A pull-up plus controlled pull-down turns a HIGH input into a LOW output and a LOW input into a HIGH output. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

LOW input leaves the pull-down open

With input 0 volts, the switch is open and the output is 5 volts.

LOW inVout=5 V\text{LOW in} \Rightarrow V_{\text{out}} = 5\ \text{V}
Inverter openNo pull-down path leaves the output HIGH.5 V5 ohmopen+-5 VHIGH

HIGH input closes the pull-down

With input 5 volts, the pull-down path closes and the output becomes 0 volts.

HIGH inVout=0 V\text{HIGH in} \Rightarrow V_{\text{out}} = 0\ \text{V}
Inverter closedThe pull-down path makes the output LOW.5 V5 ohmclosed1 A+-0 V+-5 VLOW