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As mentioned previously,
there are two ways of assigning the boolean values 0 and 1 to the two
voltage levels Low and High of a circuit. In the positive logic
interpretation,
and
. In negative
logic,
and
. In consequence, the
identification of the logic function produced by a given circuit
depends on which of these two interpretations is used.
*Example:* The TTL chips with part numbers 7408 and 7432 generate
outputs according to the function table below. The interpretations of
these outputs according to the two logic conventions are shown.

Comparing the tables on the right with the known truth
tables for the basic boolean functions, we find that in positive logic
the 7408 performs the AND function and the 7432 performs the OR. In
negative logic, the 7408 is an OR gate and the 7432 is an AND. As a
general rule, the boolean function produced by a chip, as
interpreted in negative logic, is the dual of the positive logic
function.

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Robert Moniot
2011-01-24