Below, equal, and above threshold produce different ideal switch decisions. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The threshold rule is strict

The ideal switch closes only when the measured voltage is above the threshold. Equal to the threshold is not above it.

closed only if Vm>Vthreshold\text{closed only if }V_m>V_{\text{threshold}}
Strict threshold ladderThe middle row is equal to threshold and remains open.openlampaboveoff

Below, equal, and above are different rows

The measured value changes while the threshold stays fixed. The decision column is derived from the strict comparison.

VmVthresholddecision0 V1 VLOW1 V1 VLOW2 V1 VHIGH\begin{array}{c|c|c}V_m&V_{\text{threshold}}&\text{decision}\\0\ \text{V}&1\ \text{V}&LOW\\1\ \text{V}&1\ \text{V}&LOW\\2\ \text{V}&1\ \text{V}&HIGH\\\end{array}
Strict threshold ladderThe rendered row is equal to the threshold.openlampaboveoff

Equal is still low for a strict above-threshold gate

For the rendered row, measured voltage and threshold are both 1 volt, so the ideal switch stays open.

1 V=1 VLOW1\ \text{V}=1\ \text{V}\Rightarrow \text{LOW}
Strict threshold ladderThe equal row is not above the threshold.openlampaboveoff