vault backup: 2025-02-24 10:58:29

education/computer engineering/ECE2700/Karnaugh Maps.md

@@ -4,8 +4,17 @@ A Karnaugh map is an alternative to a truth table for representing a function in
 
 Given the above truth table, the columns are labelled with $x_1$, and the rows are labelled with $x_2$.
 
-To find a minimal boolean expression with a ka, we need to find the smallest number of product terms  ($x_1$, $x_2$) that should produce a 1 for all instances where the cell in a table is $1$. 
+To find a minimal boolean expression with a Karnaugh map, we need to find the smallest number of product terms  ($x_1$, $x_2$) that should produce a 1 for all instances where the cell in a table is $1$. 
+
+# Two Variable Maps
 
 ![[Pasted image 20250224104850.png]]
 
-Given the map described in the above image, the output is $1$ for the row where $x_2$ is equal to 1. Similarly, the output is $1$ for the column where $x_2$. By ORing the condition where $x_1$ is zero ($\overline{x_1}$), and the condition where $x_2$ is one ($x_1$), we can find a minimal expression for the truth table.
+- Given the map described in the above image, the output is $1$ for the row where $x_2$ is equal to 1.
+- Similarly, the output is $1$ for the column where $x_1$ is equal to zero.
+- By ORing the condition where $x_1$ is zero ($\overline{x_1}$), and the condition where $x_2$ is one ($x_1$), we can find a minimal expression for the truth table.
+
+# Three Variable Maps
+![[Pasted image 20250224105753.png]]
+
+A three variable Karnaugh map