{"id":130,"date":"2011-05-21T04:11:05","date_gmt":"2011-05-21T04:11:05","guid":{"rendered":"http:\/\/www.sydneysmith.com\/wordpress\/?p=130"},"modified":"2017-05-14T01:39:41","modified_gmt":"2017-05-14T01:39:41","slug":"the-hp67-and-non-normalized-numbers","status":"publish","type":"post","link":"https:\/\/www.sydneysmith.com\/wordpress\/130\/the-hp67-and-non-normalized-numbers\/","title":{"rendered":"The HP67 and Non-Normalized Numbers"},"content":{"rendered":"<p>This is an interesting side note for fanatics. You can skip this if you are not a fanatic.<\/p>\n<p>NOTE: If you have a HP97 don&#8217;t use non-normalized numbers (NNNs).<br \/>\nThe HP97 is a printing version of the HP67. NNNs burn out the print head on a HP97.<\/p>\n<p>The HP calculators used binary coded decimal (BCD) to fit numbers into registers (X, Y Z, T) and into memories.<br \/>\nInternally, numbers were stored in SCIentific notation with a 10 digit mantissa and a 2 digit exponent. When you add a sign to the mantissa and to the exponent you end up with 14 BCD digits: SMMMMMMMMMMSEE. S is 0 if the mantissa or exponent is positive and 9 if negative.<\/p>\n<p>14 BCD digits occupy 15 display positions as the decimal point is always right of the first mantissa digit and, on the HP67, a decimal point occupies a display position of its own.<\/p>\n<p>BCD defines meanings for 0-9 but each four-bit nibble can also hold other values (0x0a &#8211; 0x0f in hexadecimal notation).<br \/>\nThe display uses values outside of 0-9 to display the messages you see such as &#8220;Error&#8221; and &#8220;Crd&#8221;.<\/p>\n<p>Nibble values in registers display as: 0-9 = 0-9; A = \u201cr\u201d, B= \u201cC\u201d, C=\u201do\u201d, D=\u201dd\u201d, E=\u201dE\u201d, F=\u201d \u201c.<\/p>\n<p>The 14 BCD digits occupy 7 bytes of memory. Each program step occupies 1 byte (even if it is 3 keystrokes).<\/p>\n<p>One way of creating NNNs was to key in program steps, write these to a mag card and then write a data header over the start of the card (f W\/Data, insert card, turn the calculator off midway through the write). You could then load the card back in, as data, and see what appeared in the storage registers.<\/p>\n<p>A more interesting way involved getting the program counter outside of steps 000-224 (it would point into a storage register) and then keying in program steps there.<\/p>\n<p>See also:<br \/>\n<a href=\"http:\/\/holyjoe.org\/hp\/nnn.htm\">Holy Joe<\/a><br \/>\nmy notes from 22 Dec 2005<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting side note for fanatics. You can skip this if you are not a fanatic. NOTE: If you have a HP97 don&#8217;t use non-normalized numbers (NNNs). The HP97 is a printing version of the HP67. NNNs burn out the print head on a HP97. The HP calculators used binary coded decimal (BCD) &hellip; <a href=\"https:\/\/www.sydneysmith.com\/wordpress\/130\/the-hp67-and-non-normalized-numbers\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">The HP67 and Non-Normalized Numbers<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[16,5,3],"tags":[],"_links":{"self":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/130"}],"collection":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/comments?post=130"}],"version-history":[{"count":1,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/130\/revisions"}],"predecessor-version":[{"id":1545,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/130\/revisions\/1545"}],"wp:attachment":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/media?parent=130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/categories?post=130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/tags?post=130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}