I think two... But I can't say how many chips since at this moment it would be shout in the dark... It looks like you already have some documentation since you are talking about binary tree communication
No, really there is no documentation yet available. The binary tree communication protocol is described in the technical specs overview section on the Bitmine webpage I linked in the OP:
Tree or daisy chain configuration ready
Larger scale designs can see their performances degraded by the propagation time needed for a new Bitcoin job to walk through the daisy chain of chips till the last IC, wasting hundreds or even thousands of clock cycles. The A1 addresses this issue in a completely new way by using a binary tree structure where each chip propagates the work to two children nodes in the tree, reducing the propagation time to just 8 clock cycles for a tree of 511 ICs! The A1 can also be configured to work in the traditional daisy chain mode where smaller arrays or simpler design is required.