X-Number Manual - Frames

<body stylesrc="XHelp.htm" bgcolor="#FFFFFF">  <p align="center"><a name="Manual" target="_self"><font face="Arial"><strong>X# Calculator</strong></font></a><font face="Arial"><strong><br> Operating Instructions</strong></font></p> <p align="left"><font face="Arial"><strong>Introduction</strong></font></p> <p align="left"><font size="2" face="Arial">The X# Calculator has been designed to show how numbers can be entered in a phonetic way by using the concept of Verbal Numerals and the algorithms described in Patent Nr. 5,623,433 for a structured data-entry procedure.</font></p> <p align="left"><font size="2" face="Arial">In addition, it incorporates some thoughts of the author on the usage of a dual display and a single memory key in a way that could prove to be more efficient than that method used in current calculators.</font></p> <p align="left"><font size="2" face="Arial">The keys [<strong>H</strong>], [<strong>T</strong>] and [<strong>M</strong>]  represent the  quantities "hundred ", "thousand" and "million."  Also, notice that the [<strong>m</strong>] key refers to the single "memory" key.</font></p> <p><a name="Displays" target="_self"><font color="#000000" face="Arial"><strong>Displays</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">Every calculator has two registers, one to hold the number being entered (input register) and another to hold the current result value (accumulator register). Both are displayed in a single display, therefore, when a new data-entry operation is pressed, the new number replaces the accumulated value. To avoid this, the X-Number Calculator contains two displays:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="5%"><font color="#000000" face="Arial"><strong>x</strong></font></td> <td width="25%"><font color="#000000" face="Arial">Result Display</font></td> <td width="70%"><font color="#000000" face="Arial">to display the accumulator register</font></td> </tr> <tr> <td width="5%"><font color="#000000" face="Arial"><strong>n</strong></font></td> <td width="25%"><font color="#000000" face="Arial">Input Display</font></td> <td width="70%"><font color="#000000" face="Arial">to display the input register</font></td> </tr> </table> </center></div> <p><font size="2" face="Arial">Every time a user starts a new data-entry operation, the new value is displayed in the Input Display as it is being entered. The value of the Result Display will be cleared automatically if no arithmetic operator preceded the data-entry operation, otherwise it will remain unchanged until the [=] or a new operator key [+ - / *] is pressed, at which time the Result Display will be updated and the Input Display will be cleared.</font></p> <p><font size="2" face="Arial">Try the following examples:</font></p> <blockquote> <p><font face="Arial">6 + 9 =<br> 6 + 9 = / 3 - 1 =</font></p> </blockquote> <p><font size="2" face="Arial">The final value in the Result Display should be "4."</font></p> <p><a name="Clear" target="_self"><font color="#000000" face="Arial"><strong>Clear</strong></font></a><font color="#000000" face="Arial"><strong> Keys</strong></font></p> <p><font color="#000000" size="2" face="Arial">Two "clear" function keys are provided:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="10%"><font color="#000000" face="Arial"><strong>CE</strong></font></td> <td colspan="2" width="80%"><font color="#000000" face="Arial">Clear Entry</font></td> </tr> <tr> <td width="10%"><font color="#000000" face="Arial"><strong>C</strong></font></td> <td colspan="2" width="90%"><font color="#000000" face="Arial">Clear Result/Memory/All</font></td> </tr> </table> </center></div> <p><font size="2" face="Arial">There are three possible clear operations:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="20%"><font face="Arial"><strong>[CE]</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Clears the Input Display</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[m][C]</strong></font></td> <td width="80%"><font face="Arial">Clears the Memory Register</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[C][C] </strong></font></td> <td width="80%"><font face="Arial">Clears all registers and displays</font></td> </tr> </table> </center></div> <p><font size="2" face="Arial">Try the following examples:</font></p> <p><font face="Arial">25 + 30 [CE] - 5 + 30 = [m] + + 7 [C] =</font></p> <p><font size="2" face="Arial">The Result Display should show "M 7" where the "M" indicates that there are something in the memory (in this case the number 50). Now try:</font></p> <p><font face="Arial">[m][C]</font></p> <p><font size="2" face="Arial">This clears the memory and the Result Display shows "7."</font></p> <p><a name="Memory" target="_self"><font color="#000000" face="Arial"><strong>Memory</strong></font></a><font color="#000000" face="Arial"><strong> Operations</strong></font></p> <p><font color="#000000" size="2" face="Arial">This is one of the main functional differences with standard calculators. Standard calculators provide with four memory keys to handle its memory operations: [M+] [M-] [MR] and [MC]. The X-Number calculator contains only one memory key: [<strong>m</strong>].</font></p> <p><font color="#000000" size="2" face="Arial">In the X-Number approach, the memory is considered as an independent object which contains the value of the "Memory Register."</font></p> <p><font color="#000000" size="2" face="Arial">The memory key is used to change or manipulate the memory value when the Input Display is clear.</font></p> <p><font color="#000000" size="2" face="Arial">As in most standard calculators, the Result Display shows an "M" icon whenever the memory value is different from zero.</font></p> <p><font color="#000000" size="2" face="Arial">The following are valid operations for the memory key:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="20%"><font face="Arial"><strong>[m][+]</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Adds the Result Display to the Memory</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[m][- ]</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Subtracts the Result Display from the Memory</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[m][* ] </strong></font></td> <td width="80%"><font color="#000000" face="Arial">Multiplies the Memory by the Result Display</font></td> </tr> <tr> <td><font face="Arial"><strong>[m][/ ] </strong></font></td> <td><font color="#000000" face="Arial">Divides the Memory by the Result Display</font></td> </tr> <tr> <td><font face="Arial"><strong>[m][^ ] </strong></font></td> <td><font color="#000000" face="Arial">Elevates the Memory to the power in the Result Display</font></td> </tr> <tr> <td><font face="Arial"><strong>[m][C] </strong></font></td> <td><font color="#000000" face="Arial">Clears the Memory</font></td> </tr> <tr> <td><font face="Arial"><strong>[m][=] </strong></font></td> <td><font color="#000000" face="Arial">Replaces the Result Display with the Memory value</font></td> </tr> <tr> <td><font face="Arial"><strong>[m][Swap] </strong></font></td> <td><font color="#000000" face="Arial">Swaps the Result Display with the Memory value</font></td> </tr> </table> </center></div> <p><font color="#000000" size="2" face="Arial">Since the memory is basically an object, the following sequences are also valid:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="20%"><font face="Arial"><strong>[+][m]=</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Adds the Memory to the Result Display</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[- ][m]=</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Subtracts the the Memory from the Result Display</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[* ][m]=</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Multiplies the Result Display by the Memory</font></td> </tr> <tr> <td><font face="Arial"><strong>[/ ][m]=</strong></font></td> <td><font color="#000000" face="Arial">Divides the Result Display by the Memory</font></td> </tr> <tr> <td><font face="Arial"><strong>[^ ][m]=</strong></font></td> <td><font color="#000000" face="Arial">Elevates the Result Display to the power in Memory</font></td> </tr> </table> </center></div> <p><font color="#000000" size="2" face="Arial">Try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">5 + 9 = [m]+<br> 3 + 4 =<br> [m][Swap] / [m] =<br> [m][C]</font></p> <p><font color="#000000" size="2" face="Arial">At the end of the sequence, the result display should show "2" and the memory should be empty.</font></p> <p><a name="Structured" target="_self"><font color="#000000" size="3" face="Arial"><strong>Structured</strong></font></a><font color="#000000" size="3" face="Arial"><strong> Data-Entry</strong></font></p> <p><font color="#000000" size="2" face="Arial">The X-Number calculator numerical keyboard will behave like any other standard 10-key pad. However, when any of the three structured keys: [<strong>H</strong>], [<strong>T</strong>], or [<strong>M</strong>] are pressed, the data-entry mode will be changed automatically to <strong>structured mode</strong>. This change will be reflected in the shape of the parentheses that surround the arithmetic operator in the Input Display. Round parentheses means <strong>Standard Mode</strong>. Square parentheses means <strong>Structured Mode.</strong></font></p> <p><font color="#000000" size="2" face="Arial">While in Structured Mode, the data-entry can be done by pressing the [<strong>H</strong>], [<strong>T</strong>], or [<strong>M</strong>] keys to replace the words "Hundred", "Thousand" or "Million" within the verbal expression of the number. In many cases this could lead to a significant reduction in the number of keystrokes required to enter the number, for example, try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">[M]35 + 9[T]5 = [m]+<br> -3[H][T]7H + [T][H] =</font></p> <p><font color="#000000" size="2" face="Arial">At the end of the sequence, the result display should show "709440."</font></p> <p><font color="#000000" size="2" face="Arial">The use of the structured procedure does not preclude the use of the standard procedure during the course of the same number input operation. For example, the same result could be obtained by any of the following sequences:</font></p> <p><font color="#000000" size="3" face="Arial">23001207<br> 23[M]1[T]2[H]7<br> 23[M]1[T]207<br> 23[M][T]2[H]7<br> 23[M][T]207<br> 23[M]1207.</font></p> <p><a name="Swap" target="_self"><font color="#000000" size="3" face="Arial"><strong>Swap Key</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">The [Swap] key (double pointed arc) can be used in two different ways:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="20%"><font face="Arial"><strong>[Swap]</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Swaps the Data-Entry mode in the Input Display</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[m][Swap]</strong></font></td> <td width="80%"><font face="Arial">Swaps the value in the Result Display with the Memory</font></td> </tr> </table> </center></div> <p><font color="#000000" size="2" face="Arial">To use the [Swap] key to change the Data-Entry mode, the Input Display must contain a value, this is because the calculator always start in Standard Mode. Swapping the mode may be useful when the user wants to keep appending digits to the number after entering a value in structured mode. As example, try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">3[T]1[Swap]20=</font></p> <p><font color="#000000" size="2" face="Arial">This will append the digits "2" and "0" to the number 3001 yielding "300120."</font></p> <p><font color="#000000" size="2" face="Arial">By the same token, if a number has been entered in Standard Mode, pressing the [Swap] key will change the mode to Structured Mode. As example, try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">3001[Swap]20=</font></p> <p><font color="#000000" size="2" face="Arial">This will change "3001" to structured mode and will yield "3120."</font></p> <p><font color="#000000" size="2" face="Arial">The second use of the [Swap] key is to swap the value in the Result Display with the value stored in memory. This requires that the Input Display is clear. Example:</font></p> <p><font color="#000000" size="3" face="Arial">25+5=[m]+<br> 80+20=<br> [m][Swap]</font></p> <p><font color="#000000" size="2" face="Arial">At the end of the sequence, the result display should show "30" and the memory should contain "100".</font></p> <p><a name="Undo" target="_self"><font color="#000000" size="3" face="Arial"><strong>Undo Key</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">The [Undo] key (left pointed arrow) will undo the effect of the previous keystrokes during a Data-Entry operation, or the effect of pressing an arithmetical operator.</font></p> <p><font color="#000000" size="2" face="Arial">Try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">2[M]+5[T]6[Undo][Undo][H]*3[Undo]</font></p> <p><font color="#000000" size="2" face="Arial">At the end of the sequence, the Result Display should show "2000500." </font></p> <p><a name="Constant" target="_self"><font color="#000000" size="3" face="Arial"><strong>Constant Key</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">The [K] key can be used at any time to set the calculator to "Constant Mode." This is indicated by the "K" icon in the Input Display.</font></p> <p><font color="#000000" size="2" face="Arial">When in "Constant Mode," the last entry will remain displayed in the Input Display, so that pressing the [=] key several times will repeat the displayed operation multiple times.</font></p> <p><font color="#000000" size="2" face="Arial">Try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">20+5[K]===[-]=</font></p> <p><font color="#000000" size="2" face="Arial">At the end of the sequence, the Result Display should show "30" and the Input Display should show the operation "-5" ready to be executed again if the [=] key is pressed.</font></p> <p><a name="Dollar" target="_self"><font color="#000000" size="3" face="Arial"><strong>Dollar Key</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">The [$] key can be used at any time to cause all the operations to be rounded to two decimals (cents) and displayed as such in the Result Display. Notice that the intermediate results are not rounded, only the displayed value is rounded.</font></p> <p><font color="#000000" size="2" face="Arial">Try the following sequence:</font></p> <p><font color="#000000" size="3" face="Arial">20/3=[$][$]</font></p> <p><font color="#000000" size="2" face="Arial">the Result Display should show "6.67" after the first use of [$].</font></p> <p><a name="Ten" target="_self"><font color="#000000" size="3" face="Arial"><strong>Ten Key Pad</strong></font></a><font color="#000000" size="3" face="Arial"><strong> and Dot Key</strong></font></p> <p><font color="#000000" size="2" face="Arial">Notice that the standard data-entry mode is the default mode in the X-Number system, therefore the behavior of the digit keys is the same way as any standard numerical keyboard.</font></p> <p><font color="#000000" size="2" face="Arial">The [dot] key is also the same - However, if the user is entering a number in Structured Mode, pressing the [dot] key will stop the Structured Mode. Decimals can only be entered in Standard Mode. Pressing an structure key after the decimal point is entered will append two, three or six decimal zeroes to the decimal portion of the number.</font></p> <p><a name="Operators" target="_self"><font color="#000000" size="3" face="Arial"><strong>Operators</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">The behavior of the arithmetic operator keys [+ - / * ^] is the same as any standard calculator. The only difference is that one more operator has been added: [^].</font></p> <p><font color="#000000" size="2" face="Arial">The [^] key is the "power" operator. It allows to elevate the value in the Result Display to the power value entered in the Input Display. For Example:</font></p> <p><font color="#000000" size="3" face="Arial">2^3=</font></p> <p><font color="#000000" size="2" face="Arial">will yield "8" in the Result Display.</font></p> <p><a name="Functions" target="_self"><font color="#000000" size="3" face="Arial"><strong>Functions</strong></font></a></p> <p><font color="#000000" size="2" face="Arial">Three functions are provided with the X-Number calculator:</font></p> <div align="center"><center> <table border="1" cellpadding="2" cellspacing="1" width="90%"> <tr> <td width="20%"><font face="Arial"><strong>[+/-]</strong></font></td> <td width="80%"><font color="#000000" face="Arial">Changes the symbol in the Result Display.</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[1/x]</strong></font></td> <td width="80%"><font face="Arial">Replaces the Result Display with its Inverse value.</font></td> </tr> <tr> <td width="20%"><font face="Arial"><strong>[Sqrt] </strong></font></td> <td width="80%"><font face="Arial">Replaces the Result Display with its Square Root.</font></td> </tr> </table> </center></div> <p> </p> <p><font color="#000000" size="2" face="Arial">For Example:</font></p> <p><font color="#000000" size="3" face="Arial">4^2=[Sqrt][1/x][+/-]</font></p> <p><font color="#000000" size="2" face="Arial">will yield "-0.25" in the Result Display.</font></p>  </body>