Page 51 - Concise Encyclopedia of Robotics

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Bongard problem + + * Boolean Algebra

• What is the difference between the contents of the boxes on opposite
sides of the heavy, vertical line?
In this case, the boxes on the left contain four dots or straight lines
each; those on the right contain five dots or straight lines each. The dif-
ference between the boxes on the left and those on the right, therefore, is
in the number of dots or straight lines they contain.
See also OBJECT RECOGNITION.
BOOLEAN ALGEBRA
Boolean algebra is a system of mathematical logic using the numbers 0
and 1 with the operations AND (multiplication), OR (addition), and NOT
(negation). Combinations of these operations are NAND (NOT AND)
and NOR (NOT OR). Boolean functions are used in the design of digital
logic circuits.
In Boolean algebra, X AND Y is written XY or X*Y. NOT X is written
with a line or tilde over the quantity, or as a minus sign followed by the
quantity. X OR Y is written X+Y. The first table shows the values of these
functions,where 0 indicates “falsity”and 1 indicates “truth.”The statements

Boolean algebra: basic operations
X Y X X * Y X + Y
0 0 1 0 0
0 1 1 0 1
1 0 0 0 1
1 1 0 1 1

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