Consider you are looking for an element at index 100 in a 8 bit value range (1-256). Your binary search progress will consider following indices:

128 ? Too big

64 ? Too small

64 + 32 ? Too small

64 + 32 + 16 ? Too big

64 + 32 + 8 ? Too big

64 + 32 + 4 ? Found

It is easy to to notice that in every step you are testing the most significant bit not tested yet and if it does not overflow the result it is added to the partial solution until the final result is found.

So following characteristics of the greedy choice can be pointed:

There is a candidate set composed of 8 bits of the number to find. Greedy selection considering in every step the most significant bit not used yet. Checking if that bit can be added to the final solution locally looking at the bit and the result assembled so far. If the sum does not overflow that bit makes part of the final solution. The final solution can identified when the composed sum is equal to the searched one.

Of course no backtracking is ever needed so this is a perfect greedy algorithm.