[SciPy-user] Naive Question about Data Representations

[David Warde-Farley]

On 20-Jun-08, at 9:48 PM, Brian Lewis wrote:

> Sorry for my naivety.
>
> Can someone explain how it is possible to store more than 1 32-bit  
> integer on a 32-bit system?  I hope this questions makes my  
> confusion obvious.

If by "32-bit system" you mean "32-bit processor/operating system",  
this refers to the number of bits in a memory address, and by  
extension that the system can deal with 2^32 distinct memory  
addresses / locations (4 GB on a 32-bit system, though you can't  
usually use a full 4GB of physical memory since lots of addresses are  
reserved for use by the system for things like I/O devices).

A 32-bit integer will occupy 4 bytes of system memory (8 bits per  
byte), and any valid memory address will have to be such a 32-bit  
integer, but you could store much, much bigger numbers by just  
occupying more bytes of memory. For example, the long long type in C  
occupies 8 bytes = 64 bits.

While any given programming language may not support it directly, you  
could store an integer as big as your system's memory would allow, for  
example you could allocate 4 megabytes and use it to store a 33554432  
bit number if you wanted, or 2 gigabytes and store a 17179869184-bit  
number. Working with it in your programs wouldn't be pleasant, but it  
would be possible.

David