1、Today: Bits, Bytes,Representing information as bits Bit-level manipulations,Binary Representations,Encoding Byte Values,Byte = 8 bits The smallest addressable unit of memory Binary: 000000002 to 111111112 Decimal: 010 to 25510 Hexadecimal: 0016 to FF16 Base 16 number representation Use characters 0

2、to 9 and A to F Write FA1D37B16 in C as 0 xFA1D37B 0 xfa1d37b 0 xFa1D37b Converting between binary and hexadecimal 1111001010110110110010 11 1100 1010 1101 1011 0010 1111 0010 1011 0110 1100 10 Converting 2n to hexadecimal,0 x3CADB2,Converting between Binary and Decimal,Binary to Decimal,Converting

3、between Binary and Decimal,Decimal to Binary,Converting between Binary and Decimal,Decimal to Binary ( fractional binary number ),Converting between Hexadecimal and Decimal,Hexadecimal to Decimal,Decimal to Hexadecimal Converting to binary Binary to Hexadecimal,Decimal to Hexadecimal As an example,

4、consider the conversion of decimal 314156 The hexadecimal representation : 0 x4CB2C,Converting between Hexadecimal and Decimal,Byte-Oriented Memory Organization,Programs Refer to Virtual Addresses Conceptually very large array of bytes（0 2w-1） Actually implemented with hierarchy of different memory

5、types System provides address space private to particular “process” Compiler + Run-Time System Control Allocation Where different program objects should be stored All allocation within single virtual address space,Machine Words,Machine Has “Word Size” Nominal size of integer-valued data Including ad

6、dresses Some 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

7、formats Fractions or multiples of word size Always integral number of bytes,Word-Oriented Memory Organization,Addresses Specify Byte Locations Address of first byte in word Addresses of successive words differ by 4 (32-bit) or 8 (64-bit),Data Representations,Byte Ordering,How should bytes within a m

8、ulti-byte word be ordered in memory? Conventions Big Endian: Sun, PPC Mac, Internet Least significant byte has highest address Little Endian: x86 Least significant byte has lowest address,Byte Ordering Example,Big Endian Least significant byte has highest address Little Endian Least significant byte

9、 has lowest address Example Variable x has 4-byte representation 0 x01234567 Address given by void show_bytes(pointer start, int len) int i; for (i = 0; i 0 xBE 010000012 - 101111102 0 x00 - 0 xFF 000000002 - 111111112 0 x69 & 0 x55 - 0 x41 011010012 & 010101012 - 010000012 0 x69 | 0 x55 - 0 x7D 011

10、010012 | 010101012 - 011111012,Masking Operation,A mask is a bit pattern that indicates a selected set of bits within a word Examples X & 0 xFF 00 00 00 FF X | 0 xFF X 0 xFF 0 will yield a mask of all ones, instead of 0 xFFFFFFFF,Contrast: Logic Operations in C,Contrast to Logical Operators &, |, !

11、View 0 as “False” Anything nonzero as “True” Always return 0 or 1 Early termination Examples (char data type) !0 x41 - 0 x00 !0 x00 - 0 x01 !0 x41 - 0 x01 0 x69 & 0 x55 - 0 x01 0 x69 | 0 x55 - 0 x01 a & 5/a ( avoids 5/0 ) p & *p ( avoids null pointer access ),Shift Operations,Left Shift: x y Shift bit-vector x right y positi