B)^B = AA^B2

A(A^B)^A = B3

ABEnd

*y*x

Page 21: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 21 – CS 105

Main PointsMain Points

It’s All About Bits & BytesIt’s All About Bits & Bytes Numbers Programs Text

Different Machines Follow Different ConventionsDifferent Machines Follow Different Conventions Word size Byte ordering Representations

Boolean Algebra is Mathematical BasisBoolean Algebra is Mathematical Basis Basic form encodes “false” as 0, “true” as 1 General form like bit-level operations in C

Good for representing & manipulating sets

Page 22: Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

– 22 – CS 105

Practice ProblemsPractice Problems

• 2.52.5

• 2.82.8

• 2.142.14

• 2.232.23