Please show all work.

Create a Turing Machine (i.e., write out the full transition table) that counts in binary - have it first put a 0, then change that to a 1, then change that to a 10, then 11, then 100, 101, etc. Have it do this infinitely. Assume a completely blank tape when you start - you can add whatever delimiting symbols you want. You can have the number expand to either the left or right, whichever you find more convenient