Промежуточные таблицы истинности:
X1∧X2:

(X1∧X2)∧X3:

((X1∧X2)∧X3)∧X4:

¬X1:

F∧(((X1∧X2)∧X3)∧X4):

(¬X1)∧X2:

((¬X1)∧X2)∧X1:

(((¬X1)∧X2)∧X1)∧X3:

((((¬X1)∧X2)∧X1)∧X3)∧X1:

(((((¬X1)∧X2)∧X1)∧X3)∧X1)∧X3:

((((((¬X1)∧X2)∧X1)∧X3)∧X1)∧X3)∧X4:

(F∧(((X1∧X2)∧X3)∧X4))≡(((((((¬X1)∧X2)∧X1)∧X3)∧X1)∧X3)∧X4):

Общая таблица истинности:

Логическая схема:

---

Совершенная дизъюнктивная нормальная форма (СДНФ):

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

---

Совершенная конъюнктивная нормальная форма (СКНФ):

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

---

Построение полинома Жегалкина:

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

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 = 1 => С₁₀₀₀₀ = 1 ⊕ 1 = 0
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 = 1 => С₁₁₀₀₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10100) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₁₀₁₀₀ = 1 => С₁₀₁₀₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₀₁₀ = 1 => С₁₀₀₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₀₁ = 1 => С₁₀₀₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 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 = 1 => С₀₁₀₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(00110) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₁₁₀ = 1 => С₀₀₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(00101) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₀₁ = 1 => С₀₀₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
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 = 1 => С₁₁₁₀₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11010) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₀₁₀ ⊕ С₁₁₀₁₀ = 1 => С₁₁₀₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11001) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₀₁ ⊕ С₁₁₀₀₁ = 1 => С₁₁₀₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₀₁₁₀ = 1 => С₁₀₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₀₁₀₁ = 1 => С₁₀₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(10011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₀₀₁₁ = 1 => С₁₀₀₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01110) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₀₁₁₁₀ = 1 => С₀₁₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01101) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₀₁₁₀₁ = 1 => С₀₁₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01011) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₀₁₁ = 1 => С₀₁₀₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(00111) = С₀₀₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₀₁₁₁ = 1 => С₀₀₁₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11110) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₁₀ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₀₁₁₀ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₁₀ ⊕ С₁₀₁₁₀ ⊕ С₀₁₁₁₀ ⊕ С₁₁₁₁₀ = 1 => С₁₁₁₁₀ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11101) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₁₀₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₀₁ ⊕ С₁₁₁₀₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₁₀₁ ⊕ С₀₁₁₀₁ ⊕ С₁₁₁₀₁ = 1 => С₁₁₁₀₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(11011) = С₀₀₀₀₀ ⊕ С₁₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₁₁₀₀₀ ⊕ С₁₀₀₁₀ ⊕ С₁₀₀₀₁ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₀₁₁ ⊕ С₁₁₀₁₀ ⊕ С₁₁₀₀₁ ⊕ С₁₀₀₁₁ ⊕ С₀₁₀₁₁ ⊕ С₁₁₀₁₁ = 1 => С₁₁₀₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 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 = 1 => С₁₀₁₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F_ж(01111) = С₀₀₀₀₀ ⊕ С₀₁₀₀₀ ⊕ С₀₀₁₀₀ ⊕ С₀₀₀₁₀ ⊕ С₀₀₀₀₁ ⊕ С₀₁₁₀₀ ⊕ С₀₁₀₁₀ ⊕ С₀₁₀₀₁ ⊕ С₀₀₁₁₀ ⊕ С₀₀₁₀₁ ⊕ С₀₀₀₁₁ ⊕ С₀₁₁₁₀ ⊕ С₀₁₁₀₁ ⊕ С₀₁₀₁₁ ⊕ С₀₀₁₁₁ ⊕ С₀₁₁₁₁ = 1 => С₀₁₁₁₁ = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
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 = 0 => С₁₁₁₁₁ = 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 = 1

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