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CMU CS 15213 - Lecture

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Bits, Bytes, and Integers August 28, 2008Binary RepresentationsEncoding Byte ValuesByte-Oriented Memory OrganizationMachine WordsWord-Oriented Memory OrganizationData RepresentationsByte OrderingByte Ordering ExampleReading Byte-Reversed ListingsExamining Data Representationsshow_bytes Execution ExampleRepresenting IntegersRepresenting PointersRepresenting StringsBoolean AlgebraApplication of Boolean AlgebraGeneral Boolean AlgebrasRepresenting & Manipulating SetsBit-Level Operations in CContrast: Logic Operations in CShift OperationsInteger C PuzzlesEncoding IntegersEncoding Example (Cont.)Numeric RangesValues for Different Word SizesUnsigned & Signed Numeric ValuesMapping Between Signed & UnsignedMapping Signed  UnsignedSlide 31Relation between Signed & UnsignedSigned vs. Unsigned in CCasting SurprisesExplanation of Casting SurprisesCode Security Example #1Typical UsageMalicious UsageSign ExtensionSign Extension ExampleWhy Should I Use Unsigned?Complement & IncrementComp. & Incr. ExamplesUnsigned AdditionVisualizing Integer AdditionVisualizing Unsigned AdditionMathematical PropertiesTwo’s Complement AdditionTAdd OverflowVisualizing 2’s Comp. AdditionCharacterizing TAddMathematical Properties of TAddMultiplicationUnsigned Multiplication in CCode Security Example #2XDR CodeXDR VulnerabilitySigned Multiplication in CPower-of-2 Multiply with ShiftCompiled Multiplication CodeUnsigned Power-of-2 Divide with ShiftCompiled Unsigned Division CodeSigned Power-of-2 Divide with ShiftCorrect Power-of-2 DivideCorrect Power-of-2 Divide (Cont.)Compiled Signed Division CodeProperties of Unsigned ArithmeticProperties of Two’s Comp. ArithmeticInteger C Puzzles RevisitedBits, Bytes, and IntegersAugust 28, 2008Bits, Bytes, and IntegersAugust 28, 2008TopicsTopicsRepresenting information as bitsBit-level manipulationsBoolean algebraExpressing in CRepresentations of IntegersBasic properties and operationsImplications for C15-213 F ‘08class02.ppt15-213“The Class That Gives CMU Its Zip!”– 2 –15-213, F ‘08Binary 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 213Electronic ImplementationElectronic ImplementationEasy to store with bistable elementsReliably transmitted on noisy and inaccurate wires 0.0V0.5V2.8V3.3V0 1 0– 3 –15-213, F ‘08Encoding Byte ValuesEncoding Byte ValuesByte = 8 bitsByte = 8 bitsBinary 000000002 to 111111112Decimal: 010to 25510First digit must not be 0 in CHexadecimal 0016 to FF16Base 16 number representationUse characters ‘0’ to ‘9’ and ‘A’ to ‘F’Write FA1D37B16 in C as 0xFA1D37B»Or 0xfa1d37b0 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 1111HexDecimalBinary– 4 –15-213, F ‘08Byte-Oriented Memory OrganizationByte-Oriented Memory OrganizationPrograms Refer to Virtual AddressesPrograms Refer to Virtual AddressesConceptually very large array of bytesActually implemented with hierarchy of different memory typesSystem provides address space private to particular “process”Program being executedProgram can clobber its own data, but not that of othersCompiler + Run-Time System Control AllocationCompiler + Run-Time System Control AllocationWhere different program objects should be storedAll allocation within single virtual address space• • •00•••0FF•••F– 5 –15-213, F ‘08Machine WordsMachine WordsMachine Has “Word Size”Machine Has “Word Size”Nominal size of integer-valued dataIncluding addressesMost current machines use 32 bits (4 bytes) wordsLimits addresses to 4GBBecoming too small for memory-intensive applicationsHigh-end systems use 64 bits (8 bytes) wordsPotential address space  1.8 X 1019 bytesx86-64 machines support 48-bit addresses: 256 TerabytesMachines support multiple data formatsFractions or multiples of word sizeAlways integral number of bytes– 6 –15-213, F ‘08Word-Oriented Memory OrganizationWord-Oriented Memory OrganizationAddresses 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)00000001000200030004000500060007000800090010001132-bitWordsBytes Addr.001200130014001564-bitWordsAddr =??Addr =??Addr =??Addr =??Addr =??Addr =??000000040008001200000008– 7 –15-213, F ‘08Data RepresentationsData RepresentationsSizes 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– 8 –15-213, F ‘08Byte OrderingByte OrderingHow should bytes within multi-byte word be ordered in How should bytes within multi-byte word be ordered in memory?memory?ConventionsConventionsBig Endian: Sun, PPC Mac, InternetLeast significant byte has highest addressLittle Endian: x86Least significant byte has lowest address– 9 –15-213, F ‘08Byte Ordering ExampleByte Ordering ExampleBig EndianBig EndianLeast significant byte has highest addressLittle EndianLittle EndianLeast significant byte has lowest addressExampleExampleVariable x has 4-byte representation 0x01234567Address given by &x is 0x1000x100 0x101 0x102 0x10301 23 45 670x100 0x101 0x102 0x10367 45 23 01Big EndianLittle Endian01 23 45 6767 45 23 01– 10 –15-213, F ‘08Reading Byte-Reversed ListingsReading Byte-Reversed ListingsDisassemblyDisassemblyText representation of binary machine codeGenerated by program that reads the machine codeExample 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 32 bits: 0x000012abSplit into bytes: 00 00 12 abReverse: ab 12 00 00– 11 –15-213, F ‘08Examining Data RepresentationsExamining Data RepresentationsCode to Print Byte Representation of DataCode to Print Byte Representation of DataCasting pointer to unsigned char * creates byte arraytypedef unsigned


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