From 8009812a1f98ffcd23822160ae62a6aee9d39ccb Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 13 Jan 2025 12:35:49 -0700 Subject: [PATCH] vault backup: 2025-01-13 12:35:49 --- .../ECE2700/Binary Logic.md | 20 +------------------ 1 file changed, 1 insertion(+), 19 deletions(-) diff --git a/education/computer engineering/ECE2700/Binary Logic.md b/education/computer engineering/ECE2700/Binary Logic.md index dabc9ff..2596420 100644 --- a/education/computer engineering/ECE2700/Binary Logic.md +++ b/education/computer engineering/ECE2700/Binary Logic.md @@ -1,23 +1,5 @@ # Properties of Boolean Algebra -| 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 | | | | -| 14. Combining | | | | | -| 15. DeMorgan's Theorem | | | | | -| 16. | | | | | -| 17. Consensus | | | | | +| 17. Consensus | | | | | # Logic Gates