Таблица истинности для функции F∧(XYZ)≡(XY∨XZ)∧(YX∨ZY):


Промежуточные таблицы истинности:
XY∨XZ:
XYXZXY∨XZ
000
011
101
111

YX∨ZY:
YXZYYX∨ZY
000
011
101
111

F∧XYZ:
FXYZF∧XYZ
000
010
100
111

(XY∨XZ)∧(YX∨ZY):
XYXZYXZYXY∨XZYX∨ZY(XY∨XZ)∧(YX∨ZY)
0000000
0001010
0010010
0011010
0100100
0101111
0110111
0111111
1000100
1001111
1010111
1011111
1100100
1101111
1110111
1111111

(F∧XYZ)≡((XY∨XZ)∧(YX∨ZY)):
FXYZXYXZYXZYF∧XYZXY∨XZYX∨ZY(XY∨XZ)∧(YX∨ZY)(F∧XYZ)≡((XY∨XZ)∧(YX∨ZY))
00000000001
00000100101
00001000101
00001100101
00010001001
00010101110
00011001110
00011101110
00100001001
00100101110
00101001110
00101101110
00110001001
00110101110
00111001110
00111101110
01000000001
01000100101
01001000101
01001100101
01010001001
01010101110
01011001110
01011101110
01100001001
01100101110
01101001110
01101101110
01110001001
01110101110
01111001110
01111101110
10000000001
10000100101
10001000101
10001100101
10010001001
10010101110
10011001110
10011101110
10100001001
10100101110
10101001110
10101101110
10110001001
10110101110
10111001110
10111101110
11000010000
11000110100
11001010100
11001110100
11010011000
11010111111
11011011111
11011111111
11100011000
11100111111
11101011111
11101111111
11110011000
11110111111
11111011111
11111111111

Общая таблица истинности:

FXYZXYXZYXZYXY∨XZYX∨ZYF∧XYZ(XY∨XZ)∧(YX∨ZY)F∧(XYZ)≡(XY∨XZ)∧(YX∨ZY)
00000000001
00000101001
00001001001
00001101001
00010010001
00010111010
00011011010
00011111010
00100010001
00100111010
00101011010
00101111010
00110010001
00110111010
00111011010
00111111010
01000000001
01000101001
01001001001
01001101001
01010010001
01010111010
01011011010
01011111010
01100010001
01100111010
01101011010
01101111010
01110010001
01110111010
01111011010
01111111010
10000000001
10000101001
10001001001
10001101001
10010010001
10010111010
10011011010
10011111010
10100010001
10100111010
10101011010
10101111010
10110010001
10110111010
10111011010
10111111010
11000000100
11000101100
11001001100
11001101100
11010010100
11010111111
11011011111
11011111111
11100010100
11100111111
11101011111
11101111111
11110010100
11110111111
11111011111
11111111111

Логическая схема:

Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
FXYZXYXZYXZYF
0000001
0000011
0000101
0000111
0001001
0001010
0001100
0001110
0010001
0010010
0010100
0010110
0011001
0011010
0011100
0011110
0100001
0100011
0100101
0100111
0101001
0101010
0101100
0101110
0110001
0110010
0110100
0110110
0111001
0111010
0111100
0111110
1000001
1000011
1000101
1000111
1001001
1001010
1001100
1001110
1010001
1010010
1010100
1010110
1011001
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101011
1101101
1101111
1110000
1110011
1110101
1110111
1111000
1111011
1111101
1111111
Fсднф = ¬F∧¬XYZ∧¬XY∧¬XZ∧¬YX∧¬ZY ∨ ¬F∧¬XYZ∧¬XY∧¬XZ∧¬YX∧ZY ∨ ¬F∧¬XYZ∧¬XY∧¬XZ∧YX∧¬ZY ∨ ¬F∧¬XYZ∧¬XY∧¬XZ∧YX∧ZY ∨ ¬F∧¬XYZ∧¬XY∧XZ∧¬YX∧¬ZY ∨ ¬F∧¬XYZ∧XY∧¬XZ∧¬YX∧¬ZY ∨ ¬F∧¬XYZ∧XY∧XZ∧¬YX∧¬ZY ∨ ¬F∧XYZ∧¬XY∧¬XZ∧¬YX∧¬ZY ∨ ¬F∧XYZ∧¬XY∧¬XZ∧¬YX∧ZY ∨ ¬F∧XYZ∧¬XY∧¬XZ∧YX∧¬ZY ∨ ¬F∧XYZ∧¬XY∧¬XZ∧YX∧ZY ∨ ¬F∧XYZ∧¬XY∧XZ∧¬YX∧¬ZY ∨ ¬F∧XYZ∧XY∧¬XZ∧¬YX∧¬ZY ∨ ¬F∧XYZ∧XY∧XZ∧¬YX∧¬ZY ∨ F∧¬XYZ∧¬XY∧¬XZ∧¬YX∧¬ZY ∨ F∧¬XYZ∧¬XY∧¬XZ∧¬YX∧ZY ∨ F∧¬XYZ∧¬XY∧¬XZ∧YX∧¬ZY ∨ F∧¬XYZ∧¬XY∧¬XZ∧YX∧ZY ∨ F∧¬XYZ∧¬XY∧XZ∧¬YX∧¬ZY ∨ F∧¬XYZ∧XY∧¬XZ∧¬YX∧¬ZY ∨ F∧¬XYZ∧XY∧XZ∧¬YX∧¬ZY ∨ F∧XYZ∧¬XY∧XZ∧¬YX∧ZY ∨ F∧XYZ∧¬XY∧XZ∧YX∧¬ZY ∨ F∧XYZ∧¬XY∧XZ∧YX∧ZY ∨ F∧XYZ∧XY∧¬XZ∧¬YX∧ZY ∨ F∧XYZ∧XY∧¬XZ∧YX∧¬ZY ∨ F∧XYZ∧XY∧¬XZ∧YX∧ZY ∨ F∧XYZ∧XY∧XZ∧¬YX∧ZY ∨ F∧XYZ∧XY∧XZ∧YX∧¬ZY ∨ F∧XYZ∧XY∧XZ∧YX∧ZY
Логическая cхема:

Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
FXYZXYXZYXZYF
0000001
0000011
0000101
0000111
0001001
0001010
0001100
0001110
0010001
0010010
0010100
0010110
0011001
0011010
0011100
0011110
0100001
0100011
0100101
0100111
0101001
0101010
0101100
0101110
0110001
0110010
0110100
0110110
0111001
0111010
0111100
0111110
1000001
1000011
1000101
1000111
1001001
1001010
1001100
1001110
1010001
1010010
1010100
1010110
1011001
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101011
1101101
1101111
1110000
1110011
1110101
1110111
1111000
1111011
1111101
1111111
Fскнф = (F∨XYZ∨XY∨¬XZ∨YX∨¬ZY) ∧ (F∨XYZ∨XY∨¬XZ∨¬YX∨ZY) ∧ (F∨XYZ∨XY∨¬XZ∨¬YX∨¬ZY) ∧ (F∨XYZ∨¬XY∨XZ∨YX∨¬ZY) ∧ (F∨XYZ∨¬XY∨XZ∨¬YX∨ZY) ∧ (F∨XYZ∨¬XY∨XZ∨¬YX∨¬ZY) ∧ (F∨XYZ∨¬XY∨¬XZ∨YX∨¬ZY) ∧ (F∨XYZ∨¬XY∨¬XZ∨¬YX∨ZY) ∧ (F∨XYZ∨¬XY∨¬XZ∨¬YX∨¬ZY) ∧ (F∨¬XYZ∨XY∨¬XZ∨YX∨¬ZY) ∧ (F∨¬XYZ∨XY∨¬XZ∨¬YX∨ZY) ∧ (F∨¬XYZ∨XY∨¬XZ∨¬YX∨¬ZY) ∧ (F∨¬XYZ∨¬XY∨XZ∨YX∨¬ZY) ∧ (F∨¬XYZ∨¬XY∨XZ∨¬YX∨ZY) ∧ (F∨¬XYZ∨¬XY∨XZ∨¬YX∨¬ZY) ∧ (F∨¬XYZ∨¬XY∨¬XZ∨YX∨¬ZY) ∧ (F∨¬XYZ∨¬XY∨¬XZ∨¬YX∨ZY) ∧ (F∨¬XYZ∨¬XY∨¬XZ∨¬YX∨¬ZY) ∧ (¬F∨XYZ∨XY∨¬XZ∨YX∨¬ZY) ∧ (¬F∨XYZ∨XY∨¬XZ∨¬YX∨ZY) ∧ (¬F∨XYZ∨XY∨¬XZ∨¬YX∨¬ZY) ∧ (¬F∨XYZ∨¬XY∨XZ∨YX∨¬ZY) ∧ (¬F∨XYZ∨¬XY∨XZ∨¬YX∨ZY) ∧ (¬F∨XYZ∨¬XY∨XZ∨¬YX∨¬ZY) ∧ (¬F∨XYZ∨¬XY∨¬XZ∨YX∨¬ZY) ∧ (¬F∨XYZ∨¬XY∨¬XZ∨¬YX∨ZY) ∧ (¬F∨XYZ∨¬XY∨¬XZ∨¬YX∨¬ZY) ∧ (¬F∨¬XYZ∨XY∨XZ∨YX∨ZY) ∧ (¬F∨¬XYZ∨XY∨XZ∨YX∨¬ZY) ∧ (¬F∨¬XYZ∨XY∨XZ∨¬YX∨ZY) ∧ (¬F∨¬XYZ∨XY∨XZ∨¬YX∨¬ZY) ∧ (¬F∨¬XYZ∨XY∨¬XZ∨YX∨ZY) ∧ (¬F∨¬XYZ∨¬XY∨XZ∨YX∨ZY) ∧ (¬F∨¬XYZ∨¬XY∨¬XZ∨YX∨ZY)
Логическая cхема:

Построение полинома Жегалкина:

По таблице истинности функции
FXYZXYXZYXZYFж
0000001
0000011
0000101
0000111
0001001
0001010
0001100
0001110
0010001
0010010
0010100
0010110
0011001
0011010
0011100
0011110
0100001
0100011
0100101
0100111
0101001
0101010
0101100
0101110
0110001
0110010
0110100
0110110
0111001
0111010
0111100
0111110
1000001
1000011
1000101
1000111
1001001
1001010
1001100
1001110
1010001
1010010
1010100
1010110
1011001
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101011
1101101
1101111
1110000
1110011
1110101
1110111
1111000
1111011
1111101
1111111

Построим полином Жегалкина:
Fж = C000000 ⊕ C100000∧F ⊕ C010000∧XYZ ⊕ C001000∧XY ⊕ C000100∧XZ ⊕ C000010∧YX ⊕ C000001∧ZY ⊕ C110000∧F∧XYZ ⊕ C101000∧F∧XY ⊕ C100100∧F∧XZ ⊕ C100010∧F∧YX ⊕ C100001∧F∧ZY ⊕ C011000∧XYZ∧XY ⊕ C010100∧XYZ∧XZ ⊕ C010010∧XYZ∧YX ⊕ C010001∧XYZ∧ZY ⊕ C001100∧XY∧XZ ⊕ C001010∧XY∧YX ⊕ C001001∧XY∧ZY ⊕ C000110∧XZ∧YX ⊕ C000101∧XZ∧ZY ⊕ C000011∧YX∧ZY ⊕ C111000∧F∧XYZ∧XY ⊕ C110100∧F∧XYZ∧XZ ⊕ C110010∧F∧XYZ∧YX ⊕ C110001∧F∧XYZ∧ZY ⊕ C101100∧F∧XY∧XZ ⊕ C101010∧F∧XY∧YX ⊕ C101001∧F∧XY∧ZY ⊕ C100110∧F∧XZ∧YX ⊕ C100101∧F∧XZ∧ZY ⊕ C100011∧F∧YX∧ZY ⊕ C011100∧XYZ∧XY∧XZ ⊕ C011010∧XYZ∧XY∧YX ⊕ C011001∧XYZ∧XY∧ZY ⊕ C010110∧XYZ∧XZ∧YX ⊕ C010101∧XYZ∧XZ∧ZY ⊕ C010011∧XYZ∧YX∧ZY ⊕ C001110∧XY∧XZ∧YX ⊕ C001101∧XY∧XZ∧ZY ⊕ C001011∧XY∧YX∧ZY ⊕ C000111∧XZ∧YX∧ZY ⊕ C111100∧F∧XYZ∧XY∧XZ ⊕ C111010∧F∧XYZ∧XY∧YX ⊕ C111001∧F∧XYZ∧XY∧ZY ⊕ C110110∧F∧XYZ∧XZ∧YX ⊕ C110101∧F∧XYZ∧XZ∧ZY ⊕ C110011∧F∧XYZ∧YX∧ZY ⊕ C101110∧F∧XY∧XZ∧YX ⊕ C101101∧F∧XY∧XZ∧ZY ⊕ C101011∧F∧XY∧YX∧ZY ⊕ C100111∧F∧XZ∧YX∧ZY ⊕ C011110∧XYZ∧XY∧XZ∧YX ⊕ C011101∧XYZ∧XY∧XZ∧ZY ⊕ C011011∧XYZ∧XY∧YX∧ZY ⊕ C010111∧XYZ∧XZ∧YX∧ZY ⊕ C001111∧XY∧XZ∧YX∧ZY ⊕ C111110∧F∧XYZ∧XY∧XZ∧YX ⊕ C111101∧F∧XYZ∧XY∧XZ∧ZY ⊕ C111011∧F∧XYZ∧XY∧YX∧ZY ⊕ C110111∧F∧XYZ∧XZ∧YX∧ZY ⊕ C101111∧F∧XY∧XZ∧YX∧ZY ⊕ C011111∧XYZ∧XY∧XZ∧YX∧ZY ⊕ C111111∧F∧XYZ∧XY∧XZ∧YX∧ZY

Так как Fж(000000) = 1, то С000000 = 1.

Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы:
Fж(100000) = С000000 ⊕ С100000 = 1 => С100000 = 1 ⊕ 1 = 0
Fж(010000) = С000000 ⊕ С010000 = 1 => С010000 = 1 ⊕ 1 = 0
Fж(001000) = С000000 ⊕ С001000 = 1 => С001000 = 1 ⊕ 1 = 0
Fж(000100) = С000000 ⊕ С000100 = 1 => С000100 = 1 ⊕ 1 = 0
Fж(000010) = С000000 ⊕ С000010 = 1 => С000010 = 1 ⊕ 1 = 0
Fж(000001) = С000000 ⊕ С000001 = 1 => С000001 = 1 ⊕ 1 = 0
Fж(110000) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С110000 = 0 => С110000 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(101000) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С101000 = 1 => С101000 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(100100) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С100100 = 1 => С100100 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(100010) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С100010 = 1 => С100010 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(100001) = С000000 ⊕ С100000 ⊕ С000001 ⊕ С100001 = 1 => С100001 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(011000) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С011000 = 1 => С011000 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010100) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С010100 = 1 => С010100 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010010) = С000000 ⊕ С010000 ⊕ С000010 ⊕ С010010 = 1 => С010010 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010001) = С000000 ⊕ С010000 ⊕ С000001 ⊕ С010001 = 1 => С010001 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001100) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С001100 = 1 => С001100 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001010) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С001010 = 0 => С001010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(001001) = С000000 ⊕ С001000 ⊕ С000001 ⊕ С001001 = 0 => С001001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(000110) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000110 = 0 => С000110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(000101) = С000000 ⊕ С000100 ⊕ С000001 ⊕ С000101 = 0 => С000101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(000011) = С000000 ⊕ С000010 ⊕ С000001 ⊕ С000011 = 1 => С000011 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(111000) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С110000 ⊕ С101000 ⊕ С011000 ⊕ С111000 = 0 => С111000 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110100) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С110000 ⊕ С100100 ⊕ С010100 ⊕ С110100 = 0 => С110100 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110010) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000010 ⊕ С110000 ⊕ С100010 ⊕ С010010 ⊕ С110010 = 0 => С110010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110001) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000001 ⊕ С110000 ⊕ С100001 ⊕ С010001 ⊕ С110001 = 0 => С110001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101100) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С101000 ⊕ С100100 ⊕ С001100 ⊕ С101100 = 1 => С101100 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(101010) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000010 ⊕ С101000 ⊕ С100010 ⊕ С001010 ⊕ С101010 = 0 => С101010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(101001) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000001 ⊕ С101000 ⊕ С100001 ⊕ С001001 ⊕ С101001 = 0 => С101001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(100110) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000010 ⊕ С100100 ⊕ С100010 ⊕ С000110 ⊕ С100110 = 0 => С100110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(100101) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000001 ⊕ С100100 ⊕ С100001 ⊕ С000101 ⊕ С100101 = 0 => С100101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(100011) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С000001 ⊕ С100010 ⊕ С100001 ⊕ С000011 ⊕ С100011 = 1 => С100011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(011100) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С011000 ⊕ С010100 ⊕ С001100 ⊕ С011100 = 1 => С011100 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(011010) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С011000 ⊕ С010010 ⊕ С001010 ⊕ С011010 = 0 => С011010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(011001) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000001 ⊕ С011000 ⊕ С010001 ⊕ С001001 ⊕ С011001 = 0 => С011001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(010110) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С010100 ⊕ С010010 ⊕ С000110 ⊕ С010110 = 0 => С010110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(010101) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000001 ⊕ С010100 ⊕ С010001 ⊕ С000101 ⊕ С010101 = 0 => С010101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(010011) = С000000 ⊕ С010000 ⊕ С000010 ⊕ С000001 ⊕ С010010 ⊕ С010001 ⊕ С000011 ⊕ С010011 = 1 => С010011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001110) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С001110 = 0 => С001110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 = 1
Fж(001101) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С001101 = 0 => С001101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 = 1
Fж(001011) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С001011 = 0 => С001011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 = 1
Fж(000111) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С000111 = 0 => С000111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 = 1
Fж(111100) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С110000 ⊕ С101000 ⊕ С100100 ⊕ С011000 ⊕ С010100 ⊕ С001100 ⊕ С111000 ⊕ С110100 ⊕ С101100 ⊕ С011100 ⊕ С111100 = 0 => С111100 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(111010) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С110000 ⊕ С101000 ⊕ С100010 ⊕ С011000 ⊕ С010010 ⊕ С001010 ⊕ С111000 ⊕ С110010 ⊕ С101010 ⊕ С011010 ⊕ С111010 = 1 => С111010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(111001) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000001 ⊕ С110000 ⊕ С101000 ⊕ С100001 ⊕ С011000 ⊕ С010001 ⊕ С001001 ⊕ С111000 ⊕ С110001 ⊕ С101001 ⊕ С011001 ⊕ С111001 = 1 => С111001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(110110) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С110000 ⊕ С100100 ⊕ С100010 ⊕ С010100 ⊕ С010010 ⊕ С000110 ⊕ С110100 ⊕ С110010 ⊕ С100110 ⊕ С010110 ⊕ С110110 = 1 => С110110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(110101) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С000001 ⊕ С110000 ⊕ С100100 ⊕ С100001 ⊕ С010100 ⊕ С010001 ⊕ С000101 ⊕ С110100 ⊕ С110001 ⊕ С100101 ⊕ С010101 ⊕ С110101 = 1 => С110101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(110011) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000010 ⊕ С000001 ⊕ С110000 ⊕ С100010 ⊕ С100001 ⊕ С010010 ⊕ С010001 ⊕ С000011 ⊕ С110010 ⊕ С110001 ⊕ С100011 ⊕ С010011 ⊕ С110011 = 0 => С110011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101110) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С101000 ⊕ С100100 ⊕ С100010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С101100 ⊕ С101010 ⊕ С100110 ⊕ С001110 ⊕ С101110 = 0 => С101110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(101101) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С101000 ⊕ С100100 ⊕ С100001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С101100 ⊕ С101001 ⊕ С100101 ⊕ С001101 ⊕ С101101 = 0 => С101101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(101011) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С101000 ⊕ С100010 ⊕ С100001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С101010 ⊕ С101001 ⊕ С100011 ⊕ С001011 ⊕ С101011 = 0 => С101011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(100111) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С100100 ⊕ С100010 ⊕ С100001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С100110 ⊕ С100101 ⊕ С100011 ⊕ С000111 ⊕ С100111 = 0 => С100111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(011110) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С011000 ⊕ С010100 ⊕ С010010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С011100 ⊕ С011010 ⊕ С010110 ⊕ С001110 ⊕ С011110 = 0 => С011110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(011101) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С011000 ⊕ С010100 ⊕ С010001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С011100 ⊕ С011001 ⊕ С010101 ⊕ С001101 ⊕ С011101 = 0 => С011101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(011011) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С011000 ⊕ С010010 ⊕ С010001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С011010 ⊕ С011001 ⊕ С010011 ⊕ С001011 ⊕ С011011 = 0 => С011011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(010111) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С010100 ⊕ С010010 ⊕ С010001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С010110 ⊕ С010101 ⊕ С010011 ⊕ С000111 ⊕ С010111 = 0 => С010111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(001111) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С001111 = 0 => С001111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
Fж(111110) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С110000 ⊕ С101000 ⊕ С100100 ⊕ С100010 ⊕ С011000 ⊕ С010100 ⊕ С010010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С111000 ⊕ С110100 ⊕ С110010 ⊕ С101100 ⊕ С101010 ⊕ С100110 ⊕ С011100 ⊕ С011010 ⊕ С010110 ⊕ С001110 ⊕ С111100 ⊕ С111010 ⊕ С110110 ⊕ С101110 ⊕ С011110 ⊕ С111110 = 1 => С111110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(111101) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С110000 ⊕ С101000 ⊕ С100100 ⊕ С100001 ⊕ С011000 ⊕ С010100 ⊕ С010001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С111000 ⊕ С110100 ⊕ С110001 ⊕ С101100 ⊕ С101001 ⊕ С100101 ⊕ С011100 ⊕ С011001 ⊕ С010101 ⊕ С001101 ⊕ С111100 ⊕ С111001 ⊕ С110101 ⊕ С101101 ⊕ С011101 ⊕ С111101 = 1 => С111101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(111011) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С110000 ⊕ С101000 ⊕ С100010 ⊕ С100001 ⊕ С011000 ⊕ С010010 ⊕ С010001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С111000 ⊕ С110010 ⊕ С110001 ⊕ С101010 ⊕ С101001 ⊕ С100011 ⊕ С011010 ⊕ С011001 ⊕ С010011 ⊕ С001011 ⊕ С111010 ⊕ С111001 ⊕ С110011 ⊕ С101011 ⊕ С011011 ⊕ С111011 = 1 => С111011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(110111) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С110000 ⊕ С100100 ⊕ С100010 ⊕ С100001 ⊕ С010100 ⊕ С010010 ⊕ С010001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С110100 ⊕ С110010 ⊕ С110001 ⊕ С100110 ⊕ С100101 ⊕ С100011 ⊕ С010110 ⊕ С010101 ⊕ С010011 ⊕ С000111 ⊕ С110110 ⊕ С110101 ⊕ С110011 ⊕ С100111 ⊕ С010111 ⊕ С110111 = 1 => С110111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(101111) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С101000 ⊕ С100100 ⊕ С100010 ⊕ С100001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С101100 ⊕ С101010 ⊕ С101001 ⊕ С100110 ⊕ С100101 ⊕ С100011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С101110 ⊕ С101101 ⊕ С101011 ⊕ С100111 ⊕ С001111 ⊕ С101111 = 0 => С101111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(011111) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С011000 ⊕ С010100 ⊕ С010010 ⊕ С010001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С011100 ⊕ С011010 ⊕ С011001 ⊕ С010110 ⊕ С010101 ⊕ С010011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С011110 ⊕ С011101 ⊕ С011011 ⊕ С010111 ⊕ С001111 ⊕ С011111 = 0 => С011111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
Fж(111111) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С110000 ⊕ С101000 ⊕ С100100 ⊕ С100010 ⊕ С100001 ⊕ С011000 ⊕ С010100 ⊕ С010010 ⊕ С010001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С111000 ⊕ С110100 ⊕ С110010 ⊕ С110001 ⊕ С101100 ⊕ С101010 ⊕ С101001 ⊕ С100110 ⊕ С100101 ⊕ С100011 ⊕ С011100 ⊕ С011010 ⊕ С011001 ⊕ С010110 ⊕ С010101 ⊕ С010011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С111100 ⊕ С111010 ⊕ С111001 ⊕ С110110 ⊕ С110101 ⊕ С110011 ⊕ С101110 ⊕ С101101 ⊕ С101011 ⊕ С100111 ⊕ С011110 ⊕ С011101 ⊕ С011011 ⊕ С010111 ⊕ С001111 ⊕ С111110 ⊕ С111101 ⊕ С111011 ⊕ С110111 ⊕ С101111 ⊕ С011111 ⊕ С111111 = 1 => С111111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0

Таким образом, полином Жегалкина будет равен:
Fж = 1 ⊕ F∧XYZ ⊕ XY∧YX ⊕ XY∧ZY ⊕ XZ∧YX ⊕ XZ∧ZY ⊕ XY∧XZ∧YX ⊕ XY∧XZ∧ZY ⊕ XY∧YX∧ZY ⊕ XZ∧YX∧ZY ⊕ XY∧XZ∧YX∧ZY
Логическая схема, соответствующая полиному Жегалкина:

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