Positional numbering system.html (2077B)
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="created" content="2017-11-09 3:09:18 PM +0000"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2017-11-09 6:26:36 PM +0000"/><title>Positional numbering system</title></head><body><div>Z is a set of {-inf…0…inf} integers<br/></div><div>define an alphabet ∑</div><div>A string X of n elements from ∑: X<span style="vertical-align: sub;">n</span> is in ∑<span style="vertical-align: super;">n</span></div><div>Apply X<span style="vertical-align: sub;">n</span> to a valuation function F</div><div><br/></div><div><br/></div><div>For a base-10 system (radix = 10):</div><div><img src="Positional%20numbering%20system.resources/screenshot_1.png" height="114" width="376"/><br/></div><div><br/></div><div>How do you choose a representation?</div><div><ul><li>representation of special values/cases (e.g. 0)</li><li>range of values that can be represented</li><li>efficiency of implementation (common operations?)</li></ul></div><div><br/></div><div>Unsigned integer representation:</div><div><img src="Positional%20numbering%20system.resources/screenshot.png" height="34" width="409"/><br/></div><div><br/></div><div>Range: 2<span style="vertical-align: super;">n</span> -1 (total 2<span style="vertical-align: super;">n</span>, but one of those is 0)</div><div>Can overflow, so have to detect — carry</div><div><br/></div><div><a href="Positional%20numbering%20system.resources/Page%2028%20-%20Livescribe%203%20Starter%20Notebook.pdf">Page 28 - Livescribe 3 Starter Notebook.pdf</a><a href="Positional%20numbering%20system.resources/Page%2029%20-%20Livescribe%203%20Starter%20Notebook.pdf">Page 29 - Livescribe 3 Starter Notebook.pdf</a></div><div><br/></div></body></html>