The procedure for deriving the general solution is described. When the center viewpoint is included, Eqs. (16–18) are used as examples; when the center viewpoint is not included, the results of the study for all combinations are noted.

$$\begin}}_},}}=}}_},}+1}\oplus }}_},}}\oplus }}_},}-1}\end$$

(37)

$$\begin}}_},}}=}}_},}}\oplus }}_},}}\oplus }}_},}}\end$$

(38)

$$}_},}}} = }_} - 1,}}} \oplus }_},}}} \oplus }_} + 1,}}}$$

(39)

To solve the simultaneous equation of XOR, we make a sum of the same terms.

(37) \(\oplus\)(38)l+1

$$}_},}}} \oplus }_},} + 1}} = }_},} + 1}} \oplus }_},} + 1}} \oplus }_},}}} \oplus }_},} + 1}} \oplus }_},} - 1}} \oplus }_},} + 1}} \Rightarrow }_},}}} \oplus }_},} + 1}} = }_},}}} \oplus }_},} + 1}} \oplus }_},} - 1}} \oplus }_},} + 1}}$$

(40)

(37) \(\oplus\)(38)

$$\begin}}_},}}\oplus }}_},}}=}}_},}}\oplus }}_},}+1}\oplus }}_},}-1}\oplus }}_},}}\end$$

(41)

(37)l+1\(\oplus\)(38)

$$\begin}}_},}+1}\oplus }}_},}}=}}_},}}\oplus }}_},}+2}\oplus }}_},}}\oplus }}_},}+1}\end$$

(42)

(39) \(\oplus\)(39)l+1

$$\begin}}_},}}\oplus }}_},}+1}=}}_}-1,}}\oplus }}_}-1,}+1}\oplus }}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+1}\end$$

(43)

(42) \(\oplus\)(43)

$$\begin}}_},}+1}\oplus }}_},}}\oplus }}_},}}\oplus }}_},}+1}=}}_}-1,}}\oplus }}_}-1,}+1}\oplus }}_},}}\oplus }}_},}+2}\oplus }}_}+1,}}\oplus }}_}+1,}+1}\end$$

(44)

(41)k+1, l+1\(\oplus\)(44)

$$}_},} + 1}} \oplus }_} + 1,} + 1}} \oplus }_},}}} \oplus }_} + 1,} + 1}} \oplus }_},}}} \oplus }_},} + 1}} \beginc} }_} - 1,}}} \oplus }_} - 1,} + 1}} \oplus }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} + 1}} \oplus }_} + 1,} + 2}} } \\ \end$$

(45)

(39) \(\oplus\)(39)l+2

$$\begin}}_},}}\oplus }}_},}+2}=}}_}-1,}}\oplus }}_}-1,}+2}\oplus }}_},}}\oplus }}_},}+2}\oplus }}_}+1,}}\oplus }}_}+1,}+2}\end$$

(46)

(40)k+1, l+1\(\oplus\)(46)

$$\begin }_} + 1,} + 1}} \oplus }_} + 1,} + 2}} \oplus }_},}}} \oplus }_},} + 2}} \hfill \\ = }_} - 1,}}} \oplus }_} - 1,} + 2}} \oplus }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} + 1}} \oplus }_} + 1,} + 2}} \hfill \\ \end$$

(47)

(42) \(\oplus\)(47)k+1

$$\begin }_},} + 1}} \oplus }_} + 2,} + 1}} \oplus }_},}}} \oplus }_} + 2,} + 2}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \hfill \\ = }_},}}} \oplus }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 2,} + 1}} \oplus }_} + 2,} + 2}} \hfill \\ \end$$

(48)

(40) \(\oplus\)(43)

$$\begin}}_},}}\oplus }}_},}+1}\oplus }}_},}}\oplus }}_},}+1}=}}_}-1,}}\oplus }}_}-1,}+1}\oplus }}_},}-1}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+1}\end$$

(49)

(41) \(\oplus\)(49)k+1

$$\begin }_},}}} \oplus }_} + 1,}}} \oplus }_},}}} \oplus }_} + 1,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 1}} \hfill \\ = }_},} - 1}} \oplus }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 1}} \hfill \\ \end$$

(50)

From these results, the general formula for triple-view display (upper, center, right) is as follows

$$}}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+2}\oplus }}_}+2,}+1}\oplus }}_}+2,}+2}=}}_}+1,}+1}\oplus }}_}+2,}+1}\oplus }}_}+1,}}\oplus }}_}+2,}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+1}$$

$$}}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+2}\oplus }}_}+2,}+1}\oplus }}_}+2,}+2}=}}_},}+1}\oplus }}_}+2,}+1}\oplus }}_},}}\oplus }}_}+2,}+2}\oplus }}_}+1,}}\oplus }}_}+1,}+2}$$

$$}}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+2}\oplus }}_}+2,}+1}\oplus }}_}+2,}+2}=}}_},}+1}\oplus }}_}+1,}+1}\oplus }}_},}+1}\oplus }}_}+1,}+2}\oplus }}_}+1,}+1}\oplus }}_}+1,}+2}$$

Solving simultaneous equations with \(}}_},}}\), \(}}_},}}\), and \(}}_},}}\).

$$\begin}}_},}}=}}_},}+1}\oplus }}_},}}\oplus }}_},}-1}\end$$

(51)

$$\begin}}_},}}=}}_}+1,}}\oplus }}_},}}\oplus }}_}-1,}}\end$$

(52)

$$\begin}}_},}}=}}_}-1,}}\oplus }}_},}}\oplus }}_}+1,}}\end$$

(53)

Solve the above XOR simultaneous equations.

(51)k+1\(\oplus\)(52)l+1

$$\begin}}_}+1,}}\oplus }}_},}+1}=}}_},}+1}\oplus }}_}+1,}}\oplus }}_}-1,}+1}\oplus }}_}+1,}-1}\end$$

(54)

(51) \(\oplus\)(52)

$$\begin}}_},}}\oplus }}_},}}=}}_},}+1}\oplus }}_}+1,}}\oplus }}_}-1,}}\oplus }}_},}-1}\end$$

(55)

(51)l+1\(\oplus\)(52)k+1

$$\begin}}_},}+1}\oplus }}_}+1,}}=}}_},}+2}\oplus }}_}+2,}}\oplus }}_},}+1}\oplus }}_}+1,}}\end$$

(56)

(53)l+1\(\oplus\)(53)k+1

$$\begin}}_},}+1}\oplus }}_}+1,}}=}}_}-1,}+1}\oplus }}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+1}\oplus }}_}+2,}}\end$$

(57)

(55)k+2, l+1\(\oplus\)(57)

$$\beginc} }_} + 2,} + 1}} \oplus }_} + 2,} + 1}} \oplus }_},} + 1}} \oplus }_} + 1,}}} = }_} - 1,} + 1}} \oplus }_},}}} \oplus }_} + 2,} + 2}} \oplus }_} + 3,} + 1}} \oplus }_},} + 1}} \oplus }_} + 1,}}} } \\ \end$$

(58)

(56) \(\oplus\)(58)

$$\begin }_},} + 1}} \oplus }_} + 2,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_},} + 1}} \oplus }_} + 1,}}} \hfill \\ = }_} - 1,} + 1}} \oplus }_},}}} \oplus }_},} + 2}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \oplus }_} + 3,} + 1}} \hfill \\ \end$$

(59)

(53)k+1, l+2\(\oplus\)(53)k+3

$$\begin}}_}+1,}+2}\oplus }}_}+3,}}=}}_},}+2}\oplus }}_}+2,}}\oplus }}_}+1,}+2}\oplus }}_}+3,}}\oplus }}_}+2,}+2}\oplus }}_}+4,}}\end$$

(60)

(56) \(\oplus\)(60)

$$\beginc} }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 3,}}} = }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 3,}}} \oplus }_} + 2,} + 2}} \oplus }_} + 4,}}} } \\ \end$$

(61)

(54)k+3, l+1\(\oplus\)(61)

$$\begin }_},} + 1}} \oplus }_} + 4,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 3,} + 2}} \oplus }_} + 1,} + 2}} \oplus }_} + 3,}}} \hfill \\ = }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 3,}}} \oplus }_} + 3,} + 2}} \oplus }_} + 4,} + 1}} \hfill \\ \end$$

(62)

(53)l+1\(\oplus\)(53)k+1

$$\begin}}_},}+1}\oplus }}_}+1,}}=}}_}-1,}+1}\oplus }}_},}}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+1}\oplus }}_}+2,}}\end$$

(63)

(54) \(\oplus\)(63)

$$\beginc} }_} + 1,}}} \oplus }_},} + 1}} \oplus }_},} + 1}} \oplus }_} + 1,}}} = }_} - 1,} + 1}} \oplus }_},}}} \oplus }_} - 1,} + 1}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 2,}}} } \\ \end$$

(64)

(55) \(\oplus\)(64)k+1

$$\begin }_},}}} \oplus }_} + 2,}}} \oplus }_},}}} \oplus }_} + 1,} + 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 2,}}} \hfill \\ = }_} - 1,}}} \oplus }_},} - 1}} \oplus }_},} + 1}} \oplus }_} + 2,} - 1}} \oplus }_} + 2,} + 1}} \oplus }_} + 3,}}} \hfill \\ \end$$

(65)

From these results, the general formula for triple-view display (upper, left, right) is as follows

$$\begin }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_} + 1,}}} \oplus }_} + 3,}}} \oplus }_} + 2,} - 1}} \oplus }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_} + 2,} - 1}} \hfill \\ }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_},}}} \oplus }_} + 4,}}} \oplus }_} + 1,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \hfill \\ }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_} + 1,}}} \oplus }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_} + 2,} + 1}} \oplus }_} + 3,}}} \hfill \\ \end$$

Solving simultaneous equations with \(}}_},}}\), \(}}_},}}\), and \(}}_},}}\).

$$\begin}}_},}}=}}_},}+1}\oplus }}_},}}\oplus }}_},}-1}\end$$

(66)

$$\begin}}_},}}=}}_}+1,}}\oplus }}_},}}\oplus }}_}-1,}}\end$$

(67)

$$\begin}}_},}}=}}_},}-1}\oplus }}_},}}\oplus }}_},}+1}\end$$

(68)

Solve the above XOR simultaneous equations.

(66)k+1\(\oplus\)(67)l+1

$$\begin}}_}+1,}}\oplus }}_},}+1}=}}_},}+1}\oplus }}_}+1,}}\oplus }}_}-1,}+1}\oplus }}_}+1,}-1}\end$$

(69)

(66) \(\oplus\)(67)

$$\begin}}_},}}\oplus }}_},}}=}}_},}+1}\oplus }}_}+1,}}\oplus }}_}-1,}}\oplus }}_},}-1}\end$$

(70)

(66)l+1\(\oplus\)(67)k+1

$$\begin}}_},}+1}\oplus }}_}+1,}}=}}_},}+2}\oplus }}_}+2,}}\oplus }}_},}+1}\oplus }}_}+1,}}\end$$

(71)

(68)l+1\(\oplus\)(68)k+1

$$\begin}}_},}+1}\oplus }}_}+1,}}=}}_},}}\oplus }}_}+1,}-1}\oplus }}_},}+1}\oplus }}_}+1,}}\oplus }}_},}+2}\oplus }}_}+1,}+1}\end$$

(72)

(71) \(\oplus\)(72)

$$\beginc} }_},} + 1}} \oplus }_} + 1,}}} \oplus }_},} + 1}} \oplus }_} + 1,}}} = }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 2,}}} \oplus }_},} + 2}} \oplus }_} + 1,} + 1}} } \\ \end$$

(73)

(70)k+1, l+2\(\oplus\)(73)

$$\begin }_},} + 1}} \oplus }_} + 1,} + 2}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_},} + 1}} \oplus }_} + 1,}}} \hfill \\ = }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ \end$$

(74)

(68)l+2\(\oplus\)(68)k+2

$$\begin}}_},}+2}\oplus }}_}+2,}}=}}_},}+1}\oplus }}_}+2,}-1}\oplus }}_},}+2}\oplus }}_}+2,}}\oplus }}_},}+3}\oplus }}_}+2,}+1}\end$$

(75)

(69)k+1, l+2\(\oplus\)(75)

$$\begin }_} + 2,} + 2}} \oplus }_} + 1,} + 3}} \oplus }_},} + 2}} \oplus }_} + 2,}}} \hfill \\ = }_},} + 1}} \oplus }_} + 2,} - 1}} \oplus }_},} + 2}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ \end$$

(76)

(71) \(\oplus\)(76)l+1

$$\beginc} }_},} + 1}} \oplus }_} + 2,} + 3}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 4}} \oplus }_},} + 3}} \oplus }_} + 2,} + 1}} } \\ }_},} + 1}} \oplus }_},} + 3}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 4}} \oplus }_} + 2,} + 1}} \oplus }_} + 2,} + 3}} } \\ \end$$

(77)

(69) \(\oplus\)(72)

$$\beginc} }_} + 1,}}} \oplus }_},} + 1}} \oplus }_},} + 1}} \oplus }_} + 1,}}} = }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} - 1,} + 1}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} } \\ \end$$

(78)

(70) \(\oplus\)(78)l+1

$$\begin}}_},}}\oplus }}_}+1,}+1}\oplus }}_},}}\oplus }}_},}+2}\oplus }}_},}+2}\oplus }}_}+1,}+1}\\ =}}_}-1,}}\oplus }}_}-1,}+2}\oplus }}_},}-1}\oplus }}_},}+3}\oplus }}_}+1,}}\oplus }}_}+1,}+2}\end$$

(79)

From these results, the general formula for triple-view display (upper, left, bottom) is as follows

$$\begin }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_},} + 1}} \oplus }_} + 1,} + 2}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_},} + 1}} \oplus }_} + 1,}}} \hfill \\ }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_},}}} \oplus }_} + 2,} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_},} + 2}} \oplus }_} + 2,}}} \hfill \\ }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 1,} + 2}} \oplus }_} + 2,} + 1}} \hfill \\ \end$$

Solving simultaneous equations with \(}}_},}}\), \(}}_},}}\), and \(}}_},}}\).

$$\begin}}_},}}=}}_}+1,}}\oplus }}_},}}\oplus }}_}-1,}}\end$$

(80)

$$\begin}}_},}}=}}_}-1,}}\oplus }}_},}}\oplus }}_}+1,}}\end$$

(81)

$$\begin}}_},}}=}}_},}-1}\oplus }}_},}}\oplus }}_},}+1}\end$$

(82)

Solve the above XOR simultaneous equations.

(80) \(\oplus\)(81)k+2

$$\begin}}_},}}\oplus }}_}+2,}}=}}_},}}\oplus }}_}+2,}}\oplus }}_}-1,}}\oplus }}_}+3,}}\end$$

(83)

(80) \(\oplus\)(81)

$$\begin}}_},}}\oplus }}_},}}=}}_}-1,}}\oplus }}_}+1,}}\oplus }}_}-1,}}\oplus }}_}+1,}}\end$$

(84)

(80)k+2\(\oplus\)(81)

$$\begin}}_}+2,}}\oplus }}_},}}=}}_}-1,}}\oplus }}_}+3,}}\oplus }}_},}}\oplus }}_}+2,}}\end$$

(85)

(82) \(\oplus\)(82)k+2

$$\begin}}_},}}\oplus }}_}+2,}}=}}_},}-1}\oplus }}_}+2,}-1}\oplus }}_},}}\oplus }}_}+2,}}\oplus }}_},}+1}\oplus }}_}+2,}+1}\end$$

(86)

(84)k+1, l+1\(\oplus\)(86)

$$\begin}}_}+1,}+1}\oplus }}_}+1,}+1}\oplus }}_},}}\oplus }}_}+2,}}=}}_},}-1}\oplus }}_},}+1}\oplus }}_}+2,}-1}\oplus }}_}+2,}+1}\oplus }}_},}}\oplus }}_}+2,}}\end$$

(87)

(85) \(\oplus\)(87)

$$\begin }_} + 1,} + 1}} \oplus }_} + 2,}}} \oplus }_},}}} \oplus }_} + 1,} + 1}} \oplus }_},}}} \oplus }_} + 2,}}} \hfill \\ \beginc} }_} - 1,}}} \oplus }_},} - 1}} \oplus }_},} + 1}} \oplus }_} + 2,} - 1}} \oplus }_} + 2,} + 1}} \oplus }_} + 3,}}} } \\ \end \hfill \\ \end$$

(88)

(82)l+1\(\oplus\)(82)k+4, l+1

$$\begin}}_},}+1}\oplus }}_}+4,}+1}=}}_},}}\oplus }}_}+4,}}\oplus }}_},}+1}\oplus }}_}+4,}+1}\oplus }}_},}+2}\oplus }}_}+4,}+2}\end$$

(89)

(85)k+1\(\oplus\)(89)

$$\beginc} }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_},} + 1}} \oplus }_} + 4,} + 1}} = }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 3,}}} \oplus }_} + 4,} + 1}} \oplus }_},} + 2}} \oplus }_} + 4,} + 2}} } \\ \end$$

(90)

(83)k+1, l+2\(\oplus\)(90)

$$\begin }_} + 1,} + 2}} \oplus }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_} + 3,} + 2}} \oplus }_},} + 1}} \oplus }_} + 4,} + 1}} \hfill \\ \beginc} }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 3,}}} \oplus }_} + 3,} + 2}} \oplus }_} + 4,} + 1}} } \\ \end \hfill \\ \end$$

(91)

(82)l+1\(\oplus\)(82)k+2, l+1

$$\begin}}_},}+1}\oplus }}_}+2,}+1}=}}_},}}\oplus }}_}+2,}}\oplus }}_},}+1}\oplus }}_}+2,}+1}\oplus }}_},}+2}\oplus }}_}+2,}+2}\end$$

(92)

(84)k+1\(\oplus\)(92)

$$\begin}}_}+1,}}\oplus }}_}+1,}}\oplus }}_},}+1}\oplus }}_}+2,}+1}=}}_},}+1}\oplus }}_}+2,}+1}\oplus }}_},}}\oplus }}_},}+2}\oplus }}_}+2,}}\oplus }}_}+2,}+2}\end$$

(93)

(83)l+1\(\oplus\)(93)

$$\begin }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_},} + 1}} \oplus }_} + 2,} + 1}} \hfill \\ = }_} - 1,} + 1}} \oplus }_},}}} \oplus }_},} + 2}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \oplus }_} + 3,} + 1}} \hfill \\ \end$$

(94)

From these results, the general formula for triple-view display (left, right, bottom) is as follows

$$\begin }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_} + 2,} + 1}} \oplus }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 3,}}} \hfill \\ }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 1,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_},}}} \oplus }_} + 4,}}} \hfill \\ }_},}}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 1}} \oplus }_} + 3,} - 1}} \oplus }_} + 3,} + 1}} \oplus }_} + 4,}}} \hfill \\ = }_} + 1,}}} \oplus }_} + 2,} - 1}} \oplus }_} + 2,} - 1}} \oplus }_} + 3,}}} \oplus }_} + 1,}}} \oplus }_} + 3,}}} \hfill \\ \end$$

Solving simultaneous equations with \(}}_},}}\), \(}}_},\mathrm}\), and \(}}_},}}\).

$$\begin}}_},}}=}}_},}+1}\oplus }}_},}}\oplus }}_},}-1}\end$$

(95)

$$\begin}}_},}}=}}_}-1,}}\oplus }}_},}}\oplus }}_}+1,}}\end$$

(96)

$$\begin}}_},}}=}}_},}-1}\oplus }}_},}}\oplus }}_},}+1}\end$$

(97)

Solve the above XOR simultaneous equations.

(95) \(\oplus\)(96)k+1, l+1

$$\begin}}_},}}\oplus }}_}+1,}+1}=}}_},}}\oplus }}_}+1,}+1}\oplus }}_},}-1}\oplus }}_}+2,}+1}\end$$

(98)

(95) \(\oplus\)(96)

$$\begin}}_},}}\oplus }}_},}}=}}_}-1,}}\oplus }}_},}+1}\oplus }}_},\mathrm-1}\oplus }}_}+1,}}\end$$

(99)

(95)k+1, l+1\(\oplus\)(96)

$$\begin}}_}+1,}+1}\oplus }}_},}}=}}_}-1,}}\oplus }}_}+1,}+2}\oplus }}_},}}\oplus }}_}+1,}+1}\end$$

(100)

(97) \(\oplus\)(97)k+1, l+1

$$\begin}}_},}}\oplus }}_}+1,}+1}=}}_},}-1}\oplus }}_}+1,}}\oplus }}_},}}\oplus }}_}+1,}+1}\oplus }}_},}+1}\oplus }}_}+1,}+2}\end$$

(101)

(100) \(\oplus\)(101)

$$\beginc} }_} + 1,} + 1}} \oplus }_},}}} \oplus }_},}}} \oplus }_} + 1,} + 1}} = }_} - 1,}}} \oplus }_},} - 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_},} + 1}} \oplus }_} + 1,} + 2}} } \\ \end$$

(102)

(99)l+2\(\oplus\)(102)

$$\begin }_} + 1,} + 1}} \oplus }_},} + 2}} \oplus }_},}}} \oplus }_},} + 2}} \oplus }_},}}} \oplus }_} + 1,} + 1}} \hfill \\ = }_} - 1,}}} \oplus }_} - 1,} + 2}} \oplus }_},} - 1}} \oplus }_},} + 3}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \hfill \\ \end$$

(103)

(97) \(\oplus\)(97)k+2, l+2

$$\begin}}_},}}\oplus }}_}+2,}+2}=}}_},}-1}\oplus }}_}+2,}+1}\oplus }}_},}}\oplus }}_}+2,}+2}\oplus }}_},}+1}\oplus }}_}+2,}+3}\end$$

(104)

(98)l+2\(\oplus\)(104)

$$\begin}}_},}+2}\oplus }}_}+1,}+3}\oplus }}_},}}\oplus }}_}+2,}+2}=}}_},}-1}\oplus }}_}+2,}+1}\oplus }}_},}}\oplus }}_},}+2}\oplus }}_}+1,}+3}\oplus }}_}+2,}+2}\end$$

(105)

(100)k+1\(\oplus\)(105)l+1

$$}}_},}+3}\oplus }}_}+2,}+1}\oplus }}_}+1,}}\oplus }}_}+1,}+4}\oplus }}_},}+1}\oplus }}_}+2,}+3}\begin=}}_},}+1}\oplus }}_},}+3}\oplus }}_}+1,}}\oplus }}_}+1,}+4}\oplus }}_}+2,}+1}\oplus }}_}+2,}+3}\end$$

(106)

(99)k+1\(\oplus\)(101)l+1

$$\beginc} }_} + 1,}}} \oplus }_} + 1,}}} \oplus }_},} + 1}} \oplus }_} + 1,} + 2}} = }_},} + 1}} \oplus }_} + 1,} + 2}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} } \\ \end$$

(107)

(98)l+1\(\oplus\)(107)

$$\begin }_},} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_},} + 1}} \oplus }_} + 1,} + 2}} \hfill \\ = }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ \end$$

(108)

From these results, the general formula for triple-view display (upper, left, bottom) is as follows

$$\begin }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_},} + 1}} \oplus }_} + 1,} + 2}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_},} + 1}} \oplus }_} + 1,}}} \hfill \\ }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_},}}} \oplus }_} + 2,} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_},} + 2}} \oplus }_} + 2,}}} \hfill \\ }_},}}} \oplus }_},} + 2}} \oplus }_} + 1,} - 1}} \oplus }_} + 1,} + 3}} \oplus }_} + 2,}}} \oplus }_} + 2,} + 2}} \hfill \\ = }_} + 1,}}} \oplus }_} + 2,} + 1}} \oplus }_} + 1,}}} \oplus }_} + 1,} + 2}} \oplus }_} + 1,} + 2}} \oplus }_} + 2,} + 1}} \hfill \\ \end$$