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.

2 V<3 V2\ \text{V} < 3\ \text{V}
Pull-up inverterAn open switch leaves the output high.12 V6 ohmopen+-12 VHIGH

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.

Vout=0 V,I=2 AV_{\text{out}} = 0\ \text{V},\quad I = 2\ \text{A}
Pull-up inverterThe closed switch pulls the output low.12 V6 ohmclosed2 A+-0 V+-12 VLOW