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. How then do we represent data?
Each different “type” in a programming language has its own representation.
Next few slides discuss the representation for the common types:
Ints
Pointers
Floats
Strings

3. Representing Integers
Linux/Win/OS X: little endian
Solaris: big endian
Decimal: 15213
Binary:
Hex: B D
int A = 15213;
int B = ;
long int C = 15213; 6D 3B 00
Linux/Alpha A 3B 6D 00
Sun A 6D 3B 00
Linux C 6D 3B 00
Alpha C 3B 6D 00
Sun C 00 93 C4 FF
Linux/Alpha B C4 93 FF
Sun B
Two’s complement representation
(Covered next lecture)

4. Representing Pointers
Linux/Win/OS X: little endian
Solaris: big endian
Representing Pointers
Alpha P A0 FC FF
int B = ;
int *P = &B;
Alpha Address
Hex: F F F F F C A 0
Binary: 01 00
Sun P
Sun Address
Hex: E F F F F B C Binary: FB 2C EF FF
Linux P
Linux Address
Hex: B F F F F D Binary: FF BF D4 F8
Different compilers & machines assign different locations to objects

5. Representing Floats Float F = 15213.0; 00 B4 6D 46 Linux/W in/OS X F
Solaris F
IEEE Single Precision Floating Point Representation
Hex: D B Binary:
15213:
IEEE Single Precision Floating Point Representation
Hex: D B Binary:
(in binary)
IEEE Single Precision Floating Point Representation
Hex: D B Binary:
15213:
Not same as integer representation, but consistent across machines
Can see some relation to integer representation, but not obvious

6. Representing Strings Strings in C Compatibility 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
Final character = 0
Compatibility
Byte ordering not an issue
Text files generally platform independent
Except for different conventions of line termination character(s)!
Unix (‘\n’ = 0x0a = ^J)
Mac (‘\r’ = 0x0d = ^M)
DOS and HTTP (‘\r\n’ = 0x0d0a = ^M^J)
Linux/Win/
OS X S
Solaris S 32 31 35 33 00 32 31 35 33 00

7. ASCII Chart ASCII ‘0’ is 0x30 Reference:

8. Characters Other popular encoding standards: Unicode ISO Latin-8
16 bit code
Allows more characters: most languages can be encoded
See
The most commonly used encodings are UTF-8, UTF-16 and the now-obsolete UCS-2
UTF-8
uses one byte for any ASCII character,
These bytes have the same code values in both UTF-8 and ASCII encoding,
and up to four bytes for other characters
ISO Latin-8
8-bit encoding standard with dotted consonants
International standard for Latin letters

9. Machine-Level Code Representation
Encode Program as Sequence of Instructions
Each instruction is a simple operation
Arithmetic operation
Read or write memory
Conditional branch
Instructions encoded as bytes
Alpha’s, Sun’s, Mac’s use 4 byte instructions
Reduced Instruction Set Computer (RISC)
PC’s (and intel Mac’s) use variable length instructions
Complex Instruction Set Computer (CISC)
Different instruction types and encodings for different machines
Most code is not binary compatible
Programs are Byte Sequences Too!

10. Representing Instructions
int sum(int x, int y) {
return x+y; } 00 30 42
Alpha sum 01 80 FA 6B E0 08 81 C3
Solaris sum 90 02 00 09 E5 8B 55 89
PC sum 45 0C 03 08 EC 5D C3
For this example, Alpha & Sun use two 4-byte instructions
Use differing numbers of instructions in other cases
PC uses 7 instructions with lengths 1, 2, and 3 bytes
Same for NT, OSX (intel) and for Linux
NT / Linux/OSX not fully binary compatible
Different processors use totally different instructions and encodings

11. What do we know now? A computer is a processor and RAM.
Everything else is peripheral
Everything is 1’s and 0’s.
A processor executes instructions
Instructions are encoded in 1’s and 0’s
each instruction has binary representation
RAM stores 1’s and 0’s
We interpret these 1’s and 0’s based on context
Every type is interpreted from binary
integers: binary
float: special representation in binary
char: binary (ASCII encoding)

12. How do we get to bits?
We write programs in an abstract language like C How do we get to the binary representation? Compilers & Assemblers! We write x = 5. The compiler changes it into mov 5, 0x005F The assembler changes it into: 80483c7: 8b 45 5F

13. Manipulating bits
Since all information is in the form of bits, we must manipulate bits when programming at low levels
We did some of this with the show_bytes program.
To understand how to do more, we must understand Boolean algebra
We can manipulate bits from C; this is where C and hardware meet.

14. Boolean Algebra Developed by George Boole in 19th Century And Or Not
Algebraic representation of logic
Encode “True” as 1 and “False” as 0
And
A&B = 1 when both A=1 and B=1 Or
A|B = 1 when either A=1 or B=1
Not
~A = 1 when A=0
Exclusive-Or (Xor)
A^B = 1 when either A=1 or B=1, but not both

15. Application of Boolean Algebra
Applied to Digital Systems by Claude Shannon
1937 MIT Master’s Thesis
Reason about networks of relay switches
Encode closed switch as 1, open switch as 0
A&~B
Connection when
A&~B | ~A&B A ~A ~B B
~A&B
= A^B

16. Representing & Manipulating Sets
Representation
Width w bit vector represents subsets of {0, …, w–1}
aj = 1 if j  A
{ 0, 3, 5, 6 }
{ 0, 2, 4, 6 }
Operations
& Intersection { 0, 6 }
| Union { 0, 2, 3, 4, 5, 6 }
^ Symmetric difference { 2, 3, 4, 5 }
~ Complement { 1, 3, 5, 7 }

17. General Boolean Algebras
Operate on Bit Vectors
Operations applied bitwise
Let x = 105 and y = 85 (think about how this is actually stored)
x & y: x | y: x ^ y ~y
All of the Properties of Boolean Algebra Apply
& | ^ ~

18. Bit-Level Operations in C
Operations &, |, ~, ^ Available in C
Apply to any “integral” data type
long, int, short, char, unsigned
View arguments as bit vectors
Arguments applied bit-wise
Examples (Char data type)
~0x41 --> 0xBE
~ >
~0x00 --> 0xFF
~ >
0x69 & 0x55 --> 0x41
& >
0x69 | 0x55 --> 0x7D
| >

19. Contrast: Logic Operations in C
Contrast to Logical Operators
&&, ||, !
View 0 as “False”
Anything nonzero as “True”
Always return 0 or 1
Early termination
Examples (char data type)
c = ‘A’ then !c is !0x41 --> 0x00
c = ‘\0’ then !c is !0x00 --> 0x01
c = ‘A’ the !!c is !!0x41 --> 0x01
0x69 && 0x55 --> 0x01
0x69 || 0x55 --> 0x01
p && *p++ (avoids null pointer access)
Or p && (*p = 10) also protects
Works because of short-circuit evaluation in C