Tiny Core is a very small linux distribution, the basic version having a 12MB image and the plus version installed here has a whopping 64 megabyte image.
The requirements aren't too massive either
An absolute minimum of RAM is 46mb. TC won't boot with anything less, no matter how many terabytes of swap you have.
Microcore runs with 28mb of ram.
The minimum cpu is i486DX (486 with a math processor).
A recommended configuration:
Pentium 2 or better, 128mb of ram + some swap
The distro and more information can be found here http://www.tinycorelinux.com/
Twitter: @Purkkaviritys