Таблица истинности для функции ¬X∧A∧N∧D∧¬Y∨Z:


Промежуточные таблицы истинности:
¬X:
X¬X
01
10

¬Y:
Y¬Y
01
10

(¬X)∧A:
XA¬X(¬X)∧A
0010
0111
1000
1100

((¬X)∧A)∧N:
XAN¬X(¬X)∧A((¬X)∧A)∧N
000100
001100
010110
011111
100000
101000
110000
111000

(((¬X)∧A)∧N)∧D:
XAND¬X(¬X)∧A((¬X)∧A)∧N(((¬X)∧A)∧N)∧D
00001000
00011000
00101000
00111000
01001100
01011100
01101110
01111111
10000000
10010000
10100000
10110000
11000000
11010000
11100000
11110000

((((¬X)∧A)∧N)∧D)∧(¬Y):
XANDY¬X(¬X)∧A((¬X)∧A)∧N(((¬X)∧A)∧N)∧D¬Y((((¬X)∧A)∧N)∧D)∧(¬Y)
00000100010
00001100000
00010100010
00011100000
00100100010
00101100000
00110100010
00111100000
01000110010
01001110000
01010110010
01011110000
01100111010
01101111000
01110111111
01111111100
10000000010
10001000000
10010000010
10011000000
10100000010
10101000000
10110000010
10111000000
11000000010
11001000000
11010000010
11011000000
11100000010
11101000000
11110000010
11111000000

(((((¬X)∧A)∧N)∧D)∧(¬Y))∨Z:
XANDYZ¬X(¬X)∧A((¬X)∧A)∧N(((¬X)∧A)∧N)∧D¬Y((((¬X)∧A)∧N)∧D)∧(¬Y)(((((¬X)∧A)∧N)∧D)∧(¬Y))∨Z
0000001000100
0000011000101
0000101000000
0000111000001
0001001000100
0001011000101
0001101000000
0001111000001
0010001000100
0010011000101
0010101000000
0010111000001
0011001000100
0011011000101
0011101000000
0011111000001
0100001100100
0100011100101
0100101100000
0100111100001
0101001100100
0101011100101
0101101100000
0101111100001
0110001110100
0110011110101
0110101110000
0110111110001
0111001111111
0111011111111
0111101111000
0111111111001
1000000000100
1000010000101
1000100000000
1000110000001
1001000000100
1001010000101
1001100000000
1001110000001
1010000000100
1010010000101
1010100000000
1010110000001
1011000000100
1011010000101
1011100000000
1011110000001
1100000000100
1100010000101
1100100000000
1100110000001
1101000000100
1101010000101
1101100000000
1101110000001
1110000000100
1110010000101
1110100000000
1110110000001
1111000000100
1111010000101
1111100000000
1111110000001

Общая таблица истинности:

XANDYZ¬X¬Y(¬X)∧A((¬X)∧A)∧N(((¬X)∧A)∧N)∧D((((¬X)∧A)∧N)∧D)∧(¬Y)¬X∧A∧N∧D∧¬Y∨Z
0000001100000
0000011100001
0000101000000
0000111000001
0001001100000
0001011100001
0001101000000
0001111000001
0010001100000
0010011100001
0010101000000
0010111000001
0011001100000
0011011100001
0011101000000
0011111000001
0100001110000
0100011110001
0100101010000
0100111010001
0101001110000
0101011110001
0101101010000
0101111010001
0110001111000
0110011111001
0110101011000
0110111011001
0111001111111
0111011111111
0111101011100
0111111011101
1000000100000
1000010100001
1000100000000
1000110000001
1001000100000
1001010100001
1001100000000
1001110000001
1010000100000
1010010100001
1010100000000
1010110000001
1011000100000
1011010100001
1011100000000
1011110000001
1100000100000
1100010100001
1100100000000
1100110000001
1101000100000
1101010100001
1101100000000
1101110000001
1110000100000
1110010100001
1110100000000
1110110000001
1111000100000
1111010100001
1111100000000
1111110000001

Логическая схема:

Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
XANDYZF
0000000
0000011
0000100
0000111
0001000
0001011
0001100
0001111
0010000
0010011
0010100
0010111
0011000
0011011
0011100
0011111
0100000
0100011
0100100
0100111
0101000
0101011
0101100
0101111
0110000
0110011
0110100
0110111
0111001
0111011
0111100
0111111
1000000
1000011
1000100
1000111
1001000
1001011
1001100
1001111
1010000
1010011
1010100
1010111
1011000
1011011
1011100
1011111
1100000
1100011
1100100
1100111
1101000
1101011
1101100
1101111
1110000
1110011
1110100
1110111
1111000
1111011
1111100
1111111
Fсднф = ¬X∧¬A∧¬N∧¬D∧¬Y∧Z ∨ ¬X∧¬A∧¬N∧¬D∧Y∧Z ∨ ¬X∧¬A∧¬N∧D∧¬Y∧Z ∨ ¬X∧¬A∧¬N∧D∧Y∧Z ∨ ¬X∧¬A∧N∧¬D∧¬Y∧Z ∨ ¬X∧¬A∧N∧¬D∧Y∧Z ∨ ¬X∧¬A∧N∧D∧¬Y∧Z ∨ ¬X∧¬A∧N∧D∧Y∧Z ∨ ¬X∧A∧¬N∧¬D∧¬Y∧Z ∨ ¬X∧A∧¬N∧¬D∧Y∧Z ∨ ¬X∧A∧¬N∧D∧¬Y∧Z ∨ ¬X∧A∧¬N∧D∧Y∧Z ∨ ¬X∧A∧N∧¬D∧¬Y∧Z ∨ ¬X∧A∧N∧¬D∧Y∧Z ∨ ¬X∧A∧N∧D∧¬Y∧¬Z ∨ ¬X∧A∧N∧D∧¬Y∧Z ∨ ¬X∧A∧N∧D∧Y∧Z ∨ X∧¬A∧¬N∧¬D∧¬Y∧Z ∨ X∧¬A∧¬N∧¬D∧Y∧Z ∨ X∧¬A∧¬N∧D∧¬Y∧Z ∨ X∧¬A∧¬N∧D∧Y∧Z ∨ X∧¬A∧N∧¬D∧¬Y∧Z ∨ X∧¬A∧N∧¬D∧Y∧Z ∨ X∧¬A∧N∧D∧¬Y∧Z ∨ X∧¬A∧N∧D∧Y∧Z ∨ X∧A∧¬N∧¬D∧¬Y∧Z ∨ X∧A∧¬N∧¬D∧Y∧Z ∨ X∧A∧¬N∧D∧¬Y∧Z ∨ X∧A∧¬N∧D∧Y∧Z ∨ X∧A∧N∧¬D∧¬Y∧Z ∨ X∧A∧N∧¬D∧Y∧Z ∨ X∧A∧N∧D∧¬Y∧Z ∨ X∧A∧N∧D∧Y∧Z
Логическая cхема:

Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
XANDYZF
0000000
0000011
0000100
0000111
0001000
0001011
0001100
0001111
0010000
0010011
0010100
0010111
0011000
0011011
0011100
0011111
0100000
0100011
0100100
0100111
0101000
0101011
0101100
0101111
0110000
0110011
0110100
0110111
0111001
0111011
0111100
0111111
1000000
1000011
1000100
1000111
1001000
1001011
1001100
1001111
1010000
1010011
1010100
1010111
1011000
1011011
1011100
1011111
1100000
1100011
1100100
1100111
1101000
1101011
1101100
1101111
1110000
1110011
1110100
1110111
1111000
1111011
1111100
1111111
Fскнф = (X∨A∨N∨D∨Y∨Z) ∧ (X∨A∨N∨D∨¬Y∨Z) ∧ (X∨A∨N∨¬D∨Y∨Z) ∧ (X∨A∨N∨¬D∨¬Y∨Z) ∧ (X∨A∨¬N∨D∨Y∨Z) ∧ (X∨A∨¬N∨D∨¬Y∨Z) ∧ (X∨A∨¬N∨¬D∨Y∨Z) ∧ (X∨A∨¬N∨¬D∨¬Y∨Z) ∧ (X∨¬A∨N∨D∨Y∨Z) ∧ (X∨¬A∨N∨D∨¬Y∨Z) ∧ (X∨¬A∨N∨¬D∨Y∨Z) ∧ (X∨¬A∨N∨¬D∨¬Y∨Z) ∧ (X∨¬A∨¬N∨D∨Y∨Z) ∧ (X∨¬A∨¬N∨D∨¬Y∨Z) ∧ (X∨¬A∨¬N∨¬D∨¬Y∨Z) ∧ (¬X∨A∨N∨D∨Y∨Z) ∧ (¬X∨A∨N∨D∨¬Y∨Z) ∧ (¬X∨A∨N∨¬D∨Y∨Z) ∧ (¬X∨A∨N∨¬D∨¬Y∨Z) ∧ (¬X∨A∨¬N∨D∨Y∨Z) ∧ (¬X∨A∨¬N∨D∨¬Y∨Z) ∧ (¬X∨A∨¬N∨¬D∨Y∨Z) ∧ (¬X∨A∨¬N∨¬D∨¬Y∨Z) ∧ (¬X∨¬A∨N∨D∨Y∨Z) ∧ (¬X∨¬A∨N∨D∨¬Y∨Z) ∧ (¬X∨¬A∨N∨¬D∨Y∨Z) ∧ (¬X∨¬A∨N∨¬D∨¬Y∨Z) ∧ (¬X∨¬A∨¬N∨D∨Y∨Z) ∧ (¬X∨¬A∨¬N∨D∨¬Y∨Z) ∧ (¬X∨¬A∨¬N∨¬D∨Y∨Z) ∧ (¬X∨¬A∨¬N∨¬D∨¬Y∨Z)
Логическая cхема:

Построение полинома Жегалкина:

По таблице истинности функции
XANDYZFж
0000000
0000011
0000100
0000111
0001000
0001011
0001100
0001111
0010000
0010011
0010100
0010111
0011000
0011011
0011100
0011111
0100000
0100011
0100100
0100111
0101000
0101011
0101100
0101111
0110000
0110011
0110100
0110111
0111001
0111011
0111100
0111111
1000000
1000011
1000100
1000111
1001000
1001011
1001100
1001111
1010000
1010011
1010100
1010111
1011000
1011011
1011100
1011111
1100000
1100011
1100100
1100111
1101000
1101011
1101100
1101111
1110000
1110011
1110100
1110111
1111000
1111011
1111100
1111111

Построим полином Жегалкина:
Fж = C000000 ⊕ C100000∧X ⊕ C010000∧A ⊕ C001000∧N ⊕ C000100∧D ⊕ C000010∧Y ⊕ C000001∧Z ⊕ C110000∧X∧A ⊕ C101000∧X∧N ⊕ C100100∧X∧D ⊕ C100010∧X∧Y ⊕ C100001∧X∧Z ⊕ C011000∧A∧N ⊕ C010100∧A∧D ⊕ C010010∧A∧Y ⊕ C010001∧A∧Z ⊕ C001100∧N∧D ⊕ C001010∧N∧Y ⊕ C001001∧N∧Z ⊕ C000110∧D∧Y ⊕ C000101∧D∧Z ⊕ C000011∧Y∧Z ⊕ C111000∧X∧A∧N ⊕ C110100∧X∧A∧D ⊕ C110010∧X∧A∧Y ⊕ C110001∧X∧A∧Z ⊕ C101100∧X∧N∧D ⊕ C101010∧X∧N∧Y ⊕ C101001∧X∧N∧Z ⊕ C100110∧X∧D∧Y ⊕ C100101∧X∧D∧Z ⊕ C100011∧X∧Y∧Z ⊕ C011100∧A∧N∧D ⊕ C011010∧A∧N∧Y ⊕ C011001∧A∧N∧Z ⊕ C010110∧A∧D∧Y ⊕ C010101∧A∧D∧Z ⊕ C010011∧A∧Y∧Z ⊕ C001110∧N∧D∧Y ⊕ C001101∧N∧D∧Z ⊕ C001011∧N∧Y∧Z ⊕ C000111∧D∧Y∧Z ⊕ C111100∧X∧A∧N∧D ⊕ C111010∧X∧A∧N∧Y ⊕ C111001∧X∧A∧N∧Z ⊕ C110110∧X∧A∧D∧Y ⊕ C110101∧X∧A∧D∧Z ⊕ C110011∧X∧A∧Y∧Z ⊕ C101110∧X∧N∧D∧Y ⊕ C101101∧X∧N∧D∧Z ⊕ C101011∧X∧N∧Y∧Z ⊕ C100111∧X∧D∧Y∧Z ⊕ C011110∧A∧N∧D∧Y ⊕ C011101∧A∧N∧D∧Z ⊕ C011011∧A∧N∧Y∧Z ⊕ C010111∧A∧D∧Y∧Z ⊕ C001111∧N∧D∧Y∧Z ⊕ C111110∧X∧A∧N∧D∧Y ⊕ C111101∧X∧A∧N∧D∧Z ⊕ C111011∧X∧A∧N∧Y∧Z ⊕ C110111∧X∧A∧D∧Y∧Z ⊕ C101111∧X∧N∧D∧Y∧Z ⊕ C011111∧A∧N∧D∧Y∧Z ⊕ C111111∧X∧A∧N∧D∧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 = 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 = 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 = 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 = 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 = 1 => С010001 = 0 ⊕ 0 ⊕ 1 ⊕ 1 = 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 = 1 => С001001 = 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
Fж(000110) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000110 = 0 => С000110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(000101) = С000000 ⊕ С000100 ⊕ С000001 ⊕ С000101 = 1 => С000101 = 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
Fж(000011) = С000000 ⊕ С000010 ⊕ С000001 ⊕ С000011 = 1 => С000011 = 0 ⊕ 0 ⊕ 1 ⊕ 1 = 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 = 1 => С110001 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С101001 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С100101 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(100011) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С000001 ⊕ С100010 ⊕ С100001 ⊕ С000011 ⊕ С100011 = 1 => С100011 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(011100) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С011000 ⊕ С010100 ⊕ С001100 ⊕ С011100 = 1 => С011100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
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 = 1 => С011001 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С010101 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010011) = С000000 ⊕ С010000 ⊕ С000010 ⊕ С000001 ⊕ С010010 ⊕ С010001 ⊕ С000011 ⊕ С010011 = 1 => С010011 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С001101 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001011) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С001011 = 1 => С001011 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(000111) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С000111 = 1 => С000111 = 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 ⊕ 1 ⊕ 0 = 1
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 = 1 => С111001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С110101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С101101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Fж(011101) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С011000 ⊕ С010100 ⊕ С010001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С011100 ⊕ С011001 ⊕ С010101 ⊕ С001101 ⊕ С011101 = 1 => С011101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
Fж(011011) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С011000 ⊕ С010010 ⊕ С010001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С011010 ⊕ С011001 ⊕ С010011 ⊕ С001011 ⊕ С011011 = 1 => С011011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001111) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С001100 ⊕ С001010 ⊕ С001001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С001110 ⊕ С001101 ⊕ С001011 ⊕ С000111 ⊕ С001111 = 1 => С001111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 0 => С111110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 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 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 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 ⊕ 0 ⊕ 1 ⊕ 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 = 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 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 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 = 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 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 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 = 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 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
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 ⊕ 1 ⊕ 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 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 1

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

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