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In-Depth Information
Table 4.11
Parsimonious solutions designed with the NOR (“R”) system.
Rule Name
Rule #
Rule Table
Parsimonious Solution
Size
AND
8
1000
RRRaabb
7
OR
14
1110
RRRabab
7
NAND
7
0111
RRRRRRaaabbaa = RR0RRaabb
13
NOR
1
0001
Rab
3
LT
2
0010
RaRbb
5
GT
4
0100
RRbaa
5
LOE
11
1011
RRRRbaRabaa = RR0Rbab
11
GOE
13
1101
RRRaRaRabaa = RR0aRab
11
XOR
6
0110
RRRabRRaabb
11
NXOR
9
1001
RRRaRRbbbaa
11
MUX
172 10101100 RRRabRcac
9
IF
202 11001010 RRRRbacab
9
MAJ
232 11101000 RRRaRbcRRabac
13
MIN
23 00010111 RRRRRRRabccacbb
15
EVEN
105 01101001 RRRRRRRaaRRRRbcRRbcabacbbcc
27
ODD
150 10010110 RRRRRRbRRacRRaRRcRRacabbbabbc
29
NLM39
39 00100111 RRRRRRcacbbac
13
NLM27
27 00011011 RRRRRRcaaccbb
13
NLM115
115 01110011 RRRaRRRabbbcc
13
NLM103
103 01100111 RRRRcRRRcbbccRbab
17
used in order to design these parsimonious solutions and, as happened with
the NAND system where the use of 1 could have improved the compactness
of three expressions, here the use of 0 would have also reduced the length of
three expressions, as the zero element was discovered and used in the design
of these parsimonious expressions. Indeed, as you can easily verify by draw-
ing the expression trees of the solutions presented in Table 4.11, the zero
module that was discovered and integrated in some of the parsimonious so-
lutions makes use of a total of five nodes ((
a
nor
a
) nor
a
) that could have
been easily replaced by just the one “0”.
It is interesting to note that, for the two-input functions, the NOR system
and the NAND system are exactly the same in terms of compactness of solu-
tions (both add up to a total of 84 nodes) (compare Tables 4.10 and 4.11).
However, for the three-input functions, the NAND system performs slightly
better than the NOR system with a total of 150 nodes, whereas the NOR
