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
0001000
0010000
0011000
0100000
0101000
0110000
0111000
1000000
1001000
1010000
1011000
1100100
1101100
1110110
1111111

(((A∧B)∧C)∧X)∧Y:
ABCXYA∧B(A∧B)∧C((A∧B)∧C)∧X(((A∧B)∧C)∧X)∧Y
000000000
000010000
000100000
000110000
001000000
001010000
001100000
001110000
010000000
010010000
010100000
010110000
011000000
011010000
011100000
011110000
100000000
100010000
100100000
100110000
101000000
101010000
101100000
101110000
110001000
110011000
110101000
110111000
111001100
111011100
111101110
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
00000100000
00001000000
00001100000
00010000000
00010100000
00011000000
00011100000
00100000000
00100100000
00101000000
00101100000
00110000000
00110100000
00111000000
00111100000
01000000000
01000100000
01001000000
01001100000
01010000000
01010100000
01011000000
01011100000
01100000000
01100100000
01101000000
01101100000
01110000000
01110100000
01111000000
01111100000
10000000000
10000100000
10001000000
10001100000
10010000000
10010100000
10011000000
10011100000
10100000000
10100100000
10101000000
10101100000
10110000000
10110100000
10111000000
10111100000
11000010000
11000110000
11001010000
11001110000
11010010000
11010110000
11011010000
11011110000
11100011000
11100111000
11101011000
11101111000
11110011100
11110111100
11111011110
11111111111

Общая таблица истинности:

ABCXYZA∧B(A∧B)∧C((A∧B)∧C)∧X(((A∧B)∧C)∧X)∧Y(A∧B∧C)∧X∧Y∧Z
00000000000
00000100000
00001000000
00001100000
00010000000
00010100000
00011000000
00011100000
00100000000
00100100000
00101000000
00101100000
00110000000
00110100000
00111000000
00111100000
01000000000
01000100000
01001000000
01001100000
01010000000
01010100000
01011000000
01011100000
01100000000
01100100000
01101000000
01101100000
01110000000
01110100000
01111000000
01111100000
10000000000
10000100000
10001000000
10001100000
10010000000
10010100000
10011000000
10011100000
10100000000
10100100000
10101000000
10101100000
10110000000
10110100000
10111000000
10111100000
11000010000
11000110000
11001010000
11001110000
11010010000
11010110000
11011010000
11011110000
11100011000
11100111000
11101011000
11101111000
11110011100
11110111100
11111011110
11111111111

Логическая схема:

Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
ABCXYZF
0000000
0000010
0000100
0000110
0001000
0001010
0001100
0001110
0010000
0010010
0010100
0010110
0011000
0011010
0011100
0011110
0100000
0100010
0100100
0100110
0101000
0101010
0101100
0101110
0110000
0110010
0110100
0110110
0111000
0111010
0111100
0111110
1000000
1000010
1000100
1000110
1001000
1001010
1001100
1001110
1010000
1010010
1010100
1010110
1011000
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101010
1101100
1101110
1110000
1110010
1110100
1110110
1111000
1111010
1111100
1111111
Fсднф = A∧B∧C∧X∧Y∧Z
Логическая cхема:

Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
ABCXYZF
0000000
0000010
0000100
0000110
0001000
0001010
0001100
0001110
0010000
0010010
0010100
0010110
0011000
0011010
0011100
0011110
0100000
0100010
0100100
0100110
0101000
0101010
0101100
0101110
0110000
0110010
0110100
0110110
0111000
0111010
0111100
0111110
1000000
1000010
1000100
1000110
1001000
1001010
1001100
1001110
1010000
1010010
1010100
1010110
1011000
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101010
1101100
1101110
1110000
1110010
1110100
1110110
1111000
1111010
1111100
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) ∧ (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:

Построение полинома Жегалкина:

По таблице истинности функции
ABCXYZFж
0000000
0000010
0000100
0000110
0001000
0001010
0001100
0001110
0010000
0010010
0010100
0010110
0011000
0011010
0011100
0011110
0100000
0100010
0100100
0100110
0101000
0101010
0101100
0101110
0110000
0110010
0110100
0110110
0111000
0111010
0111100
0111110
1000000
1000010
1000100
1000110
1001000
1001010
1001100
1001110
1010000
1010010
1010100
1010110
1011000
1011010
1011100
1011110
1100000
1100010
1100100
1100110
1101000
1101010
1101100
1101110
1110000
1110010
1110100
1110110
1111000
1111010
1111100
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 = 0 => С000100 = 0 ⊕ 0 = 0
Fж(000010) = С000000 ⊕ С000010 = 0 => С000010 = 0 ⊕ 0 = 0
Fж(000001) = С000000 ⊕ С000001 = 0 => С000001 = 0 ⊕ 0 = 0
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 = 0 => С100100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100010) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С100010 = 0 => С100010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100001) = С000000 ⊕ С100000 ⊕ С000001 ⊕ С100001 = 0 => С100001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011000) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С011000 = 0 => С011000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010100) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С010100 = 0 => С010100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010010) = С000000 ⊕ С010000 ⊕ С000010 ⊕ С010010 = 0 => С010010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010001) = С000000 ⊕ С010000 ⊕ С000001 ⊕ С010001 = 0 => С010001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001100) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С001100 = 0 => С001100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001010) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С001010 = 0 => С001010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001001) = С000000 ⊕ С001000 ⊕ С000001 ⊕ С001001 = 0 => С001001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(000110) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000110 = 0 => С000110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(000101) = С000000 ⊕ С000100 ⊕ С000001 ⊕ С000101 = 0 => С000101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(000011) = С000000 ⊕ С000010 ⊕ С000001 ⊕ С000011 = 0 => С000011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(111000) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С110000 ⊕ С101000 ⊕ С011000 ⊕ С111000 = 0 => С111000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110100) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С110000 ⊕ С100100 ⊕ С010100 ⊕ С110100 = 0 => С110100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110010) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000010 ⊕ С110000 ⊕ С100010 ⊕ С010010 ⊕ С110010 = 0 => С110010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110001) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000001 ⊕ С110000 ⊕ С100001 ⊕ С010001 ⊕ С110001 = 0 => С110001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101100) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С101000 ⊕ С100100 ⊕ С001100 ⊕ С101100 = 0 => С101100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101010) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000010 ⊕ С101000 ⊕ С100010 ⊕ С001010 ⊕ С101010 = 0 => С101010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101001) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000001 ⊕ С101000 ⊕ С100001 ⊕ С001001 ⊕ С101001 = 0 => С101001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100110) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000010 ⊕ С100100 ⊕ С100010 ⊕ С000110 ⊕ С100110 = 0 => С100110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100101) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000001 ⊕ С100100 ⊕ С100001 ⊕ С000101 ⊕ С100101 = 0 => С100101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100011) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С000001 ⊕ С100010 ⊕ С100001 ⊕ С000011 ⊕ С100011 = 0 => С100011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011100) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С011000 ⊕ С010100 ⊕ С001100 ⊕ С011100 = 0 => С011100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011010) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С011000 ⊕ С010010 ⊕ С001010 ⊕ С011010 = 0 => С011010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011001) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000001 ⊕ С011000 ⊕ С010001 ⊕ С001001 ⊕ С011001 = 0 => С011001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010110) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С010100 ⊕ С010010 ⊕ С000110 ⊕ С010110 = 0 => С010110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010101) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000001 ⊕ С010100 ⊕ С010001 ⊕ С000101 ⊕ С010101 = 0 => С010101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010011) = С000000 ⊕ С010000 ⊕ С000010 ⊕ С000001 ⊕ С010010 ⊕ С010001 ⊕ С000011 ⊕ С010011 = 0 => С010011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001110) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С001110 = 0 => С001110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001101) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С001101 = 0 => С001101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001011) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С001011 = 0 => С001011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(000111) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С000111 = 0 => С000111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(111100) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С110000 ⊕ С101000 ⊕ С100100 ⊕ С011000 ⊕ С010100 ⊕ С001100 ⊕ С111000 ⊕ С110100 ⊕ С101100 ⊕ С011100 ⊕ С111100 = 0 => С111100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 0 => С111010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(111001) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С001000 ⊕ С000001 ⊕ С110000 ⊕ С101000 ⊕ С100001 ⊕ С011000 ⊕ С010001 ⊕ С001001 ⊕ С111000 ⊕ С110001 ⊕ С101001 ⊕ С011001 ⊕ С111001 = 0 => С111001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110110) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С110000 ⊕ С100100 ⊕ С100010 ⊕ С010100 ⊕ С010010 ⊕ С000110 ⊕ С110100 ⊕ С110010 ⊕ С100110 ⊕ С010110 ⊕ С110110 = 0 => С110110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110101) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С000001 ⊕ С110000 ⊕ С100100 ⊕ С100001 ⊕ С010100 ⊕ С010001 ⊕ С000101 ⊕ С110100 ⊕ С110001 ⊕ С100101 ⊕ С010101 ⊕ С110101 = 0 => С110101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110011) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000010 ⊕ С000001 ⊕ С110000 ⊕ С100010 ⊕ С100001 ⊕ С010010 ⊕ С010001 ⊕ С000011 ⊕ С110010 ⊕ С110001 ⊕ С100011 ⊕ С010011 ⊕ С110011 = 0 => С110011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101101) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С101000 ⊕ С100100 ⊕ С100001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С101100 ⊕ С101001 ⊕ С100101 ⊕ С001101 ⊕ С101101 = 0 => С101101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101011) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С101000 ⊕ С100010 ⊕ С100001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С101010 ⊕ С101001 ⊕ С100011 ⊕ С001011 ⊕ С101011 = 0 => С101011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100111) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С100100 ⊕ С100010 ⊕ С100001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С100110 ⊕ С100101 ⊕ С100011 ⊕ С000111 ⊕ С100111 = 0 => С100111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011110) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С011000 ⊕ С010100 ⊕ С010010 ⊕ С001100 ⊕ С001010 ⊕ С000110 ⊕ С011100 ⊕ С011010 ⊕ С010110 ⊕ С001110 ⊕ С011110 = 0 => С011110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011101) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С011000 ⊕ С010100 ⊕ С010001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С011100 ⊕ С011001 ⊕ С010101 ⊕ С001101 ⊕ С011101 = 0 => С011101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(011011) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С011000 ⊕ С010010 ⊕ С010001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С011010 ⊕ С011001 ⊕ С010011 ⊕ С001011 ⊕ С011011 = 0 => С011011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(010111) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С010100 ⊕ С010010 ⊕ С010001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С010110 ⊕ С010101 ⊕ С010011 ⊕ С000111 ⊕ С010111 = 0 => С010111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(001111) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С001111 = 0 => С001111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 => С111110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 => С111101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 => С111011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 => С110111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1

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

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