An input-controls-output scan treats the controlled switch as inverting the input, so an open input gives V_out = 12 V and a closed input gives V_out = 0 V row by row. The arithmetic is exact only for the stated input states, output voltages, switch states, and rows in the ideal pull-up and ideal controlled-switch model. Real pull-up circuits add resistor tolerance, switch contact resistance, leakage, input impedance, supply tolerance, probe/calibration limits, finite precision, and measurement uncertainty.
A controlled switch can make a high input produce a low output in this ideal pull-up model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Open input gives high output
When the controlled switch is open, the output is 12 volts. The controlled switch is only the circuit role of a transistor here; gain, saturation, base or gate current, and CMOS details are deferred.
open input⇒Vout=12V
Closed input gives low output
When the controlled switch closes, the output becomes 0 volts.