A NAND pull-down puts two switches in series, so one open input breaks the path and the output stays HIGH until both inputs are HIGH. The four rows read 0,0 to 1,1 with output 1, 1, 1, 0 exactly for the ideal switch model; real gates add threshold spread, fanout loading, leakage, propagation delay, supply variation, contact resistance, noise, temperature drift, and voltage and timing measurement uncertainty.
A NAND table becomes readable when the series pull-down path is scanned row by row. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
NAND asks whether the series path is complete
A NAND pull-down has two switches in series. One open switch is enough to break the path, so the output stays HIGH until both inputs are HIGH.
series path complete⇒Y=0
Four input rows make the series rule scannable
The pull-down column changes only on the final row. The output bit column is helper-pinned, so the compact digits cannot drift away from the rendered switch graph.
After the row scan, the standard table is just the compact form of the same four helper calls. The table is useful because the network already earned every cell.