Таблица истинности для функции F≡¬(B∧V∧C)∧(D∧¬B)∧V∧¬A∧B:
Промежуточные таблицы истинности:
B∧V:
(B∧V)∧C:
¬B:
D∧(¬B):
¬((B∧V)∧C):
¬A:
(¬((B∧V)∧C))∧(D∧(¬B)):
((¬((B∧V)∧C))∧(D∧(¬B)))∧V:
(((¬((B∧V)∧C))∧(D∧(¬B)))∧V)∧(¬A):
((((¬((B∧V)∧C))∧(D∧(¬B)))∧V)∧(¬A))∧B:
F≡(((((¬((B∧V)∧C))∧(D∧(¬B)))∧V)∧(¬A))∧B):
Общая таблица истинности:
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:Fсднф = ¬F∧¬B∧¬V∧¬C∧¬D∧¬A ∨ ¬F∧¬B∧¬V∧¬C∧¬D∧A ∨ ¬F∧¬B∧¬V∧¬C∧D∧¬A ∨ ¬F∧¬B∧¬V∧¬C∧D∧A ∨ ¬F∧¬B∧¬V∧C∧¬D∧¬A ∨ ¬F∧¬B∧¬V∧C∧¬D∧A ∨ ¬F∧¬B∧¬V∧C∧D∧¬A ∨ ¬F∧¬B∧¬V∧C∧D∧A ∨ ¬F∧¬B∧V∧¬C∧¬D∧¬A ∨ ¬F∧¬B∧V∧¬C∧¬D∧A ∨ ¬F∧¬B∧V∧¬C∧D∧¬A ∨ ¬F∧¬B∧V∧¬C∧D∧A ∨ ¬F∧¬B∧V∧C∧¬D∧¬A ∨ ¬F∧¬B∧V∧C∧¬D∧A ∨ ¬F∧¬B∧V∧C∧D∧¬A ∨ ¬F∧¬B∧V∧C∧D∧A ∨ ¬F∧B∧¬V∧¬C∧¬D∧¬A ∨ ¬F∧B∧¬V∧¬C∧¬D∧A ∨ ¬F∧B∧¬V∧¬C∧D∧¬A ∨ ¬F∧B∧¬V∧¬C∧D∧A ∨ ¬F∧B∧¬V∧C∧¬D∧¬A ∨ ¬F∧B∧¬V∧C∧¬D∧A ∨ ¬F∧B∧¬V∧C∧D∧¬A ∨ ¬F∧B∧¬V∧C∧D∧A ∨ ¬F∧B∧V∧¬C∧¬D∧¬A ∨ ¬F∧B∧V∧¬C∧¬D∧A ∨ ¬F∧B∧V∧¬C∧D∧¬A ∨ ¬F∧B∧V∧¬C∧D∧A ∨ ¬F∧B∧V∧C∧¬D∧¬A ∨ ¬F∧B∧V∧C∧¬D∧A ∨ ¬F∧B∧V∧C∧D∧¬A ∨ ¬F∧B∧V∧C∧D∧A
Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:Fскнф = (¬F∨B∨V∨C∨D∨A) ∧ (¬F∨B∨V∨C∨D∨¬A) ∧ (¬F∨B∨V∨C∨¬D∨A) ∧ (¬F∨B∨V∨C∨¬D∨¬A) ∧ (¬F∨B∨V∨¬C∨D∨A) ∧ (¬F∨B∨V∨¬C∨D∨¬A) ∧ (¬F∨B∨V∨¬C∨¬D∨A) ∧ (¬F∨B∨V∨¬C∨¬D∨¬A) ∧ (¬F∨B∨¬V∨C∨D∨A) ∧ (¬F∨B∨¬V∨C∨D∨¬A) ∧ (¬F∨B∨¬V∨C∨¬D∨A) ∧ (¬F∨B∨¬V∨C∨¬D∨¬A) ∧ (¬F∨B∨¬V∨¬C∨D∨A) ∧ (¬F∨B∨¬V∨¬C∨D∨¬A) ∧ (¬F∨B∨¬V∨¬C∨¬D∨A) ∧ (¬F∨B∨¬V∨¬C∨¬D∨¬A) ∧ (¬F∨¬B∨V∨C∨D∨A) ∧ (¬F∨¬B∨V∨C∨D∨¬A) ∧ (¬F∨¬B∨V∨C∨¬D∨A) ∧ (¬F∨¬B∨V∨C∨¬D∨¬A) ∧ (¬F∨¬B∨V∨¬C∨D∨A) ∧ (¬F∨¬B∨V∨¬C∨D∨¬A) ∧ (¬F∨¬B∨V∨¬C∨¬D∨A) ∧ (¬F∨¬B∨V∨¬C∨¬D∨¬A) ∧ (¬F∨¬B∨¬V∨C∨D∨A) ∧ (¬F∨¬B∨¬V∨C∨D∨¬A) ∧ (¬F∨¬B∨¬V∨C∨¬D∨A) ∧ (¬F∨¬B∨¬V∨C∨¬D∨¬A) ∧ (¬F∨¬B∨¬V∨¬C∨D∨A) ∧ (¬F∨¬B∨¬V∨¬C∨D∨¬A) ∧ (¬F∨¬B∨¬V∨¬C∨¬D∨A) ∧ (¬F∨¬B∨¬V∨¬C∨¬D∨¬A)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функцииПостроим полином Жегалкина:
Fж = C000000 ⊕ C100000∧F ⊕ C010000∧B ⊕ C001000∧V ⊕ C000100∧C ⊕ C000010∧D ⊕ C000001∧A ⊕ C110000∧F∧B ⊕ C101000∧F∧V ⊕ C100100∧F∧C ⊕ C100010∧F∧D ⊕ C100001∧F∧A ⊕ C011000∧B∧V ⊕ C010100∧B∧C ⊕ C010010∧B∧D ⊕ C010001∧B∧A ⊕ C001100∧V∧C ⊕ C001010∧V∧D ⊕ C001001∧V∧A ⊕ C000110∧C∧D ⊕ C000101∧C∧A ⊕ C000011∧D∧A ⊕ C111000∧F∧B∧V ⊕ C110100∧F∧B∧C ⊕ C110010∧F∧B∧D ⊕ C110001∧F∧B∧A ⊕ C101100∧F∧V∧C ⊕ C101010∧F∧V∧D ⊕ C101001∧F∧V∧A ⊕ C100110∧F∧C∧D ⊕ C100101∧F∧C∧A ⊕ C100011∧F∧D∧A ⊕ C011100∧B∧V∧C ⊕ C011010∧B∧V∧D ⊕ C011001∧B∧V∧A ⊕ C010110∧B∧C∧D ⊕ C010101∧B∧C∧A ⊕ C010011∧B∧D∧A ⊕ C001110∧V∧C∧D ⊕ C001101∧V∧C∧A ⊕ C001011∧V∧D∧A ⊕ C000111∧C∧D∧A ⊕ C111100∧F∧B∧V∧C ⊕ C111010∧F∧B∧V∧D ⊕ C111001∧F∧B∧V∧A ⊕ C110110∧F∧B∧C∧D ⊕ C110101∧F∧B∧C∧A ⊕ C110011∧F∧B∧D∧A ⊕ C101110∧F∧V∧C∧D ⊕ C101101∧F∧V∧C∧A ⊕ C101011∧F∧V∧D∧A ⊕ C100111∧F∧C∧D∧A ⊕ C011110∧B∧V∧C∧D ⊕ C011101∧B∧V∧C∧A ⊕ C011011∧B∧V∧D∧A ⊕ C010111∧B∧C∧D∧A ⊕ C001111∧V∧C∧D∧A ⊕ C111110∧F∧B∧V∧C∧D ⊕ C111101∧F∧B∧V∧C∧A ⊕ C111011∧F∧B∧V∧D∧A ⊕ C110111∧F∧B∧C∧D∧A ⊕ C101111∧F∧V∧C∧D∧A ⊕ C011111∧B∧V∧C∧D∧A ⊕ C111111∧F∧B∧V∧C∧D∧A
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 = 0 => С100000 = 1 ⊕ 0 = 1
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 ⊕ 1 ⊕ 0 ⊕ 0 = 0
Fж(101000) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С101000 = 0 => С101000 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
Fж(100100) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С100100 = 0 => С100100 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
Fж(100010) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С100010 = 0 => С100010 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
Fж(100001) = С000000 ⊕ С100000 ⊕ С000001 ⊕ С100001 = 0 => С100001 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 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 = 1 => С001010 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001001) = С000000 ⊕ С001000 ⊕ С000001 ⊕ С001001 = 1 => С001001 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(000110) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000110 = 1 => С000110 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(000101) = С000000 ⊕ С000100 ⊕ С000001 ⊕ С000101 = 1 => С000101 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
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 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110100) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000100 ⊕ С110000 ⊕ С100100 ⊕ С010100 ⊕ С110100 = 0 => С110100 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110010) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000010 ⊕ С110000 ⊕ С100010 ⊕ С010010 ⊕ С110010 = 0 => С110010 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(110001) = С000000 ⊕ С100000 ⊕ С010000 ⊕ С000001 ⊕ С110000 ⊕ С100001 ⊕ С010001 ⊕ С110001 = 0 => С110001 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101100) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000100 ⊕ С101000 ⊕ С100100 ⊕ С001100 ⊕ С101100 = 0 => С101100 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101010) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000010 ⊕ С101000 ⊕ С100010 ⊕ С001010 ⊕ С101010 = 0 => С101010 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(101001) = С000000 ⊕ С100000 ⊕ С001000 ⊕ С000001 ⊕ С101000 ⊕ С100001 ⊕ С001001 ⊕ С101001 = 0 => С101001 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100110) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000010 ⊕ С100100 ⊕ С100010 ⊕ С000110 ⊕ С100110 = 0 => С100110 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100101) = С000000 ⊕ С100000 ⊕ С000100 ⊕ С000001 ⊕ С100100 ⊕ С100001 ⊕ С000101 ⊕ С100101 = 0 => С100101 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Fж(100011) = С000000 ⊕ С100000 ⊕ С000010 ⊕ С000001 ⊕ С100010 ⊕ С100001 ⊕ С000011 ⊕ С100011 = 0 => С100011 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 1 => С011010 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(011001) = С000000 ⊕ С010000 ⊕ С001000 ⊕ С000001 ⊕ С011000 ⊕ С010001 ⊕ С001001 ⊕ С011001 = 1 => С011001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010110) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000010 ⊕ С010100 ⊕ С010010 ⊕ С000110 ⊕ С010110 = 1 => С010110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(010101) = С000000 ⊕ С010000 ⊕ С000100 ⊕ С000001 ⊕ С010100 ⊕ С010001 ⊕ С000101 ⊕ С010101 = 1 => С010101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С001110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001101) = С000000 ⊕ С001000 ⊕ С000100 ⊕ С000001 ⊕ С001100 ⊕ С001001 ⊕ С000101 ⊕ С001101 = 1 => С001101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(001011) = С000000 ⊕ С001000 ⊕ С000010 ⊕ С000001 ⊕ С001010 ⊕ С001001 ⊕ С000011 ⊕ С001011 = 1 => С001011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Fж(000111) = С000000 ⊕ С000100 ⊕ С000010 ⊕ С000001 ⊕ С000110 ⊕ С000101 ⊕ С000011 ⊕ С000111 = 1 => С000111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 ⊕ 1 ⊕ 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 = 1 => С011110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 ⊕ 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 ⊕ 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 = 1 ⊕ 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 ⊕ 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 = 1 ⊕ 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 ⊕ 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 = 1 ⊕ 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 ⊕ 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 = 1 ⊕ 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 ⊕ 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 = 1 => С011111 = 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 ⊕ 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 = 0 => С111111 = 1 ⊕ 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 ⊕ 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
Таким образом, полином Жегалкина будет равен:
Fж = 1 ⊕ F
Логическая схема, соответствующая полиному Жегалкина: