1. Comp Org & Assembly Lang
Bits and Bytes
Topics
Why bits?
Representing information as bits
Binary / Hexadecimal
Byte representations
Numbers
Characters and strings
Instructions
Bit-level manipulations
Boolean algebra
Expressing in C

2. 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 is private to particular “process”
Program being executed
Program can clobber its own data, but not that of others

3. Byte-Oriented Memory Organization
Virtual memory is organized by the OS
VM is implemented by the Compiler + Run-Time System Control Allocation (or process manager)
Where different program objects should be stored
Multiple mechanisms: static, stack, and heap
In any case, all allocation within single virtual address space

4. Machine Words Machine (or processor) Has “Word Size”
Nominal size of integer-valued data
Including addresses
Last generation machines used 32 bits (4 bytes) words
Limits addresses to 4GB
Becoming too small for memory-intensive applications
We’ll use 32 bits as the word size in this class
Most current systems use 64 bits (8 bytes) words
Potential address space = 264  1.8 X 1019 bytes
Machines support multiple data formats
Fractions or multiples of word size
Always integral number of bytes

5. Word-Oriented Memory Organization
32-bit
Words
64-bit
Words
Bytes
Addr.
0000
Addr = ??
0001
Addresses Specify Byte Locations
Address of first byte in word
Addresses of successive words differ by 4 (32-bit) or 8 (64-bit)
0002
0000
Addr = ??
0003
0004
0000
Addr = ??
0005
0006
0004
0007
0008
Addr = ??
0009
0010
0008
Addr = ??
0011
0008
0012
Addr = ??
0013
0014
0012
0015

6. Data Representations Sizes of C Objects (in Bytes)
C Data Type Alpha (RIP) Typical 32-bit Intel IA32
unsigned 4 4 4
int 4 4 4
long int 8 4 4
char 1 1 1
short 2 2 2
float 4 4 4
double 8 8 8
long double 8/16† 8 10/12
char * 8 4 4
Or any other pointer
(† Depends on compiler&OS, 128bit FP is done in software)

7. Byte Ordering
How should bytes within a multi-byte word be ordered in memory?
Conventions
Sun’s, PowerPC Mac’s are “Big Endian” machines
Least significant byte has highest address
Intel machines (including PC’s and Mac’s) and most ARM are “Little Endian” machines
Least significant byte has lowest address
Some architecture is “bi-endian”, i.e. has a switch. Eg, ARM
Most networking hardware is “Big-Endian”
See for a history of “endian-ness”
Aside: “endian” is from Gulliver’s Travels , a book written by Jonathan Swift, in 1726.

8. Endian is a function of hardware
Byte Ordering Example
Big Endian
Least significant byte (e.g., 67) has highest address
Little Endian
Least significant byte has lowest address
Example
Variable x has 4-byte representation 0x
Address given by &x is 0x100
Endian is a function of hardware
Big Endian
0x100
0x101
0x102
0x103 01 23 45 67 01 23 45 67
Little Endian
0x100
0x101
0x102
0x103 67 45 23 01 67 45 23 01

9. Why does endian-ness matter?
What is Lady Gaga’s age?
Web Server
(solaris box)
Web Client (browser) 28
(intel box)
0x C
469,762,048
Displayed as
0x 1C
Interpreted as
0x C

10. Why does endian-ness matter?
Your machine
(solaris box)
Your client’s machine
(intel box)
Spreadsheet created on big-endian machine
Spreadsheet read on big-endian machine
Final cost: $ 28
Final cost: $ 469,762,048
Stored as
Displayed as
0x C
0x 1C
Interpreted as
0x C

11. Reading Byte-Reversed Listings
Disassembly
Text representation of binary machine code
Generated by program that reads the machine code
Example Fragment
Address Instruction Code Assembly Rendition
: 5b pop %ebx
: 81 c3 ab add $0x12ab,%ebx
804836c: 83 bb cmpl $0x0,0x28(%ebx)
Deciphering Numbers
Value: 0x12ab
Pad to 4 bytes: 0x000012ab
Split into bytes: ab
Reverse: ab

12. Examining Data Representations
Code to Print Byte Representation of Data
Casting pointer to unsigned char * creates byte array
typedef unsigned char *byte_pointer;
void show_bytes(byte_pointer start, int len) {
int i;
for (i = 0; i < len; i++)
printf("0x%p\t0x%.2x\n",
start+i, start[i]);
printf("\n"); }
This program is described in section of the textbook
Don’t need the 0x for pointers in some compilers
Printf directives:
%p: Print pointer
%x: Print Hexadecimal
%.2x means print only 2 digits of hex
See /home/barr/Student/comp210/examples/showBytes.c

13. show_bytes Execution Example
int a = 15213;
printf("int a = %d;\n”, a);
show_bytes((byte_pointer) &a, sizeof(int));
Real representation:
15213
B D
Result (Linux):
int a = 15213;
0x11ffffcb8 0x6d
0x11ffffcb9 0x3b
0x11ffffcba 0x00
0x11ffffcbb 0x00
Address of bytes
Content stored at the address

14. show_bytes Execution Example
int a = 15213;
printf("int a = %d;\n”, a);
show_bytes((byte_pointer) &a, sizeof(int));
float b = ;
printf(”float b = %f;\n”, b);
show_bytes((byte_pointer) &b, sizeof(float));
char c[10] = “abcd”;
printf(”string c = %s;\n”, c);
show_bytes((byte_pointer) &c, 10*sizeof(char));

15. Summary of the Main Points
It’s All About Bits & Bytes
Numbers
Programs
Text
Different Machines Follow Different Conventions for
Word size
Byte ordering
Representations
Boolean Algebra is the Mathematical Basis
Basic form encodes “false” as 0, “true” as 1
General form like bit-level operations in C
Good for representing & manipulating sets