optimization - Truth table with 5 inputs and 3 outputs -


i have make truth table 5 inputs , 3 outputs, this:

a b c d e red green blue
0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 1
0 0 0 1 0 0 0 1 . . . . 1 1 0 1 0 0 1 1
. . . 1 1 1 1 1 1 0 1

etc. (in total 32 rows, numbers in rgb table represents number of 1's in each row in binary i.e in row 1 1 0 1 0 there 3 1's, 3 in binary 0 1 1).

i present result of in atanua (http://sol.gfxile.net/atanua/index.html) tool (so fore example when press button e, blue light shine, when pressing b d green , blue light shine , on). there requirement can use and, or, not operands, , each operand can have 2 inputs. although i'm using karnaugh map minimize it, still many records results each output long (especially last one).

i tried simplify more adding of 3 output boolean functions one, , minimization process ended pretty well:

a + b + c + d

it seems work fine (but there 1 output light, works in red green blue column separately). concern fact have 3 outputs (three lights, not one), , possible after kind of minimization? there solution in atanua? or have make 3 separate boolean functions, no matter how long (and there lot of them after minimization)?

edit: whole truth table :)

a b c d e r g b

0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 1
0 0 0 1 0 0 0 1
0 0 0 1 1 0 1 0
0 0 1 0 0 0 0 1
0 0 1 0 1 0 1 0
0 0 1 1 0 0 1 0
0 0 1 1 1 0 1 1
0 1 0 0 0 0 0 1
0 1 0 0 1 0 1 0
0 1 0 1 0 0 1 0
0 1 0 1 1 0 1 1
0 1 1 0 0 0 1 0
0 1 1 0 1 0 1 1
0 1 1 1 0 0 1 1
0 1 1 1 1 1 0 0
1 0 0 0 0 0 0 1
1 0 0 0 1 0 1 0
1 0 0 1 0 0 1 0
1 0 0 1 1 0 1 1
1 0 1 0 0 0 1 0
1 0 1 0 1 0 1 1
1 0 1 1 0 0 1 1
1 0 1 1 1 1 0 0
1 1 0 0 0 0 1 0
1 1 0 0 1 0 1 1
1 1 0 1 0 0 1 1
1 1 0 1 1 1 0 0
1 1 1 0 0 0 1 1
1 1 1 0 1 1 0 0
1 1 1 1 0 1 0 0
1 1 1 1 1 1 0 1
, karnaugh map each color (~is gate not, * and, + or):
red:
bcde+acde+abde+abce+abcd
green:
~a~bde+~ac~de+~acd~e+~bcd~e+~ab~ce+b~cd~e+bc~d~e+a~b~ce+a~b~cd+a~bc~d+ab~c~d

blue:
~a~b~c~de+~a~b~cd~e+~a~bc~d~e+~a~bcde+~ab~c~d~e+~ab~cde+~abc~de+~abcd~e+a~b~c~d~e+a~b~cde+a~bc~de+a~bcd~e+ab~c~de+ab~cd~e+abc~d~e+abcde

have admit formulas ugly, it's not complicated implement logic gatters, because can reuse parts.

a -----+------+------------- - - -       not     |        +------|--and- ~ab        |      |   |       and-----|---|-- ~a~b        +--and-+   |        |   +--|---|-- a~b       not    and--|-- ab b -----+------+---+---------- - - -

here example created combinations of [not]a , [not]b. can same c , d. can combination of [not]a , [not]b , [not]c , [not]d combining wire each "box" , gatter (e.g. abcd take ab wire , cd wire).


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