A Logic Problem

A Logic Problem (5.2)

In some recent consulting work, Dr. Abner Mallity has run into an odd circuit. Of course for him, most circuits are odd and confusing. Nevertheless, here is the circuit.

There is a pulse input to a counter. The counter has N output bits. Each bit is part of the number at the output of the counter. V₁ is the LSB and V_N is the MSB.
The counter output has N voltages, V₁ through V_N. Only the first two are shown.
Apparently, the output of the op-amp is a signal to control temperature. The goal is to produce a linearly increasing temperature.
The resistors are chosen so that R₁ = 2 R₂ = 4 R₃ etc.
Predict the output of the op-amp.

Mallilty has an Up-Down counter. He wants you to predict the output voltage, and wants you to describe the signals he can get from the circuit above, and the circuit below.