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# 3 Boolean Operator Diagrams

In all of these figures, a white pixel indicates a 0 value, and a black pixel indicates a 1 value8. The images were generated using the AVS network shown in Figure 6, using the ip_logical image processing module. However, this module considers white pixels to be 1 and black pixels to be 0; this is the reason for the ip_logical NOT modules just after reading the input images and just before writing the output images.

Figure 7 shows the input images, each contains a single circle at a different offset. The region inside the circle is defined to be 1, the region outside is 0.

 [left] [right]

Figure 8 illustrates the effect of combining Figures 7a and 7b using the boolean operators AND, NAND, OR, NOR, and XOR respectively.

 [and] [nand] [or] [nor] [xor]

Feature to note are:

• Figure 8a, depicting AND, is black in the region where both of the input images in Figure 7 are black. This is consistent with the definition of the AND operation.
• Figure 8c, depicting OR, is black in the region where either of the input images in Figure 7 are black. This is consistent with the definition of the OR operation.
• Figure 8e, depicting XOR, is black in the regions where only one, but not both, of the input images in Figure 7 are black. This is consistent with the definition of the XOR operation.
• NAND is, by definition, a negated AND, and, similarly, NOR is a negated OR. This is reflected in Figure 8 by these two pairs or images (Figures 8a - 8b, and 8c - 8d) being ``opposite'', in the sense that what is black in one is white in the other, and vice-verso.
These diagrams are also called VENN DIAGRAMS (John Venn, 1834-1923, [1, Section 2.3, Page 13]), and are frequently used as demonstrative aids in elementary boolean logic and set theory (where AND corresponds to set intersection and OR corresponds to set union).

Next: 4 Surface Normal Vector Up: Scientific Visualisation 3 1999 Previous: 2.3.3 Animation presentation
Kevin Pulo
2000-08-22