From b51fce6bacdfe72c3451705bb538b53b28ada9a1 Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 13 Jan 2025 13:19:26 -0700 Subject: [PATCH] vault backup: 2025-01-13 13:19:26 --- .../computer engineering/ECE2700/Binary Logic.md | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/education/computer engineering/ECE2700/Binary Logic.md b/education/computer engineering/ECE2700/Binary Logic.md index 8972cea..1ae7770 100644 --- a/education/computer engineering/ECE2700/Binary Logic.md +++ b/education/computer engineering/ECE2700/Binary Logic.md @@ -24,7 +24,21 @@ | 16. | $x + \overline{x} \cdot y = x + y$ | | $x \cdot (\overline{x} + y) = x \cdot y$ | | | 17. Consensus | $x \cdot y + y \cdot z + \overline{x} \cdot z = x \cdot y + \overline{x} \cdot z$ | | $(x + y) \cdot (y + z) \cdot (\overline{x} + z) = (x + y) \cdot (\overline{x} + z)$ | | # Synthesis +In the context of binary logic, synthesis refers to the act of creating a boolean expression that evaluates to match a given truth table. +This is done by creating a product term for each entry in the table that has an output of $1$, that also evaluates to $1$, then ORing each product term together and then simplifying. + +Example: + +Given the below truth table, synthesize a boolean expression that corresponds. + +| $x_1$ | $x_2$ | $f(x_1, x_2)$ | +| ----- | ----- | ------------- | +| 0 | 0 | 1 | +| 0 | 1 | 1 | +| 1 | 0 | 0 | +| 1 | 1 | 1 | +- # Logic Gates