NAND, NOR and inversion symbols

The output circle complements the whole result

NAND complements AND; NOR complements OR:

For input order 00, 01, 10, 11, NAND gives 1, 1, 1, 0 and NOR gives 1, 0, 0, 0. An inverted output is still a valid logic signal.

Move inversions with De Morgan’s laws

Moving an output inversion^{iinversion The NOT operation exchanges 0 and 1. An overline applies NOT to the entire expression covered by the line.} to both inputs also changes AND to OR, or OR to AND. Merely moving the circles preserves neither the symbol nor the function. At inputs 01, NAND gives 1 but an AND of the complemented inputs gives 0.

Active-low describes assertion

An active-low^{iactive-low A convention in which a signal is asserted at 0. The suffix _n often marks this convention; the specification defines the behavior.} request is asserted at zero. The suffix _n is a naming convention, not an automatic circuit operation. If either of two active-low requests must trigger an active-high alarm, then

Each short overline complements one named signal. The final long overline complements their AND as a whole, so a NAND implements this function. Inputs 11 mean no request and produce alarm=0; inputs 01 assert the first request and produce alarm=1. Keep a signal’s numeric value, asserted meaning and inversion symbols distinct.