Промежуточные таблицы истинности:
¬B:

¬A:

¬C:

D∧C:

(D∧C)∧(¬B):

((D∧C)∧(¬B))∧(¬A):

D∧(¬B):

(D∧(¬B))∧A:

E∧(¬C):

(E∧(¬C))∧B:

((E∧(¬C))∧B)∧A:

C∧B:

(C∧B)∧A:

(((D∧C)∧(¬B))∧(¬A))∨((D∧(¬B))∧A):

((((D∧C)∧(¬B))∧(¬A))∨((D∧(¬B))∧A))∨(((E∧(¬C))∧B)∧A):

(((((D∧C)∧(¬B))∧(¬A))∨((D∧(¬B))∧A))∨(((E∧(¬C))∧B)∧A))∨((C∧B)∧A):

Общая таблица истинности:

Логическая схема:

---

Совершенная дизъюнктивная нормальная форма (СДНФ):

По таблице истинности:
F_сднф = ¬D∧¬C∧B∧A∧E ∨ ¬D∧C∧B∧A∧¬E ∨ ¬D∧C∧B∧A∧E ∨ D∧¬C∧¬B∧A∧¬E ∨ D∧¬C∧¬B∧A∧E ∨ D∧¬C∧B∧A∧E ∨ D∧C∧¬B∧¬A∧¬E ∨ D∧C∧¬B∧¬A∧E ∨ D∧C∧¬B∧A∧¬E ∨ D∧C∧¬B∧A∧E ∨ D∧C∧B∧A∧¬E ∨ D∧C∧B∧A∧E
Логическая cхема:

---

Совершенная конъюнктивная нормальная форма (СКНФ):

По таблице истинности:
F_скнф = (D∨C∨B∨A∨E) ∧ (D∨C∨B∨A∨¬E) ∧ (D∨C∨B∨¬A∨E) ∧ (D∨C∨B∨¬A∨¬E) ∧ (D∨C∨¬B∨A∨E) ∧ (D∨C∨¬B∨A∨¬E) ∧ (D∨C∨¬B∨¬A∨E) ∧ (D∨¬C∨B∨A∨E) ∧ (D∨¬C∨B∨A∨¬E) ∧ (D∨¬C∨B∨¬A∨E) ∧ (D∨¬C∨B∨¬A∨¬E) ∧ (D∨¬C∨¬B∨A∨E) ∧ (D∨¬C∨¬B∨A∨¬E) ∧ (¬D∨C∨B∨A∨E) ∧ (¬D∨C∨B∨A∨¬E) ∧ (¬D∨C∨¬B∨A∨E) ∧ (¬D∨C∨¬B∨A∨¬E) ∧ (¬D∨C∨¬B∨¬A∨E) ∧ (¬D∨¬C∨¬B∨A∨E) ∧ (¬D∨¬C∨¬B∨A∨¬E)
Логическая cхема:

---

Построение полинома Жегалкина:

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

Так как F_ж(00000) = 0, то С₀₀₀₀₀ = 0.

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

Таким образом, полином Жегалкина будет равен:
F_ж = D∧C ⊕ D∧A ⊕ D∧C∧B ⊕ D∧C∧A ⊕ D∧B∧A ⊕ C∧B∧A ⊕ B∧A∧E ⊕ D∧C∧B∧A ⊕ C∧B∧A∧E
Логическая схема, соответствующая полиному Жегалкина: