Промежуточные таблицы истинности:
X1→X2:

X2→X3:

X3→X4:

X4→X5:

X5→X1:

(X1→X2)∧(X2→X3):

((X1→X2)∧(X2→X3))∧(X3→X4):

(((X1→X2)∧(X2→X3))∧(X3→X4))∧(X4→X5):

((((X1→X2)∧(X2→X3))∧(X3→X4))∧(X4→X5))∧(X5→X1):

(((((X1→X2)∧(X2→X3))∧(X3→X4))∧(X4→X5))∧(X5→X1))≡1:

Общая таблица истинности:

Логическая схема:

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Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
F_сднф = ¬X1∧¬X2∧¬X3∧¬X4∧¬X5 ∨ X1∧X2∧X3∧X4∧X5
Логическая cхема:

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Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
F_скнф = (X1∨X2∨X3∨X4∨¬X5) ∧ (X1∨X2∨X3∨¬X4∨X5) ∧ (X1∨X2∨X3∨¬X4∨¬X5) ∧ (X1∨X2∨¬X3∨X4∨X5) ∧ (X1∨X2∨¬X3∨X4∨¬X5) ∧ (X1∨X2∨¬X3∨¬X4∨X5) ∧ (X1∨X2∨¬X3∨¬X4∨¬X5) ∧ (X1∨¬X2∨X3∨X4∨X5) ∧ (X1∨¬X2∨X3∨X4∨¬X5) ∧ (X1∨¬X2∨X3∨¬X4∨X5) ∧ (X1∨¬X2∨X3∨¬X4∨¬X5) ∧ (X1∨¬X2∨¬X3∨X4∨X5) ∧ (X1∨¬X2∨¬X3∨X4∨¬X5) ∧ (X1∨¬X2∨¬X3∨¬X4∨X5) ∧ (X1∨¬X2∨¬X3∨¬X4∨¬X5) ∧ (¬X1∨X2∨X3∨X4∨X5) ∧ (¬X1∨X2∨X3∨X4∨¬X5) ∧ (¬X1∨X2∨X3∨¬X4∨X5) ∧ (¬X1∨X2∨X3∨¬X4∨¬X5) ∧ (¬X1∨X2∨¬X3∨X4∨X5) ∧ (¬X1∨X2∨¬X3∨X4∨¬X5) ∧ (¬X1∨X2∨¬X3∨¬X4∨X5) ∧ (¬X1∨X2∨¬X3∨¬X4∨¬X5) ∧ (¬X1∨¬X2∨X3∨X4∨X5) ∧ (¬X1∨¬X2∨X3∨X4∨¬X5) ∧ (¬X1∨¬X2∨X3∨¬X4∨X5) ∧ (¬X1∨¬X2∨X3∨¬X4∨¬X5) ∧ (¬X1∨¬X2∨¬X3∨X4∨X5) ∧ (¬X1∨¬X2∨¬X3∨X4∨¬X5) ∧ (¬X1∨¬X2∨¬X3∨¬X4∨X5)
Логическая cхема:

---

Построение полинома Жегалкина:

По таблице истинности функции
Построим полином Жегалкина:
F_ж = C₀₀₀₀₀ ⊕ C₁₀₀₀₀∧X1 ⊕ C₀₁₀₀₀∧X2 ⊕ C₀₀₁₀₀∧X3 ⊕ C₀₀₀₁₀∧X4 ⊕ C₀₀₀₀₁∧X5 ⊕ C₁₁₀₀₀∧X1∧X2 ⊕ C₁₀₁₀₀∧X1∧X3 ⊕ C₁₀₀₁₀∧X1∧X4 ⊕ C₁₀₀₀₁∧X1∧X5 ⊕ C₀₁₁₀₀∧X2∧X3 ⊕ C₀₁₀₁₀∧X2∧X4 ⊕ C₀₁₀₀₁∧X2∧X5 ⊕ C₀₀₁₁₀∧X3∧X4 ⊕ C₀₀₁₀₁∧X3∧X5 ⊕ C₀₀₀₁₁∧X4∧X5 ⊕ C₁₁₁₀₀∧X1∧X2∧X3 ⊕ C₁₁₀₁₀∧X1∧X2∧X4 ⊕ C₁₁₀₀₁∧X1∧X2∧X5 ⊕ C₁₀₁₁₀∧X1∧X3∧X4 ⊕ C₁₀₁₀₁∧X1∧X3∧X5 ⊕ C₁₀₀₁₁∧X1∧X4∧X5 ⊕ C₀₁₁₁₀∧X2∧X3∧X4 ⊕ C₀₁₁₀₁∧X2∧X3∧X5 ⊕ C₀₁₀₁₁∧X2∧X4∧X5 ⊕ C₀₀₁₁₁∧X3∧X4∧X5 ⊕ C₁₁₁₁₀∧X1∧X2∧X3∧X4 ⊕ C₁₁₁₀₁∧X1∧X2∧X3∧X5 ⊕ C₁₁₀₁₁∧X1∧X2∧X4∧X5 ⊕ C₁₀₁₁₁∧X1∧X3∧X4∧X5 ⊕ C₀₁₁₁₁∧X2∧X3∧X4∧X5 ⊕ C₁₁₁₁₁∧X1∧X2∧X3∧X4∧X5

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 = 0 => С₀₁₀₀₀ = 1 ⊕ 0 = 1
F_ж(00100) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ = 0 => С₀₀₁₀₀ = 1 ⊕ 0 = 1
F_ж(00010) = С₀₀₀₀₀ ⊕ С₀₀₀₁₀ = 0 => С₀₀₀₁₀ = 1 ⊕ 0 = 1
F_ж(00001) = С₀₀₀₀₀ ⊕ С₀₀₀₀₁ = 0 => С₀₀₀₀₁ = 1 ⊕ 0 = 1
F_ж(11000) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₁₁₀₀₀ = 0 => С₁₁₀₀₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10100) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₁₀₁₀₀ = 0 => С₁₀₁₀₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₀₁₀ = 0 => С₁₀₀₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₀₁ = 0 => С₁₀₀₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01100) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₁₁₀₀ = 0 => С₀₁₁₀₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01010) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₁₀₁₀ = 0 => С₀₁₀₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01001) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₀₀₁ = 0 => С₀₁₀₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(00110) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₁₁₀ = 0 => С₀₀₁₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(00101) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₀₁ = 0 => С₀₀₁₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(00011) = С₀₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₀₁₁ = 0 => С₀₀₀₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11100) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₀₁₁₀₀ ⊕ С₁₁₁₀₀ = 0 => С₁₁₁₀₀ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₀₁₀ ⊕ С₁₁₀₁₀ = 0 => С₁₁₀₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₀₁ ⊕ С₁₁₀₀₁ = 0 => С₁₁₀₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₀₁₁₀ = 0 => С₁₀₁₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₀₁₀₁ = 0 => С₁₀₁₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₀₀₁₁ = 0 => С₁₀₀₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01110) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₀₁₁₁₀ = 0 => С₀₁₁₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01101) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₀₁₁₀₁ = 0 => С₀₁₁₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01011) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₀₁₁ = 0 => С₀₁₀₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(00111) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₀₁₁₁ = 0 => С₀₀₁₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₁₀ ⊕ С₁₀₁₁₀ ⊕ С₀₁₁₁₀ ⊕ С₁₁₁₁₀ = 0 => С₁₁₁₁₀ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₁₀₁ ⊕ С₀₁₁₀₁ ⊕ С₁₁₁₀₁ = 0 => С₁₁₁₀₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(11011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₁₀₁₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₁₀₁₁ ⊕ С₁₁₀₁₁ = 0 => С₁₁₀₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(10111) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₀₁₁₀ ⊕ С₁₀₁₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₁₀₁₁₁ = 0 => С₁₀₁₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1
F_ж(01111) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₁₁₀ ⊕ С₀₁₁₀₁ ⊕ С₀₁₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₀₁₁₁₁ = 0 => С₀₁₁₁₁ = 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 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 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 = 0

Таким образом, полином Жегалкина будет равен:
F_ж = 1 ⊕ X1 ⊕ X2 ⊕ X3 ⊕ X4 ⊕ X5 ⊕ X1∧X2 ⊕ X1∧X3 ⊕ X1∧X4 ⊕ X1∧X5 ⊕ X2∧X3 ⊕ X2∧X4 ⊕ X2∧X5 ⊕ X3∧X4 ⊕ X3∧X5 ⊕ X4∧X5 ⊕ X1∧X2∧X3 ⊕ X1∧X2∧X4 ⊕ X1∧X2∧X5 ⊕ X1∧X3∧X4 ⊕ X1∧X3∧X5 ⊕ X1∧X4∧X5 ⊕ X2∧X3∧X4 ⊕ X2∧X3∧X5 ⊕ X2∧X4∧X5 ⊕ X3∧X4∧X5 ⊕ X1∧X2∧X3∧X4 ⊕ X1∧X2∧X3∧X5 ⊕ X1∧X2∧X4∧X5 ⊕ X1∧X3∧X4∧X5 ⊕ X2∧X3∧X4∧X5
Логическая схема, соответствующая полиному Жегалкина: