演算法則 - mirrnagi

ブール代数 > 演算法則

変数の値や変数は０と１の二つだけ
計算の優先順位　(括弧) → NOT → AND → OR　他は知らぬ

公式１

基本演算

• NOT

0 = 1
1 = 0

• AND

0 ･ 0 = 0
0 ･ 1 = 0
1 ･ 0 = 0
1 ･ 1 = 1

• OR

0 ･ 0 = 0
0 ･ 1 = 1
1 ･ 0 = 1
1 ･ 1 = 1

交換則

A + B = B + A
A ･ B = B ･ A
A ⊕ B = B ⊕ A

結合則

A + B + C = ( A + B ) + C = A ( + B + C )
A ･ B ･ C = ( A ･ B ) ･ C = A ( ･ B ･ C )

分配則

A ･ ( B + C ) = A ･ B + A ･ C
A + B ･ C = ( A + B ) ･ ( A + C )

二重否定

NOT NOT A = A
NOT NOT NOT A = NOT A

公式２

---

A ･ 1 = A
A ･ 0 = 0
A + 1 = 1
A + 0 = A

べき等則

A + A = A
A ･ A = A

相補則

A + A = 1
A ･ A = 0

公式３

吸収則

A + A ･ B = A
A ( A + B ) = A

---

( A + B ) ･ ( A + B ) = A
A + A ･ B = A + B
A + A ･ B = A + B
( A + B ) ･ ( A + C ) = A ･ C + A ･ B

公式４ ド・モルガンの定理

A + B + C + D + ... = A ･ B ･ C ･ D ･ ...
A ･ B ･ C ･ D ･ ... = A + B + C + D + ...