When it is completed in late 2004, the world's most powerful computer will be ASCI Purple.
It is expected to carry out 100 trillion operations per second.
A spokesman for IBM, who are building the computer, said ASCI Purple would be nearly as powerful as the human brain.
But some scientists believe our brains can carry out around 10,000 trillion operations per second.
A supercomputer, which can process over 200 trillion operations per second, is expected to be built within the next two years.
It is being built to replace ASCI White - formerly the world's most powerful computer - which occupies a space the size of two basketball courts at the Lawrence Livermore National Laboratory in California.