From c0fd3b66ab5b9a81f1862ab6dcb17f9ce2590d46 Mon Sep 17 00:00:00 2001 From: arc Date: Fri, 10 Jan 2025 09:32:02 -0700 Subject: [PATCH] vault backup: 2025-01-10 09:32:02 --- .../computer engineering/ECE2700/Binary Logic.md | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/education/computer engineering/ECE2700/Binary Logic.md b/education/computer engineering/ECE2700/Binary Logic.md index 8f2c669..0856cdb 100644 --- a/education/computer engineering/ECE2700/Binary Logic.md +++ b/education/computer engineering/ECE2700/Binary Logic.md @@ -22,11 +22,20 @@ An AND gate will only output a 1 if *both* inputs are a one. | 1 | 0 | 0 | | 1 | 1 | 1 | ## Mathematical Expression -An AND operation is mathematically expressed using a times symbol, or with no symbol at all +An AND operation is mathematically expressed using a times symbol, or with no symbol at all: $$ y = x_1 \cdot x_2 = x_1x_2$$ # NAND Gate A NAND gate outputs a 1 *unless* both inputs are enabled. ## Truth Table -| \ No newline at end of file +| $x_1$ | $x_2$ | $y$ | +| ----- | ----- | --- | +| 0 | 0 | 1 | +| 0 | 1 | 1 | +| 1 | 0 | 1 | +| 1 | 1 | 0 | +## Mathematical Expression +A NAND operation is mathematically expressed using a bar over an AND operation: +$$ y = \overline{x_1 \cdot x_2}$$ +