Таблица истинности для функции A∧B∧C∨X∨Y∨Z:


Промежуточные таблицы истинности:
A∧B:
ABA∧B
000
010
100
111

(A∧B)∧C:
ABCA∧B(A∧B)∧C
00000
00100
01000
01100
10000
10100
11010
11111

((A∧B)∧C)∨X:
ABCXA∧B(A∧B)∧C((A∧B)∧C)∨X
0000000
0001001
0010000
0011001
0100000
0101001
0110000
0111001
1000000
1001001
1010000
1011001
1100100
1101101
1110111
1111111

(((A∧B)∧C)∨X)∨Y:
ABCXYA∧B(A∧B)∧C((A∧B)∧C)∨X(((A∧B)∧C)∨X)∨Y
000000000
000010001
000100011
000110011
001000000
001010001
001100011
001110011
010000000
010010001
010100011
010110011
011000000
011010001
011100011
011110011
100000000
100010001
100100011
100110011
101000000
101010001
101100011
101110011
110001000
110011001
110101011
110111011
111001111
111011111
111101111
111111111

((((A∧B)∧C)∨X)∨Y)∨Z:
ABCXYZA∧B(A∧B)∧C((A∧B)∧C)∨X(((A∧B)∧C)∨X)∨Y((((A∧B)∧C)∨X)∨Y)∨Z
00000000000
00000100001
00001000011
00001100011
00010000111
00010100111
00011000111
00011100111
00100000000
00100100001
00101000011
00101100011
00110000111
00110100111
00111000111
00111100111
01000000000
01000100001
01001000011
01001100011
01010000111
01010100111
01011000111
01011100111
01100000000
01100100001
01101000011
01101100011
01110000111
01110100111
01111000111
01111100111
10000000000
10000100001
10001000011
10001100011
10010000111
10010100111
10011000111
10011100111
10100000000
10100100001
10101000011
10101100011
10110000111
10110100111
10111000111
10111100111
11000010000
11000110001
11001010011
11001110011
11010010111
11010110111
11011010111
11011110111
11100011111
11100111111
11101011111
11101111111
11110011111
11110111111
11111011111
11111111111

Общая таблица истинности:

ABCXYZA∧B(A∧B)∧C((A∧B)∧C)∨X(((A∧B)∧C)∨X)∨YA∧B∧C∨X∨Y∨Z
00000000000
00000100001
00001000011
00001100011
00010000111
00010100111
00011000111
00011100111
00100000000
00100100001
00101000011
00101100011
00110000111
00110100111
00111000111
00111100111
01000000000
01000100001
01001000011
01001100011
01010000111
01010100111
01011000111
01011100111
01100000000
01100100001
01101000011
01101100011
01110000111
01110100111
01111000111
01111100111
10000000000
10000100001
10001000011
10001100011
10010000111
10010100111
10011000111
10011100111
10100000000
10100100001
10101000011
10101100011
10110000111
10110100111
10111000111
10111100111
11000010000
11000110001
11001010011
11001110011
11010010111
11010110111
11011010111
11011110111
11100011111
11100111111
11101011111
11101111111
11110011111
11110111111
11111011111
11111111111

Логическая схема:

Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
ABCXYZF
0000000
0000011
0000101
0000111
0001001
0001011
0001101
0001111
0010000
0010011
0010101
0010111
0011001
0011011
0011101
0011111
0100000
0100011
0100101
0100111
0101001
0101011
0101101
0101111
0110000
0110011
0110101
0110111
0111001
0111011
0111101
0111111
1000000
1000011
1000101
1000111
1001001
1001011
1001101
1001111
1010000
1010011
1010101
1010111
1011001
1011011
1011101
1011111
1100000
1100011
1100101
1100111
1101001
1101011
1101101
1101111
1110001
1110011
1110101
1110111
1111001
1111011
1111101
1111111
Fсднф = ¬A∧¬B∧¬C∧¬X∧¬Y∧Z ∨ ¬A∧¬B∧¬C∧¬X∧Y∧¬Z ∨ ¬A∧¬B∧¬C∧¬X∧Y∧Z ∨ ¬A∧¬B∧¬C∧X∧¬Y∧¬Z ∨ ¬A∧¬B∧¬C∧X∧¬Y∧Z ∨ ¬A∧¬B∧¬C∧X∧Y∧¬Z ∨ ¬A∧¬B∧¬C∧X∧Y∧Z ∨ ¬A∧¬B∧C∧¬X∧¬Y∧Z ∨ ¬A∧¬B∧C∧¬X∧Y∧¬Z ∨ ¬A∧¬B∧C∧¬X∧Y∧Z ∨ ¬A∧¬B∧C∧X∧¬Y∧¬Z ∨ ¬A∧¬B∧C∧X∧¬Y∧Z ∨ ¬A∧¬B∧C∧X∧Y∧¬Z ∨ ¬A∧¬B∧C∧X∧Y∧Z ∨ ¬A∧B∧¬C∧¬X∧¬Y∧Z ∨ ¬A∧B∧¬C∧¬X∧Y∧¬Z ∨ ¬A∧B∧¬C∧¬X∧Y∧Z ∨ ¬A∧B∧¬C∧X∧¬Y∧¬Z ∨ ¬A∧B∧¬C∧X∧¬Y∧Z ∨ ¬A∧B∧¬C∧X∧Y∧¬Z ∨ ¬A∧B∧¬C∧X∧Y∧Z ∨ ¬A∧B∧C∧¬X∧¬Y∧Z ∨ ¬A∧B∧C∧¬X∧Y∧¬Z ∨ ¬A∧B∧C∧¬X∧Y∧Z ∨ ¬A∧B∧C∧X∧¬Y∧¬Z ∨ ¬A∧B∧C∧X∧¬Y∧Z ∨ ¬A∧B∧C∧X∧Y∧¬Z ∨ ¬A∧B∧C∧X∧Y∧Z ∨ A∧¬B∧¬C∧¬X∧¬Y∧Z ∨ A∧¬B∧¬C∧¬X∧Y∧¬Z ∨ A∧¬B∧¬C∧¬X∧Y∧Z ∨ A∧¬B∧¬C∧X∧¬Y∧¬Z ∨ A∧¬B∧¬C∧X∧¬Y∧Z ∨ A∧¬B∧¬C∧X∧Y∧¬Z ∨ A∧¬B∧¬C∧X∧Y∧Z ∨ A∧¬B∧C∧¬X∧¬Y∧Z ∨ A∧¬B∧C∧¬X∧Y∧¬Z ∨ A∧¬B∧C∧¬X∧Y∧Z ∨ A∧¬B∧C∧X∧¬Y∧¬Z ∨ A∧¬B∧C∧X∧¬Y∧Z ∨ A∧¬B∧C∧X∧Y∧¬Z ∨ A∧¬B∧C∧X∧Y∧Z ∨ A∧B∧¬C∧¬X∧¬Y∧Z ∨ A∧B∧¬C∧¬X∧Y∧¬Z ∨ A∧B∧¬C∧¬X∧Y∧Z ∨ A∧B∧¬C∧X∧¬Y∧¬Z ∨ A∧B∧¬C∧X∧¬Y∧Z ∨ A∧B∧¬C∧X∧Y∧¬Z ∨ A∧B∧¬C∧X∧Y∧Z ∨ A∧B∧C∧¬X∧¬Y∧¬Z ∨ A∧B∧C∧¬X∧¬Y∧Z ∨ A∧B∧C∧¬X∧Y∧¬Z ∨ A∧B∧C∧¬X∧Y∧Z ∨ A∧B∧C∧X∧¬Y∧¬Z ∨ A∧B∧C∧X∧¬Y∧Z ∨ A∧B∧C∧X∧Y∧¬Z ∨ A∧B∧C∧X∧Y∧Z
Логическая cхема:

Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
ABCXYZF
0000000
0000011
0000101
0000111
0001001
0001011
0001101
0001111
0010000
0010011
0010101
0010111
0011001
0011011
0011101
0011111
0100000
0100011
0100101
0100111
0101001
0101011
0101101
0101111
0110000
0110011
0110101
0110111
0111001
0111011
0111101
0111111
1000000
1000011
1000101
1000111
1001001
1001011
1001101
1001111
1010000
1010011
1010101
1010111
1011001
1011011
1011101
1011111
1100000
1100011
1100101
1100111
1101001
1101011
1101101
1101111
1110001
1110011
1110101
1110111
1111001
1111011
1111101
1111111
Fскнф = (A∨B∨C∨X∨Y∨Z) ∧ (A∨B∨¬C∨X∨Y∨Z) ∧ (A∨¬B∨C∨X∨Y∨Z) ∧ (A∨¬B∨¬C∨X∨Y∨Z) ∧ (¬A∨B∨C∨X∨Y∨Z) ∧ (¬A∨B∨¬C∨X∨Y∨Z) ∧ (¬A∨¬B∨C∨X∨Y∨Z)
Логическая cхема:

Построение полинома Жегалкина:

По таблице истинности функции
ABCXYZFж
0000000
0000011
0000101
0000111
0001001
0001011
0001101
0001111
0010000
0010011
0010101
0010111
0011001
0011011
0011101
0011111
0100000
0100011
0100101
0100111
0101001
0101011
0101101
0101111
0110000
0110011
0110101
0110111
0111001
0111011
0111101
0111111
1000000
1000011
1000101
1000111
1001001
1001011
1001101
1001111
1010000
1010011
1010101
1010111
1011001
1011011
1011101
1011111
1100000
1100011
1100101
1100111
1101001
1101011
1101101
1101111
1110001
1110011
1110101
1110111
1111001
1111011
1111101
1111111

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

Так как Fж(000000) = 0, то С000000 = 0.

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

Таким образом, полином Жегалкина будет равен:
Fж = X ⊕ Y ⊕ Z ⊕ X∧Y ⊕ X∧Z ⊕ Y∧Z ⊕ A∧B∧C ⊕ X∧Y∧Z ⊕ A∧B∧C∧X ⊕ A∧B∧C∧Y ⊕ A∧B∧C∧Z ⊕ A∧B∧C∧X∧Y ⊕ A∧B∧C∧X∧Z ⊕ A∧B∧C∧Y∧Z ⊕ A∧B∧C∧X∧Y∧Z
Логическая схема, соответствующая полиному Жегалкина:

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