A threshold-after-loading scan compares the node voltage to a fixed threshold before and after loading, checking that the same divider can cross the boundary V_out versus V_threshold once the load pulls the node down row by row. The arithmetic is exact only for the stated output voltages, threshold voltages, decision states, load states, and rows in the ideal resistor, ideal supply, ideal threshold model. Real dividers add resistor tolerance, source resistance, finite load impedance, input threshold spread, temperature drift, meter/probe calibration limits, finite precision, and measurement uncertainty.
A threshold decision follows the computed node voltage, so loading can change the ideal decision. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Before the load, the node is above threshold
The unloaded output is 8 volts, which is above the 7 volt threshold.
8V>7V
After the load, the node is below threshold
The loaded output is 6 volts, which is below the same threshold. This is an ideal threshold comparison; noise margins, hysteresis, and propagation delay are deferred.