Reading NAND, NOR and inversion symbols

The small circle inverts the entire output

NAND inverts an AND result; NOR inverts an OR result. NAND does not mean “AND with each input inverted.” First check the scope of the inversion^{iInversion The NOT operation, which changes 0 to 1 and 1 to 0. A bar over an expression applies NOT to the entire expression beneath it.}.

Select NAND and confirm that its output is 0 only for 11. Switch to NOR: its output is 1 only for 00. An inverted output is still a valid 0/1 signal, not a value that “has not yet been computed.”

De Morgan's laws are a way to read gates

Moving inversion from an AND output to its inputs also changes the operation to OR. Moving only the bubbles while keeping AND produces a different function. For $a=0,b=1$, NAND is 1 but $\overline a\,\overline b$ is 0: an immediate counterexample.

Active-low specifies the polarity of an asserted signal

A signal such as reset_n, which acts when it is 0, is active-low^{iActive-low A convention in which a request or function is active when its signal is 0. A trailing _n is a common naming convention; the specification defines the actual behavior.}. The _n suffix is a convention; the specification and circuit determine the behavior. To make alarm equal 1 when either request req0_n or req1_n is 0, compute

A bar over an individual signal applies NOT to that signal. The final long bar applies NOT to the entire AND of the two signals, so one NAND implements the function. Inputs 11 mean no request, hence alarm=0; inputs 01 mean the first request is active, hence alarm=1.

A signal being “active” does not always mean the value 1. Check the logic value, active condition and inversion symbol separately when reading an input.