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education/computer engineering/ECE2700/Karnaugh Maps.md
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@ -4,7 +4,8 @@ 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 $x_2$. Given the above truth table, the columns are labelled with $x_1$, and the rows are labelled with $x_2$.
To find a minimum cost implementation, we need to find the smallest number of product terms that should produce a 1 for all instances where $m = 1$ 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 $1$.
In the above example, ![[Pasted image 20250224104850.png]]
![[Pasted image 20250224104550.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.