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Table 4.12
Parsimonious solutions designed with the universal system {AND, XOR, NOT}.
Rule Name
Rule #
Rule Table
Parsimonious Solution
Size
AND
8
1000
Aab
3
OR
14
1110
XAbaNb
6
NAND
7
0111
NAab
4
NOR
1
0001
ANNab
5
LT
2
0010
ANba
4
GT
4
0100
AaNb
4
LOE
11
1011
NAaNb
5
GOE
13
1101
NANba
5
XOR
6
0110
Xab
3
NXOR
9
1001
NXab
4
MUX
172
10101100
XAbaXbc
7
IF
202
11001010
XAcaXbc
7
MAJ
232
11101000
XAcXXacbc
9
MIN
23
00010111
XNAAabXcab
10
EVEN
105
01101001
XNbXac
6
ODD
150
10010110
XXcab
5
NLM39
39
00100111
XaNAXcab
8
NLM27
27
00011011
NXAbXcab
8
NLM115
115
01110011
NANbAaNc
8
NLM103
103
01100111
XNAAbcANaNbc
12
Mux Logic
The MUX system is becoming extremely popular due to the new emerging
technology of field programmable gate arrays (FPGAs). The advantage of
this technology is that one is no longer restricted to the usual NAND or NOR
gates, as virtually any kind of universal logical system can be used to build
logical circuits. This is indeed the era of programmable gate arrays and evolv-
able hardware, and engineers all over the world are trying to find new sys-
tems that might prove more efficient in the design of digital circuits. So,
being able to find the most parsimonious representation for any kind of logi-
cal function using any kind of universal system is essential for the advance-
ment of this field, and now we know that gene expression programming is
particularly well suited for doing just that as it handles all kinds of universal
systems with the same efficiency.
 
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