Karnaugh Maps.html (7967B)
1 <?xml version="1.0" encoding="UTF-8"?> 2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3 <html><head><link rel="stylesheet" href="sitewide.css" /><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta name="exporter-version" content="Evernote Mac 6.13.1 (455785)"/><meta name="altitude" content="-4.241825557471657e-09"/><meta name="author" content="Alex Balgavy"/><meta name="created" content="2017-11-08 2:34:46 PM +0000"/><meta name="latitude" content="52.33308902708033"/><meta name="longitude" content="4.866490141020141"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2017-11-09 12:03:36 AM +0000"/><title>Karnaugh Maps</title></head><body><div><span style="font-weight: bold;">Given a truth table:</span></div><table style="border-collapse: collapse; min-width: 100%;"><colgroup><col style="width: 130px;"/><col style="width: 130px;"/><col style="width: 130px;"/><col style="width: 130px;"/><col style="width: 130px;"/></colgroup><tbody><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><br/></div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="font-weight: bold;">x₁</span></div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="font-weight: bold;">x₂</span></div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="font-weight: bold;">x₃</span></div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="font-weight: bold;">ƒ₁</span></div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₁</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="background-color: rgb(255, 255, 255);">0</span></div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div><span style="background-color: rgb(255, 255, 255);">1</span></div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₂</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₃</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₄</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₅</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₆</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₇</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>0</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₈</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>1</div></td></tr></tbody></table><div><span style="font-weight: bold;">Make a table such as this:</span></div><div>Adjacent cells can only differ in one bit!</div><div><div><br/></div><table style="border-collapse: collapse; min-width: 100%;"><colgroup><col style="width: 107px;"/><col style="width: 130px;"/><col style="width: 130px;"/><col style="width: 130px;"/><col style="width: 130px;"/></colgroup><tbody><tr><td style="border: 1px solid rgb(219, 219, 219); width: 107px; padding: 8px;"><div>A/BC </div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>00</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>01</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>11</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>10</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 107px; padding: 8px;"><div>0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₁: 1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₂: 1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₄: 1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₃: 0</div></td></tr><tr><td style="border: 1px solid rgb(219, 219, 219); width: 107px; padding: 8px;"><div>1</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₅: 0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₆: 0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₇: 0</div></td><td style="border: 1px solid rgb(219, 219, 219); width: 130px; padding: 8px;"><div>m₈: 1</div></td></tr></tbody></table><div><br/></div></div><div>Then choose groups of 1s of size 2<span style="vertical-align: super;">n</span>. They should be as big as possible. Then you see what changes within the groups, and if a bit changes to its complement so that it cancels out to 1, you don’t have to include it.</div></body></html>