Таблица истинности для функции F≡(X≡(Y→Z))∧(¬W→(X≡Y)):

Промежуточные таблицы истинности:
Y→Z:

X≡(Y→Z):

X≡Y:

¬W:

(¬W)→(X≡Y):

(X≡(Y→Z))∧((¬W)→(X≡Y)):

F≡((X≡(Y→Z))∧((¬W)→(X≡Y))):

Общая таблица истинности:

Логическая схема:

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Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
F_сднф = ¬F∧¬X∧¬Y∧¬Z∧¬W ∨ ¬F∧¬X∧¬Y∧¬Z∧W ∨ ¬F∧¬X∧¬Y∧Z∧¬W ∨ ¬F∧¬X∧¬Y∧Z∧W ∨ ¬F∧¬X∧Y∧¬Z∧¬W ∨ ¬F∧¬X∧Y∧Z∧¬W ∨ ¬F∧¬X∧Y∧Z∧W ∨ ¬F∧X∧¬Y∧¬Z∧¬W ∨ ¬F∧X∧¬Y∧Z∧¬W ∨ ¬F∧X∧Y∧¬Z∧¬W ∨ ¬F∧X∧Y∧¬Z∧W ∨ F∧¬X∧Y∧¬Z∧W ∨ F∧X∧¬Y∧¬Z∧W ∨ F∧X∧¬Y∧Z∧W ∨ F∧X∧Y∧Z∧¬W ∨ F∧X∧Y∧Z∧W
Логическая cхема:

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Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
F_скнф = (F∨X∨¬Y∨Z∨¬W) ∧ (F∨¬X∨Y∨Z∨¬W) ∧ (F∨¬X∨Y∨¬Z∨¬W) ∧ (F∨¬X∨¬Y∨¬Z∨W) ∧ (F∨¬X∨¬Y∨¬Z∨¬W) ∧ (¬F∨X∨Y∨Z∨W) ∧ (¬F∨X∨Y∨Z∨¬W) ∧ (¬F∨X∨Y∨¬Z∨W) ∧ (¬F∨X∨Y∨¬Z∨¬W) ∧ (¬F∨X∨¬Y∨Z∨W) ∧ (¬F∨X∨¬Y∨¬Z∨W) ∧ (¬F∨X∨¬Y∨¬Z∨¬W) ∧ (¬F∨¬X∨Y∨Z∨W) ∧ (¬F∨¬X∨Y∨¬Z∨W) ∧ (¬F∨¬X∨¬Y∨Z∨W) ∧ (¬F∨¬X∨¬Y∨Z∨¬W)
Логическая cхема:

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Построение полинома Жегалкина:

По таблице истинности функции
Построим полином Жегалкина:
F_ж = C₀₀₀₀₀ ⊕ C₁₀₀₀₀∧F ⊕ C₀₁₀₀₀∧X ⊕ C₀₀₁₀₀∧Y ⊕ C₀₀₀₁₀∧Z ⊕ C₀₀₀₀₁∧W ⊕ C₁₁₀₀₀∧F∧X ⊕ C₁₀₁₀₀∧F∧Y ⊕ C₁₀₀₁₀∧F∧Z ⊕ C₁₀₀₀₁∧F∧W ⊕ C₀₁₁₀₀∧X∧Y ⊕ C₀₁₀₁₀∧X∧Z ⊕ C₀₁₀₀₁∧X∧W ⊕ C₀₀₁₁₀∧Y∧Z ⊕ C₀₀₁₀₁∧Y∧W ⊕ C₀₀₀₁₁∧Z∧W ⊕ C₁₁₁₀₀∧F∧X∧Y ⊕ C₁₁₀₁₀∧F∧X∧Z ⊕ C₁₁₀₀₁∧F∧X∧W ⊕ C₁₀₁₁₀∧F∧Y∧Z ⊕ C₁₀₁₀₁∧F∧Y∧W ⊕ C₁₀₀₁₁∧F∧Z∧W ⊕ C₀₁₁₁₀∧X∧Y∧Z ⊕ C₀₁₁₀₁∧X∧Y∧W ⊕ C₀₁₀₁₁∧X∧Z∧W ⊕ C₀₀₁₁₁∧Y∧Z∧W ⊕ C₁₁₁₁₀∧F∧X∧Y∧Z ⊕ C₁₁₁₀₁∧F∧X∧Y∧W ⊕ C₁₁₀₁₁∧F∧X∧Z∧W ⊕ C₁₀₁₁₁∧F∧Y∧Z∧W ⊕ C₀₁₁₁₁∧X∧Y∧Z∧W ⊕ C₁₁₁₁₁∧F∧X∧Y∧Z∧W

Так как F_ж(00000) = 1, то С₀₀₀₀₀ = 1.

Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы:
F_ж(10000) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ = 0 => С₁₀₀₀₀ = 1 ⊕ 0 = 1
F_ж(01000) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ = 1 => С₀₁₀₀₀ = 1 ⊕ 1 = 0
F_ж(00100) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ = 1 => С₀₀₁₀₀ = 1 ⊕ 1 = 0
F_ж(00010) = С₀₀₀₀₀ ⊕ С₀₀₀₁₀ = 1 => С₀₀₀₁₀ = 1 ⊕ 1 = 0
F_ж(00001) = С₀₀₀₀₀ ⊕ С₀₀₀₀₁ = 1 => С₀₀₀₀₁ = 1 ⊕ 1 = 0
F_ж(11000) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₁₁₀₀₀ = 0 => С₁₁₀₀₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F_ж(10100) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₁₀₁₀₀ = 0 => С₁₀₁₀₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F_ж(10010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₀₁₀ = 0 => С₁₀₀₁₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F_ж(10001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₀₁ = 0 => С₁₀₀₀₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F_ж(01100) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₁₁₀₀ = 1 => С₀₁₁₀₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01010) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₁₀₁₀ = 1 => С₀₁₀₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01001) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₀₀₁ = 0 => С₀₁₀₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F_ж(00110) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₁₁₀ = 1 => С₀₀₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(00101) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₀₁ = 0 => С₀₀₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F_ж(00011) = С₀₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₀₁₁ = 1 => С₀₀₀₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11100) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₀₁₁₀₀ ⊕ С₁₁₁₀₀ = 0 => С₁₁₁₀₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F_ж(11010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₀₁₀ ⊕ С₁₁₀₁₀ = 0 => С₁₁₀₁₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F_ж(11001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₀₁ ⊕ С₁₁₀₀₁ = 1 => С₁₁₀₀₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
F_ж(10110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₀₁₁₀ = 0 => С₁₀₁₁₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F_ж(10101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₀₁₀₁ = 1 => С₁₀₁₀₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
F_ж(10011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₀₀₁₁ = 0 => С₁₀₀₁₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F_ж(01110) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₀₁₁₁₀ = 0 => С₀₁₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F_ж(01101) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₀₁₁₀₁ = 1 => С₀₁₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 0
F_ж(01011) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₀₁₁ = 0 => С₀₁₀₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F_ж(00111) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₀₁₁₁ = 1 => С₀₀₁₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F_ж(11110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₁₀ ⊕ С₁₀₁₁₀ ⊕ С₀₁₁₁₀ ⊕ С₁₁₁₁₀ = 1 => С₁₁₁₁₀ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
F_ж(11101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₁₀₁ ⊕ С₀₁₁₀₁ ⊕ С₁₁₁₀₁ = 0 => С₁₁₁₀₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F_ж(11011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₁₀₁₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₁₀₁₁ ⊕ С₁₁₀₁₁ = 1 => С₁₁₀₁₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10111) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₀₁₁₀ ⊕ С₁₀₁₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₁₀₁₁₁ = 0 => С₁₀₁₁₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 0
F_ж(01111) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₁₁₀ ⊕ С₀₁₁₀₁ ⊕ С₀₁₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₀₁₁₁₁ = 0 => С₀₁₁₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 1
F_ж(11111) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₁₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₁₁₀ ⊕ С₁₀₁₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₁₁₁₀ ⊕ С₀₁₁₀₁ ⊕ С₀₁₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₁₁₁₁₀ ⊕ С₁₁₁₀₁ ⊕ С₁₁₀₁₁ ⊕ С₁₀₁₁₁ ⊕ С₀₁₁₁₁ ⊕ С₁₁₁₁₁ = 1 => С₁₁₁₁₁ = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0

Таким образом, полином Жегалкина будет равен:
F_ж = 1 ⊕ F ⊕ X∧W ⊕ Y∧W ⊕ X∧Y∧Z ⊕ Y∧Z∧W ⊕ X∧Y∧Z∧W
Логическая схема, соответствующая полиному Жегалкина: