CSC373/406: Bits! How Programs are Stored [2011/04/03-05]

CSC373/406: Integers: Bits! How Programs are Stored [6/9]

Everything in a computer memory is a bit (0 or a 1)
8 bits = 1 byte
The byte is the smallest addressable chunk of memory on modern machines
Machines are limited in how much memory they can possibly have by their address space size
Example: most PC's are 32-bit machines, which means that there are at most 2^32 bytes of memory on the machine (about 4 GBytes)

Storing programming statements

Every statement in a program is translated (by the compiler) into one or more machine instructions
The possible machine instructions depend on the type of machine used (Intel, Sun, Apple)
On a typical Windows machine with an Intel CPU, each instruction takes up between 1 and 9 bytes
These instructions are stored in contiguous memory somewhere in the address space

Storing data

Each data type in C has its own internal representation
int: 32-bit binary number
long: 32-bit or 64-bit binary number (depends on the machine)
double: we'll discuss its format next week
char: ASCII encoding (or Unicode, which is an extension)

Using printf format strings to look at underlying representations of data

%x will print any piece of data out in hexadecimal
%p will print out a pointer

Example:

#include <stdio.h>

int main( ) {
  int a = 28;
  double b = 33333.555555;
  char c = 'c';

  printf("a: %d %x\nb: %4.1f %x\nc: %d %x\n",
         a, a, b, b, (int) c, c);
}

Conversion between decimal, binary, and hex

In base 10, the nth digit from the right in the number represents the number of 10^n 's in the number

Example: 2538

Digit	Offset from the right	Represents
8	0	8 * 10^0 = 8
3	1	3 * 10^1 = 30
5	2	5 * 10^2 = 500
8	0	2 * 10^3 = 2000

So the number is 8 + 30 + 500 + 2000 = 2538.

Converting from other bases to base 10 can be done in the same way. For example, in binary, each column represents a power of 2.

Example: 1001101

Digit	Offset from the right	Represents
1	0	1 * 2^0 = 1
0	1	0 * 2^1 = 0
1	2	1 * 2^2 = 4
1	3	1 * 2^3 = 8
0	4	0 * 2^4 = 0
0	5	0 * 2^5 = 0
1	6	1 * 2^6 = 64

So the number is 1 + 0 + 4 + 8 + 0 + 0 + 64 = 37

Example of conversion from hex

Base 16
need 16 different "digits": 0-9, A-F (so F represents 15)
Each column in a number represents a power of 16

Example: 0xA203

Digit	Offset from the right	Represents
3	0	3 * 16^0 = 3
0	1	0 * 16^1 = 0
2	2	0 * 16^2 = 512
a	3	10 * 16^3 = 40960

So the number is 3 + 0 + 512 + 40960 = 41475