An ideal threshold switch follows the computed bridge voltage, not a hand-authored label. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Use the computed bridge voltage
The unbalanced bridge gives 2 volts.
Vbridge=2V
The threshold decision follows the voltage
The bridge voltage is above the 1 volt threshold, so the ideal switch state is derived as on. Noise margins, hysteresis, and propagation delay are deferred.