$$ \newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\dx}{\text{ dx}}
\newcommand{\rang}{\text{rang}}
\newcommand{\s}{\ \ \ \ \ \ }
\newcommand{\arrows}{\s \Leftrightarrow \s}
\newcommand{\Arrows}{\s \Longleftrightarrow \s}
\newcommand{\arrow}{\s \Rightarrow \s}
\newcommand{\c}{\bcancel}
\newcommand{\v}[2]{
\begin{pmatrix}
#1 \\
#2 \\
\end{pmatrix}
}
\newcommand{\vt}[3]{
\begin{pmatrix}
#1 \\
#2 \\
#3 \\
\end{pmatrix}
}
\newcommand{\stack}[2]{
\substack{
#1 \\
#2
}
}
\newcommand{\atom}[3]{
\substack{
#1 \\
#2
}
\ce{#3}
}
$$
Karnaugh Map (K-map)
Alternative way of representing a truth table.
Can be used to generate an expression from a truth table. It is easier than the Sum of Products method for large truth tables.
Se slides: Lesson 3.pdf>page=30.
The sides of a Karnaugh map “warp” around.
The sides count in gray codes.
Procedure
- Draw the biggest rectangles you can around the $1$’s. The amount of cells in each rectangle should be described by $2^k$. (remember that the table “wraps”)
- For each rectangle write an equivalent equations that would create each rectangle and
OR them together. (example here)
Example of Karnaugh to gates
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