CSAPP笔记：Bits, Bytes and Integer02

Integers

Addition

Unsigned Addition

w is the word size(bit)

• substract 2^w from the sum

Two’s Complement Addition

negative overflow

positive overflow

Multiplication

unsigned

signed

Divide with Shift

• round down to zero

Negative(~ + 1)

When should use Unsigned?

• when performing modualr arithmetic
• using bits to represent sets

Representations in memory, pointers and strings

Byte-Oriented Memory Organization

• An address is like an index into that array

• system provides private address spaces to each “process”

• 32 bit machines Limits addresses to 4GB

gcc -m {32,64}

Word-Oriented Memory Organization

group bytes to word

• assume the address of the word is the loweset address of byte in it

Example Data Representation

Byte Ordering

how are the bytes within a word ordered in memory?

• Big Endian: internet, Sun

  least significant byte has highest address

• little Endian: x86, Arm, IOS, Windows

  least significant byte has lowest address

an example

• Variable x has 4-byte value of 0x01234567
• Address given by &x is 0x100

another example

• 15213
• binary: 0011 1011 0110 1101
• hex: 3 B 6 D

a useful code to print Byte Representation of Data

typedef unsigned char * pointer;
void show_bytes(pointer start, size_t len){
    size_t i;
    for(i = 0; i<len; ++i)
        printf("%p\t0x%.2x\n",start+i, start[i]);
}

Representing strings

• array of characters
• ASCII format
• null-terminated

Integer C Puzzles

• x<0 -> ((x*2)<0)

  False Tmin: “100000000” -> “00000000”

• ux >= 0

  True

• x&7 == 7 -> (x<<30) <0

  True “1100…000”

• ux > -1

  never true False

• x>y -> -x<-y

  False Tmin: -Tmin is still Tmin

• x*x >=0

  False

• x>0 && y>0 -> x+y > 0

  False

• x >=0 -> -x<=0

  True (Tmax)

• x <=0 -> -x>=0

  False(Tmin)

• (x|-x)>>31 == -1

  False(0)