15 213 The Class That Gives CMU Its Zip Bits and Bytes Aug 28 2003 Topics Why bits Representing information as bits Binary Hexadecimal Byte representations numbers characters and strings Instructions Bit level manipulations Boolean algebra Expressing in C class02 ppt 15 213 F 03 Why Don t Computers Use Base 10 Base 10 Number Representation That s why fingers are known as digits Natural representation for financial transactions Floating point number cannot exactly represent 1 20 Even carries through in scientific notation 1 5213 X 104 Implementing Electronically Hard to store ENIAC First electronic computer used 10 vacuum tubes digit Hard to transmit Need high precision to encode 10 signal levels on single wire Messy to implement digital logic functions Addition multiplication etc 2 15 213 F 03 Binary Representations Base 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 Implementation Easy to store with bistable elements Reliably transmitted on noisy and inaccurate wires 0 1 0 3 3V 2 8V 0 5V 0 0V 3 15 213 F 03 Byte Oriented Memory Organization Programs Refer to Virtual Addresses Conceptually very large array of bytes Actually implemented with hierarchy of different memory types SRAM DRAM disk Only allocate for regions actually used by program In Unix and Windows NT 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 Allocation Where different program objects should be stored Multiple mechanisms static stack and heap In any case all allocation within single virtual address space 4 15 213 F 03 Encoding Byte Values Byte 8 bits Binary 000000002 Decimal 010 Hexadecimal 0016 to to to 111111112 25510 FF16 Base 16 number representation Use characters 0 to 9 and A to F Write FA1D37B16 in C as 0xFA1D37B Or 0xfa1d37b 5 al y im ar c x n He De Bi 0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 A 10 1010 B 11 1011 C 12 1100 D 13 1101 E 14 1110 F 15 1111 15 213 F 03 Literary Hex Common 8 byte hex filler 0xdeadbeef Can you think of other 8 byte fillers Hex poetry Bruce the Bard Maggs 2003 61cacafe afadacad abaddeed adebfeda cacabead adeaddeb 6 15 213 F 03 Machine Words Machine Has Word Size Nominal size of integer valued data Including addresses 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 Fractions or multiples of word size Always integral number of bytes 7 15 213 F 03 Word Oriented Memory Organization 32 bit 64 bit Words Words Addresses Specify Byte Locations Address of first byte in word Addresses of successive words differ by 4 32 bit or 8 64 bit Addr 0000 Addr 0000 Addr 0004 Addr 0008 Addr 0012 8 Addr 0008 Bytes Addr 0000 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 15 213 F 03 Data Representations Sizes of C Objects in Bytes C Data Type Compaq Alpha int long int char short float double long double char Or any other pointer 9 4 8 1 2 4 8 8 8 Typical 32 bit Intel IA32 4 4 1 2 4 8 8 4 4 4 1 2 4 8 10 12 4 15 213 F 03 Byte Ordering How should bytes within multi byte word be ordered in memory Conventions Sun s Mac s are Big Endian machines Least significant byte has highest address Alphas PC s are Little Endian machines Least significant byte has lowest address 10 15 213 F 03 Byte Ordering Example Big Endian Least significant byte has highest address Little Endian Least significant byte has lowest address Example Variable x has 4 byte representation 0x01234567 Address given by x is 0x100 Big Endian 0x100 0x101 0x102 0x103 01 Little Endian 45 67 0x100 0x101 0x102 0x103 67 11 23 45 23 01 15 213 F 03 Reading Byte Reversed Listings Disassembly Text representation of binary machine code Generated by program that reads the machine code Example Fragment Address 8048365 8048366 804836c Instruction Code 5b 81 c3 ab 12 00 00 83 bb 28 00 00 00 00 Assembly Rendition pop ebx add 0x12ab ebx cmpl 0x0 0x28 ebx Deciphering Numbers Value Pad to 4 bytes Split into bytes Reverse 12 0x12ab 0x000012ab 00 00 12 ab ab 12 00 00 15 213 F 03 Examining Data Representations Code 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 13 15 213 F 03 show bytes Execution Example int a 15213 printf int a 15213 n show bytes pointer a sizeof int Result Linux int a 15213 14 0x11ffffcb8 0x6d 0x11ffffcb9 0x3b 0x11ffffcba 0x00 0x11ffffcbb 0x00 15 213 F 03 Representing Integers int A 15213 int B 15213 long int C 15213 Linux Alpha A 6D 3B 00 00 Linux Alpha B 93 C4 FF FF 15 Decimal 15213 Binary 0011 1011 0110 1101 Hex 3 B 6 D Sun A Linux C Alpha C Sun C 00 00 3B 6D 6D 3B 00 00 6D 3B 00 00 00 00 00 00 00 00 3B 6D Sun B FF FF C4 93 Two s complement representation Covered next lecture 15 213 F 03 Alpha P Representing Pointers int B 15213 int P B Alpha Address Hex 1 Binary Sun P EF FF FB 2C F F F F F C A 0 0001 1111 1111 1111 1111 1111 1100 1010 0000 A0 FC FF FF 01 00 00 00 Sun Address Hex Binary E F F F F B 2 C 1110 1111 1111 1111 1111 1011 0010 1100 Linux P Linux Address Hex Binary B F F F F 8 D 4 1011 1111 1111 1111 1111 1000 1101 0100 D4 F8 FF BF Different compilers machines assign different locations to objects 16 15 213 F 03 Representing Floats Float F 15213 0 Linux Alpha F 00 B4 6D 46 Sun F 46 6D B4 00 IEEE Single Precision Floating Point Representation Hex Binary 15213 4 6 6 D B 4 0 0 0100 0110 0110 1101 1011 0100 0000 0000 1110 1101 1011 01 Not same as integer representation but consistent across machines Can see some relation to integer representation but not obvious 17 15 213 F 03 Representing Strings Strings in C char S 6 15213 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 …
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