| 1a. | X • 0 = 0 | 1b. | X + 1 = 1 | Annulment Law | ||
| 2a. | X • 1 = X | 2b. | X + 0 = X | Identity Law | ||
| 3a. | X • X = X | 3b. | X + X = X | Idempotent Law | ||
| 4a. | X • X = 0 | 4b. | X + X = 1 | Compliment Law | ||
| 5. | X = X | Involution Law | ||||
| 6a. | X • Y = Y • X | 6b. | X + Y = Y + X | Commutative Law | ||
| 7a. | X (Y Z) = (X Y) Z = (X Z) Y = X Y Z | Associative Law | ||||
| 7b. | X + (Y + Z) = (X + Y) + Z = (X + Z) + Y = X + Y + Z | Associative Law | ||||
| 8a. | X • (Y + Z) = X Y + X Z | 8b. | X + Y Z = (X + Y) • (X + Z) | Distributive Law | ||
| 9a. | X • Y = X + Y | 9b. | X + Y = X • Y | de Morgan's Theorem | ||
| 10a. | X • (X + Y) = X | 10b. | X + X Y = X | Absorption Law | ||
| 11a. | (X + Y) • (X + Y) = X | 11b. | X Y + X Y = X | Redundancy Law | ||
| 12a. | (X + Y) • Y = XY | 12b. | X Y + Y = X + Y | Redundancy Law | ||
| 13a. | (X + Y) • (X + Z) • (Y + Z) = (X + Y) • (X + Z) | Consensus Law | ||||
| 13b. | X Y + X Z + Y Z = X Y + X Z | Consensus Law | ||||
| 14a. | X ⊕ Y = (X + Y) • (X + Y) | 14b. | X ⊕ Y = X Y + X Y | XOR Gate | ||
| 14c. | X ⊕ Y = (X • Y) • (X + Y) | XOR Gate (14a + 9a) | ||||
| 15a. | X ⊙ Y = (X + Y) • (X + Y) | 15b. | X ⊙ Y = X Y + X Y | XNOR Gate | ||
| X ⊙ Y = X ⊕ Y | 15c. | X ⊙ Y = X + Y + X Y | XNOR Gate (15b + 9b) | |||
| Standard | de Morgan's | |
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| NAND | X = A • B | X = A + B |
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| AND | X = A • B | X = A + B |
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| NOR | X = A + B | X = A • B |
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| OR | X = A + B | X = A • B |
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Last updated: Nov 27, 2022.