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imcute

Member

Registered: 2022-09-28

Posts: 176

logic gates

there are 16 possible truth tables for 2i1o logic gates:
0000(nonsense,just gives 0)
0001(and gate)
0010(nin gate(Not INclude gate))
0011(nonsense,not a)
0100(rnin gate(Reversed Not INclude gate))
0101(nonsense,b)
0110(xor gate)
0111(or gate)
1000(nor gate)
1001(xnor gate)
1010(nonsense,not b)
1011(rin gate(Reversed INclude gate))
1100(nonsense,a)
1101(in gate(INclude gate))
1110(nand gate)
1111(nonsense,just gives 1)
the non nonsenses are:
and nin rnin xor or nor xnor rin in nand
unpair not pairs:
and in rin xor or
unpair input symmetry pairs
and in xor or
so these are the elementary 2i1o gates
question are the elementary 3i10 gates?

imcute

Member

Registered: 2022-09-28

Posts: 176

Re: logic gates

answer:
there are 256 possible 3i1o truth tables
(null,a,b,ab,c,ac,bc,abc)
(insert 0~255 translated into binary,i dont want to paste this long sequence here)
fisrt remove not pairs
00000000means that a b c are irrelavent
00001111means that a,b are irrelavent
01010101means that b,c are irrelavent
00110011means that a,c are irrelavent
if 1357/2468 are identical,a is irrelavent
if 1245/3487 are identical,b is irrelavent
if 1234/5678 are identical,c is irrelavent
if 2/3 or 6/7 swap,they are ab symmetry pairs
if 2/5 or 4/7 swap,they are ac symmetry pairs
if 3/5 or 4/6 swap,they are bc symmetry pairs
the rest are elementary but maybe uninteresting gates
(the majority of them are include gates projected to each of the 3 axis)
00000001,
00010000,00010010,00010011,00010101,00010110,00010111,
00100000,00100001,00101110,
00110000,00110001,00110010,00110101,00110110,00110111,
01100000,01100001,01101000,01101001,01101110,01101111,
01110000,01110001,01110010,01110011,01110110,01111000,01111001,01111010,01111011,01111110,01111111,

Last edited by imcute (2022-10-12 15:46:06)