From WikiChip
Editing karnaugh map
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
This page supports semantic in-text annotations (e.g. "[[Is specified as::World Heritage Site]]") to build structured and queryable content provided by Semantic MediaWiki. For a comprehensive description on how to use annotations or the #ask parser function, please have a look at the getting started, in-text annotation, or inline queries help pages.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
{{title|Karnaugh Map (K-map)}} | {{title|Karnaugh Map (K-map)}} | ||
− | <div style="float: right; text-align: center; margin: 20px; width: 250px">[[File:3-input MAJ gate kmap.svg|200px]]<br />3-input [[MAJ]] gate<br /><math> | + | <div style="float: right; text-align: center; margin: 20px; width: 250px"> |
+ | [[File:3-input MAJ gate kmap.svg|200px]]<br /> | ||
+ | 3-input [[MAJ]] gate<br /> | ||
+ | <math> | ||
\begin{align} | \begin{align} | ||
f(a,b,c) =& AB+AC+BC \\ | f(a,b,c) =& AB+AC+BC \\ | ||
Line 111: | Line 114: | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
− | Each minterm in the equation is | + | Each minterm in the equation is than transferred into the K-map where each variable in the minterm represents a 1 and each complemented variable represents a 0. |
[[File:kmap example color coded (expression).svg|400px]] | [[File:kmap example color coded (expression).svg|400px]] | ||
=== from truth table === | === from truth table === | ||
Line 149: | Line 152: | ||
[[File:kmap example 2.svg|right|100px]] | [[File:kmap example 2.svg|right|100px]] | ||
− | The Karnaugh map on the | + | The Karnaugh map on the left on the other hand has two groups. One group spans both <math>B = 0</math> and <math>B = 1</math> and another that spans <math>A = 0</math> and <math>A = 1</math>. In the expression for the group that spans vertically, <math>B</math> changes yielding the expression <math>A</math>. Likewise in the expression that spans horizontally, <math>A</math> changes, yielding the expression <math>B</math>. The simplified equation for this K-map is the ORing of all the individual term - <math>f(A,B) = \sum m(1,2,3) = A+B</math>. |
Line 179: | Line 182: | ||
[[File:kmap (don't care example).svg|left|200px]] | [[File:kmap (don't care example).svg|left|200px]] | ||
− | The [[truth table]] to the Karnaugh map below is on the right and represents an [[incompletely specified function]]. Note the don't care values for two of the outputs. I.e. <math>f(0,0,0)</math> and <math>f(0,0,1)</math> should never happen. In this example, the two don't care values can be used to make the 2-cell group be a 4-cell group allowing us to eliminate a whole variable: <math>A</math>. The Boolean expression is therefore <math>f(a,b,c) = \bar B + | + | The [[truth table]] to the Karnaugh map below is on the right and represents an [[incompletely specified function]]. Note the don't care values for two of the outputs. I.e. <math>f(0,0,0)</math> and <math>f(0,0,1)</math> should never happen. In this example, the two don't care values can be used to make the 2-cell group be a 4-cell group allowing us to eliminate a whole variable: <math>A</math>. The Boolean expression is therefore <math>f(a,b,c) = \bar B + AB</math>. |
{{clear}} | {{clear}} | ||
− | |||
== Product of Sum (PoS)== | == Product of Sum (PoS)== | ||
[[File:kmap pos example.svg|200px|right]] | [[File:kmap pos example.svg|200px|right]] | ||
Line 196: | Line 198: | ||
=== 5-variable K-map=== | === 5-variable K-map=== | ||
{{empty section}} | {{empty section}} | ||
− | |||
=== 6-variable K-map=== | === 6-variable K-map=== | ||
{{empty section}} | {{empty section}} |