diff --git a/education/computer engineering/ECE2700/Binary Logic.md b/education/computer engineering/ECE2700/Binary Logic.md index 2596420..32454eb 100644 --- a/education/computer engineering/ECE2700/Binary Logic.md +++ b/education/computer engineering/ECE2700/Binary Logic.md @@ -1,5 +1,23 @@ # Properties of Boolean Algebra -| 17. Consensus | | | | | +| Number | Col. A | Col. A Description | Col. B | Col. B Description | +| ---------------------- | --------------------------------------------------------------------------------- | ------------------ | ----------------------------------------------------------------------------------- | ------------------ | +| 1. | $0 \cdot 0 = 0$ | | $1 + 1 = 1$ | | +| 2. | $1 \cdot 1 = 1$ | | $0 + 0 = 0$ | | +| 3. | $0 \cdot 1 = 1 \cdot 0 = 0$ | | $1 + 0 = 0 + 1 = 1$ | | +| 4. | if $x = 0$ then $\overline{x} = 1$ | | if $x = 1$ then $\overline{x} = 0$ | | +| 5. | $x \cdot 0 = 0$ | | $x + 1 = 1$ | | +| 6. | $x \cdot 1 = x$ | | $x + 0 = x$ | | +| 7. | $x \cdot x = x$ | | $x + x = x$ | | +| 8. | $x \cdot \overline{x} = 0$ | | $$x + \overline{x} = 1$ | | +| 9. | $\overline{\overline{x}} = x$ | | | | +| 10. Commutative | $x \cdot y = y \cdot x$ | | $x + y = y + x$ | | +| 11. Associative | $x \cdot (y \cdot z) = (x \cdot y) \cdot z$ | | $x + (y + z) = (x + y) +z$ | | +| 12. Distributive | $x \cdot (y +z) = x \cdot y + x \cdot z$ | | $x + y \cdot z = (x + y) \cdot (x + z$ | | +| 13. Absorption | $x + x \cdot y = x$ | | $x \cdot (x + y) = x$ | | +| 14. Combining | $x \cdot y + x \cdot \overline{y} = x$ | | $(x + y) \cdot (x + \overline{y}) = x$ | | +| 15. DeMorgan's Theorem | $\overline{x \cdot y} = \overline{x} + \overline{y}$ | | $x + y = \overline{x} \cdot \overline{y}$ | | +| 16. | $x + \overline{x} \cdot y = x + y$ | | $x \cdot (\overline{x} + y) = x \cdot y$ | | +| 17. Consensus | $x \cdot y + y \cdot z + \overline{x} \cdot z = x \cdot y + \overline{x} \cdot z$ | | $(x + y) \cdot (y + z) \cdot (\overline{x} + z) = (x + y) \cdot (\overline{x} + z)$ | | # Logic Gates