It's state is represented by a tape of bits, a tape head, and the instruction pointer. The instructions are:
move the tape head to the left;
move the tape head to the right;
mark the current cell;
jump if the current cell is blank.
In his report "A Variant to Turing's Theory of Computing Machines", Hao Wang describes a storage format for positive integers on the tape as a list whose members you can address by indices starting from the end of the tape. A new number gets appended to the end of the tape. Every operation on numbers spoils them while writing the new number, so to use an argument twice, you have to apply the copying subroutine, which spoils its argument and writes its two copies at the end of the tape.
This is pretty cool, you really can do anything with numbers as long as you leave a trail of uncollected garbage and can keep track of indices of current data. Sadly i can only understand a tenth of that report.