Editing Sinclair Scientific (section)

==Design==

===Sinclair Scientific===
The HP-35 used five chips, and had been developed by twenty engineers at a cost of a million dollars, leading the Texas Instruments engineers to think that Sinclair's aim to build a scientific calculator around the TMS0805 chip, which could barely handle four-function arithmetic, was impossible.<ref name=eng>{{cite web |url=http://files.righto.com/calculator/sinclair_scientific_simulator.html |title=Reversing Sinclair's amazing 1974 calculator hack - half the ROM of the HP-35 |last=Shirriff |first=Ken |access-date=9 December 2013}}</ref><ref name=reg>{{cite web |url=https://www.theregister.co.uk/2013/09/02/google_chap_reverse_engineers_sinclair_scientific_calculator/ |title=Google chap reverse engineers Sinclair Scientific Calculator |work=The Register |last=Sharwood |first=Simon |date=2 September 2013 |access-date=9 December 2013}}</ref> However, by sacrificing some speed and accuracy, Sinclair used clever algorithms to run scientific operations on a chip with room for just 320 instructions.<ref name=eng/> [[Mathematical constant|Constants]], rather than being stored in the calculator, were printed on the case below the screen.<ref name=eng/>

It displays only in scientific notation, with a five digit [[Significand|mantissa]] and a two digit [[Exponentiation|exponent]], although a sixth digit of the mantissa was stored internally.<ref name=eng/> Because of the way the processor was designed, it uses [[Reverse Polish notation]] (RPN) to input calculations.<ref name=eng/> RPN meant that the difficult implementation of brackets, and the associated recursive logic, was not necessary to implement in the hardware, but the effort was instead offloaded to the user.<ref name=rpn>{{cite web |url=http://www.calculator.org/rpn.aspx |title=What is Reverse Polish Notation? |publisher=calculator.org |access-date=10 December 2013}}</ref> Instead of an "equals" button, the {{key top|+}} or {{key top|&minus;}} keys are used to enter the initial value of a calculation, followed by subsequent operand(s) each followed by their appropriate operator(s).

To fit the program into the 320 words available on the chip, some significant modification was used.<ref name=eng/> By not using ordinary [[floating point]] numbers, which require many instructions to keep the decimal point in the right place, some space was freed up.<ref name=eng/> Trigonometric functions were implemented in about 40 instructions, and [[inverse trigonometric functions]] took almost 30 more instructions.<ref name=eng/> Logarithms are about 40 instructions, with anti-log taking about 20 more.<ref name=eng/> The code to normalize and display the computed values is roughly the same in the TI and Sinclair programs.<ref name=eng/>

The design of the algorithms meant that some calculations, such as [[Inverse trigonometric function|arccos]]0.2, could take up to 15 seconds, whereas the [[HP-35]] was designed to complete calculations in under a second.<ref name=eng/> Accuracy in scientific functions was also limited to around three digits at best, and there were a number of bugs and limitations.<ref name=eng/>

Ken Shirriff, an employee of [[Google]], reverse engineered a Sinclair Scientific in 2013 and built a simulator using the original algorithms.<ref name=eng/><ref name=reg/>

====Assembly kit====
The assembly kit consisted of eight groups of components, plus a carry case.<ref name=pm>{{cite journal |url=https://books.google.com/books?id=g-IDAAAAMBAJ&pg=PA5 |journal=Popular Mechanics |date=January 1975 |page=5 |title=What does it take to build the world's smallest scientific calculator?}}</ref> The build time was advertised as being around three hours, and required a [[soldering iron]] and a pair of cutters.<ref name=pm/><ref name=ns>{{cite journal |url=https://books.google.com/books?id=FS6D5VL2qo4C&pg=PA639 |title=Sinclair Scientific assembly kit |date=December 1975 |journal=New Scientist |page=639}}</ref> In January 1975, the kit was available for {{USD|49.95}}, half the price at the time of introduction a year earlier,<ref name=pm/> and in December 1975 it was available for {{GBP|9.95}}, less than a quarter of the introductory price.<ref name=ns/>

==={{anchor|Scientific Programmable}}Sinclair Scientific Programmable===
The Sinclair Scientific Programmable was introduced in 1975, with the same case as the [[Sinclair Oxford]].<ref name=vtss>{{cite web |url=http://www.vintage-technology.info/pages/calculators/s/sincprog.htm |title=Sinclair Scientific Programmable |publisher=Vintage Technology |access-date=10 December 2013}}</ref> It was larger than the Scientific, at {{convert |73|x|155|x|34|mm|in}}, and used a larger [[Nine-volt_battery|PP3 battery]], but could also be powered by [[mains electricity]].<ref name=vcss/><ref name=vtss/>

It had 24-step programming abilities, which meant it was highly limited for many purposes.<ref name=vtss/><ref name=lim>{{cite web |url=http://www.rskey.org/CMS/index.php/7?manufacturer=Sinclair&model=Scientific+Programmable |title=Sinclair Scientific Programmable |publisher=rskey.org |access-date=10 December 2013}}</ref> It also lacked functions for the [[natural logarithm]] and [[exponential function]].<ref name=lim/> Constants used in programs were required to be [[integer]]s, and the programming was wasteful, with start and end quotes needed to use a constant in a program.<ref name=lim/><ref>{{cite web |url=http://www.geoff.org.uk/museum/sinclair.htm |title=Scientific programmable Calculator |publisher=geoff.org.uk |access-date=4 January 2014}}</ref>

However, included with the calculator was a library of over 120 programs that performed common operations in mathematics, geometry, statistics, finance, physics, electronics, engineering, as well as fluid mechanics and materials science.<ref name=lim/><ref>{{cite web |url=http://www.wass.net/manuals/Sinclair%20Scientific%20Programmable%20Library.pdf |title=Sinclair Scientific Programmable Library |publisher=Sinclair Radionics |access-date=10 December 2013}}</ref> There were over 400 programs in the full Sinclair Program Library.<ref>{{cite journal |url=https://books.google.com/books?id=w1bp8jnrbecC&pg=PA265 |journal=New Scientist |date=October 1975 |page=265 |title=NEW! Sinclair Scientific Programmable}}</ref>

===Calculations using the Sinclair Scientific===

The Sinclair used a slightly altered [[Reverse Polish notation|Reverse Polish Notation]] method; lacking an enter key, the operation keys enter a number into the appropriate register and the calculation is performed.  For example, (1+2) × 3 could be calculated as: {{kbd|C 1 + 2 + 3 ×}} to give the result of {{samp|9.0000 00}} ({{val|9.0000|e=0}}, or 9).  The {{key top|C}} key performs a clear; pressing it sets the calculator to a state with zero in the internal registers.  Pressing "C" followed by number keys then {{key top|+}} effectively adds the number entered to the zero and stores it internally to be worked on in subsequent calculations.  If the {{key top|&minus;}} key is pressed instead, the number is subtracted from zero, effectively entering a negative number.<ref name="manual">{{cite web|title=Sinclair Scientific Operating Instructions|url=http://phils.bitboxes.co.uk/scan_and_ocr/manuals/sinclair_scientific/|url-status=dead|archive-url=https://archive.today/20140821181554/http://phils.bitboxes.co.uk/scan_and_ocr/manuals/sinclair_scientific/|archive-date=21 August 2014|access-date=20 August 2014|publisher=Sinclair Research}}</ref>

All numbers are entered in scientific notation.  After entering the mantissa part of the number, the "E" exponent key is pressed prior to entering the integer exponent of the number.  The task of ordering the operations is placed on the user, and there are no bracket keys.  The display shows only five digits, but six digits can be entered.<ref name="manual"/>  As an example 12.3×(&minus;123.4+123.456) could be entered as {{kbd|C 1 2 3 4 E 2 - 1 2 3 4 5 6 E 2 + 1 2 3 E 1 ×}} for a displayed result of {{samp|6.8880 -01}} (representing {{val|6.8880|e=-1}}, or 0.68880).

Four constants are printed on the calculator case for easy reference.  For converting to and from base 10 logarithms and natural logarithms, the natural logarithm of 10 (2.30259) and e (2.71828) are printed on the case. {{Pi}} (3.14159) and 57.2958 (180 / {{Pi}}) are also on the case for trigonometry calculations.  There was not enough internal memory to store these constants internally.  Angles are computed using radians; degree values must be converted to radians by dividing by 57.2958.  As an example, to calculate 25 sin (600×0.05°) one would enter {{kbd|C 6 E 2 + 0 0 5 × 5 7 2 9 5 8 E 1 ÷ ▲ + 2 5 E 1 ×}} to get a result of {{samp|1.2500 01}} (representing 12.5 which is equal to 25 sin(30°) ).  Sine is selected with the combination of the {{key top|▲}} key followed by the {{key top|+}} key.  The {{key top|▼}} (down) and {{key top|▲}} (up) arrow keys are function select keys.  The four operation keys ({{key top|&minus;}}, {{key top|+}}, {{key top|÷}} and {{key top|×}}) all have two other functions, activated by using one of the arrow keys.  The functions available are sine, arcsine, cosine, arccosine, tangent, arctangent, logarithm and antilogarithm.