{"id":2340,"date":"2019-07-29T20:40:17","date_gmt":"2019-07-29T20:40:17","guid":{"rendered":"http:\/\/www.sydneysmith.com\/wordpress\/?p=2340"},"modified":"2019-07-29T20:59:19","modified_gmt":"2019-07-29T20:59:19","slug":"hp-25-non-normalized-numbers","status":"publish","type":"post","link":"https:\/\/www.sydneysmith.com\/wordpress\/2340\/hp-25-non-normalized-numbers\/","title":{"rendered":"HP-25 Non-Normalized Numbers"},"content":{"rendered":"

It turns out that once you have access to some HP-25 functions that aren’t on the keyboard<\/a>, you can put a lot of interesting “numbers” on the stack. <\/p>\n

The question I wanted to check was this: when I use prgcode “ca” to give 10 in X, does it lift the stack?<\/p>\n

If there is a final value on the stack (eg 4 ENTER 5 + or 1 X<->Y X<->Y) sure – it lifts. And if you do 3 ENTER 4 CLx, you end up with 3 in Y and, after running a “ca” program step, 10 in X.<\/p>\n

There’s another one to check though: key in 5 then run “ca”. What does that do?<\/p>\n

Here’s the before:
\n\"HP-25<\/p>\n

Here’s the after:
\n\"HP-25<\/p>\n

It doesn’t look like either: lifted or didn’t. It doesn’t seem to make any sense, until you see what is actually in the X register.<\/p>\n

Here’s what that looks like:
\n\"Internal
\nYou can see ” 60.00″ is in the display (A=06000… B=20100…).<\/p>\n

But what is really interesting, is what is in C and M2 (the actual X register inside the HP-25 processor). That is “05a00000000001”. The sign is positive (first “0”). The mantissa is “5.a00000000” (next 10 digits, with a decimal point after the first one). The exponent sign is positive (next “0”), and the exponent is “01”.<\/p>\n

We have 5.a x 10^1 or 5a. That is being shown as 5 tens plus 10 ones. i.e. 60.<\/p>\n

But, but – but there’s an “a” in the digits! Yep, a non-normalized number.<\/p>\n

I hadn’t looked before but when I went to key in 2 f 3 a 4 as program steps, I noticed that 2 is prgcode “c2”, 3 is prgcode “c3” and 4 is prgcode “c4”. Interesting right? Our “ca” to “cf” prgcodes are a natural extension of the “0” to “9” keys; instead of things that coincidently give those 10 to 15 values.<\/p>\n

The 2 f 3 a 4 sequence doesn’t do what I’d hoped for. It isn’t a simple store a digit then move right one place. You get 24040.00 in the display and “023a4000000004” in C and M2. The earlier “f” got dropped.<\/p>\n

It isn’t “earlier hex digits” though. It only seems to be “f” digits (perhaps it’s overflow \/ carry related). The following gave me what I expected: c2 cb c3 ca c4 (2 b 3 a 4). C and M2 = 02b3a400000004, i.e. “2b3a4”. That displays as “31404.00” (20000 + 11*1000 + 300 + 10*10 + 4 = 20000 + 11000 + 300 + 100 + 4 = 31404).<\/p>\n

It turns out you can put non-normalized numbers in the X register of a HP-25\/C.<\/p>\n

STO 6 will happily store the non-normalized number as-is in memory 6. CLx RCL 6 will happily bring it back again (also with the hex digits intact).<\/p>\n

Some of the fancier tricks we used to do with HP-67 non-normalized numbers (such as 0.00001e+00 taking much longer to divide than 1.00000e-05; and letters in the display) are still out of reach for now. However, there is more to the HP-25 than we thought previously.<\/p>\n","protected":false},"excerpt":{"rendered":"

It turns out that once you have access to some HP-25 functions that aren’t on the keyboard, you can put a lot of interesting “numbers” on the stack.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[16,5,69],"tags":[],"_links":{"self":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/2340"}],"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=2340"}],"version-history":[{"count":4,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/2340\/revisions"}],"predecessor-version":[{"id":2347,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/2340\/revisions\/2347"}],"wp:attachment":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/media?parent=2340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/categories?post=2340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/tags?post=2340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}