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The TRUE in F9 of Figure 12.4 seems surprising. With all three ar-
guments TRUE, the Exclusive Or function is returning a TRUE. This
answer is based on the actual results of XOR gates such as the
74LVC1G386 microchip. This chip first does an XOR of the first two
arguments. This results in the top Venn diagram shown in Figure 12.5 .
The chip then cascades that resulting Venn diagram into an XOR with
the third argument. The result is that the scribbled FALSE area of the
top Venn diagram when XOR d with the TRUE third argument returns a
TRUE. Electrical engineers call this a paritygeneratoror a modulo-2
adder. Although it would be difficult to continue the Venn diagram
showing the intersection of 4, 5, or 254 circles, you can imagine how the
intersection area flips to FALSE for an even number of circles and
then back to TRUE for an odd number of circles.
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