Boolean Algebra Laws and theorems cheat sheet
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1. X + 0 = X
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1D. X·1 = X
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2. X + 1 = 1
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2D. X·0 = 0
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3. X + X = X
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3D. X·X = X
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4. (X´)´ = X
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5. X + X´ = 1
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5D. X·X´ = 0
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6. X + Y = Y + X
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6D. XY = YX
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7. (X + Y) + Z = X + (Y + Z) = X + Y + Z
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7D. (XY)Z = X(YZ) = XYZ
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8. X(Y + Z) = XY + XZ
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8D. X + YZ = (X + Y)(X + Z)
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9. XY + XY´ = X
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9D. (X + Y)(X + Y´) = X
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10. X + XY = X
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10D. X(X + Y) = X
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11. X(X´ + Y) = XY
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11D. X + X´Y = X + Y
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12. (X + Y + Z + . . .)´ = X´Y´Z´. . .
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12D. (XYZ. . .)´ = X´ + Y´ + Z´ + . . .
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13. (X + Y + Z)^D = XYZ. . .
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13D. (XYZ. . .)^D = X + Y + X + . . .
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14. (X + Y)(X´ + Z) = XZ + X´Y
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14D. XY + X´Z = (X + Z)(X´ + Y)
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15. XY + YZ + X´Z = XY + YZ
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15D. (X + Y)(Y + Z)(X´ + Z) = (X + Y)(X´ + Z)
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XOR: X @ Y = X´Y + XY´
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XNAND: (X @ Y)´ X
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Cheatography n. The art of mapping complex subjects into clear, instantly navigable reference guides.
