diff --git a/education/computer engineering/ECE2700/Karnaugh Maps.md b/education/computer engineering/ECE2700/Karnaugh Maps.md index 4177f3a..e3d8fa5 100644 --- a/education/computer engineering/ECE2700/Karnaugh Maps.md +++ b/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. \ No newline at end of file +- 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 \ No newline at end of file diff --git a/Pasted image 20250224104850.png b/education/computer engineering/ECE2700/assets/Pasted image 20250224104850.png similarity index 100% rename from Pasted image 20250224104850.png rename to education/computer engineering/ECE2700/assets/Pasted image 20250224104850.png diff --git a/education/computer engineering/ECE2700/assets/Pasted image 20250224105753.png b/education/computer engineering/ECE2700/assets/Pasted image 20250224105753.png new file mode 100644 index 0000000..691088d Binary files /dev/null and b/education/computer engineering/ECE2700/assets/Pasted image 20250224105753.png differ