Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**imcute****Member**- Registered: 2022-09-28
- Posts: 176

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?

Offline

**imcute****Member**- Registered: 2022-09-28
- Posts: 176

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)*

Offline

Pages: **1**