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Positive and Negative Logic

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, $\mbox{Low} = 0$ and $\mbox{High} = 1$. In negative logic, $\mbox{Low} = 1$ and $\mbox{High} = 0$. 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.


$A$ $B$ 7408 7432
L L L L
L H L H
H L L H
H H H H
$\rightarrow$
Positive logic
$A$ $B$ 7408 7432
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 1
     
$\downarrow$ Negative logic

   
$A$ $B$ 7408 7432
1 1 1 1
1 0 1 0
0 1 1 0
0 0 0 0
$\rightarrow$
Sort rows
$A$ $B$ 7408 7432
0 0 0 0
0 1 1 0
1 0 1 0
1 1 1 1

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.


next up previous
Next: Simplification Up: Logic Gates Previous: Logic families
Robert Moniot 2011-01-24