A pullup-inverter scan pairs a controlled switch with a pull-up resistor to invert the control, leaving V_out = 12 V below threshold and pulling V_out = 0 V with pull-up current I = V / R above threshold row by row. The arithmetic is exact only for the stated control voltages, threshold voltages, output voltages, currents, switch states, and rows in the ideal controlled-switch and ideal pull-up model. Real transistor switches add saturation voltage, leakage, gain spread, resistor tolerance, input threshold variation, probe/calibration limits, finite precision, and measurement uncertainty.
A controlled switch and pull-up resistor make a simple inverted output node. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Below threshold leaves the pull-up high
A 2 volt control is below the 3 volt threshold, so the switch stays open and the output is 12 volts.
2V<3V
Above threshold pulls the output low
A 5 volt control closes the switch. The output becomes 0 volts and the pull-up current is 2 amperes.