Abstract:
A battery-powered hand-held programmable calculator for performing arithmetic, trigonometric and logarithmic functions and displaying the results thereof is provided with the capability of being fully programmable including branching based on data value. Absolute line number addressing is provided. Program line numbers and the key code associated with an executable step are displayed. The top of the programmable memory is configured as a nonexecutable line corresponding to an automatic stop and all other programmable lines are initially programmed upon start up as being an automatic branch to the top of the memory. Key codes representing a plurality of actuated keys corresponding to a branch instruction are merged to require only one program line in memory.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates generally to calculators and more particularly to programmable electronic calculators in which keyboard operations become program instructions. In this particular type of calculator no special language is required. When a key is pressed one program step is completed. Programmable electronic calculators generally utilize memories which enable them to store instructions and data for repetitive and iterative solution. In order to enter the program into memory the user depresses the calculator keys in a given sequence. The result of each sequence step may be displayed for the convenience of the user as he progresses through his calculation. The key code for each program step may also be displayed. Key codes generally are alphanumeric representations of the keys on the keyboard. If the user wishes to modify or edit his program after initial entry into memory he must precisely determine to which key he should return in order to implement the change. To make that determination for calculators constructed according to the prior art, the user had to refer to a separate machine unique association table and a program to determine the specific key to depress relative to a particular program step. 
     For programming convenience key codes and program line numbers should be easily interpreted by a user. An object of this invention is to improve the ease of program debugging and editing by introducing a programmable calculator which displays a key position on the keyboard and absolute program line numbers. A further object of this invention is to provide a calculator having a convenient way for a user to get to the top of memory and eliminate the need for an AND key or a RETURN key. The invention provides a programmable calculator having preprogrammed branch instructions to the top of memory. 
     A further object of this invention is to provide a calculator wherein a user can program a branch instruction to another place in the program by merely actuating a single key and entering a line number address of the branch destination. Another object is to increase the utilization of available program memory by merging key codes representing a plurality of actuated keys corresponding to a branch instruction. 
     A further object is to provide an improved error display wherein the invention displays and flashes the contents of a register within an operational stack. 
     Another object is to provide an improved display wherein the invention automatically changes its format when in underflow or overflow. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a front view of a calculator according to the preferred embodiment of the present invention. 
     FIG. 2 is a block diagram of the calculator of FIG. 1. 
     FIG. 3 is a representation of the contents of seven storage registers used as a program memory in the calculator of FIG. 1. 
     FIG. 4 shows a flow diagram for the programming features of the calculator of FIG. 1. 
     FIG. 5 shows a flow diagram for implementing branch instructions in the calculator of FIG. 1. 
     FIGS. 6A and 6B illustrate a number to be displayed in normalized form and a flow diagram of a display generating routine providing an automatic change in display format. 
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to FIGS. 1 and 2, there is shown a pocket-size electronic calculator 10 including a keyboard input unit 12 for entering data and instructions into the calculator and a seven-segment LED output display unit 14 for displaying each data entry and the results of calculations performed by the calculator. As shown in FIG. 2, calculator 10 also includes an MOS control and timing circuit 16, an MOS read-only memory circuit 18 (including QUAD ROM&#39;s 1, 2 and 3), an MOS arithmetic and register circuit 20, a bipolar clock driver 22, a solid state power supply unit 24, and MOS auxiliary data storage circuit 25. 
     The MOS circuits are two-phase dynamic MOS/LSI circuits with low thresholds allowing compatibility with TTL bipolar circuits and allowing extremely low-power operation (less than one hundred milliwatts for all three circuits). They are organized to process fourteen-digit BCD words in a digit-serial, bit-serial manner. The maximum bit rate or clock frequency is 196 kilohertz, which gives a word time of 280 microseconds (permitting a floating point addition to be completed in 60 milliseconds). 
     Control and timing circuit 16, read-only memory circuit 18, arithmetic and register circuit 2, and data storage circuit 25 are tied together by a synchronization (SYNC) bus 26, an instruction (I s ) bus 28, a work select (WS) but 30, an instruction address (I a ) line 32, and a carry line 34. All operations occur on a fifty-six bit (b 0  - b 55 ) word cycle (fourteen four bit BCD digits). The timing sequence for the interconnecting busses and lines 26-34 are as shown in FIG. 3 of U.S. Pat. No. 3,863,060 filed Oct. 30, 1972, entitled &#34;General Purpose Calculator with Capability for Performing Interdisciplinary Business Calculations&#34; by France Rode, et al. 
     The SYNC bus 26 carries synchronization signals from control and timing circuit 16 to QUAD ROMS 1, 2 and 3 in read-only memory circuit 18 and to arithmetic and register circuit 20 to synchronize the calculator system. It provides one output each word time. This output also functions as a tenbit wide window (b 45  - b 54 ) during which I s  bus 28 is active. 
     The I s  bus 28 carries ten-bit instructions from the active QUAD ROM in the read-only memory circuit 18 to the other QUAD ROM&#39;s, control and timing circuit 16, arithmetic and register circuit 20, and auxiliary data storage circuit 25, each of which decodes the instructions locally and responds to or acts upon them if they pertain thereto and ignores them if they do not. For example, the ADD instruction affects arithmetic and register circuit 20 but is ignored by control and timing circuit 16. Similarly, the SET STATUS BIT 5 instruction sets a status flip-flop in control and timing circuit 16 but is ignored by arithmetic and register circuit 20. 
     The actual implementation of an instruction is delayed one word time from its receipt. For example, an instruction may require the addition of digit 2 in two of the registers in arithmetic and register circuit 20. The ADD instruction would be received by arithmetic and register circuit 20 during bit times b 45  - b 54  of word time N and the addition would actually occur during bit times b 8  - b 11  of word time N+1. Thus, while one instruction is being executed the next instruction is being fetched. 
     The WS bus 30 carries an enable signal from control and timing circuit 16 or one of the QUAD ROM&#39;s in a read-only memory circuit 18 to arithmetic and register circuit 20 to enable the instruction being executed thereby. Thus, in the example of the previous paragraph, addition occurs only during digit 2 since the adder in the arithmetic and register circuit 20 is enabled by WS bus 30 only during this portion of the word. When WS bus 30 is low, the contents of the registers in arithmetic and register circuit 20 are recirculated unchanged. Three examples of WS timing signals are shown in FIG. 3 of prior filed, commonly owned and allowed U.S. Pat. Ser. No. 3,863,060. In the first example, shown in said patent application, digit position 2 is selected out of the entire word. In the second example, the last eleven digits are selected. This corresponds to the mantissa portion of a floating point word format. In the third example, the entire word is selected. Use of the word select feature allows selective addition, transfer, shifting or comparison of portions of the registers within arithmetic and register circuit 20 with only one basic ADD, TRANSFER, SHIFT, or COMPARE instruction. Some customization in the QUAD ROM word select fields is available via masking options. 
     The I a  line 32 serially carries the addresses of the instructions to be read from the QUAD ROM&#39;s. These addresses originate from control and timing circuit 16, which contains an instruction address register that is incremented each word time unless a JUMP SUBROUTINE or a BRANCH instruction is being executed. Each address is transferred to ROM&#39;s during bit times b 19  - b 26  and is stored in an address register of each ROM. However, only one QUAD ROM is active at a time, and only the active QUAD ROM responds to an address by outputting an instruction on the I s  line 28. 
     The carry line 34 transmits the status of the carry output of the adder in arithmetic and register circuit 20 to control and timing circuit 16. The control and timing circuit uses this information to make conditional branches, dependent upon the numerical value of the contents of the registers in arithmetic and register circuit 20. 
     A BCD input/output line 35 interconnects data storage circuit 25 and the C register of arithmetic and register circuit 20. This line always outputs the contents of the C register of arithmetic and register circuit 20 unless a specific instruction to input to the C register of the arithmetic and register circuit is being executed. 
     Control and timing circuit 16 is organized to scan a five-by-eight matrix of switches in search of an interconnection that designates actuation of a key. Any type of metal-to-metal contact may be used as a key. Key bounce problems are overcome by programmed lockouts in the key entry routine. Each key has an associated six-bit code. 
     A power on circuit 36 in power supply unit 24 supplies a signal forcing the calculator to start up in a known condition when power is supplied thereto. Power is supplied to the calculator when the on-off switch of keyboard input unit 12 (see FIG. 1) is moved to the ON position. 
     The primary outputs of the calculator are five output lines 38 connected between a display decoder of arithmetic and register circuit 20 and an anode driver of output display unit 14. Data for a seven-segment display plus a decimal point is time-multiplexed onto these five output lines. A start line 40 is connected from the display decoder of arithmetic and register circuit 20 to the auxiliary data storage circuit 25 and a cathode driver of output display unit 14 and indicates when the digit 0 occurs. 
     A mode switch 2 is provided having a program and a run position. When switch 2 is in program position, an input line to the control and timing circuit 16 is grounded. This sets one of the 12 internal status bits. The status of this status bit is interrogated by the microprocessor and the key code which has been generated is either stored in the appropriate location in digital storage circuit 25 or decoded and executed by arithmetic and register circuit 20. 
     The Control and Timing Circuit 16, Read Only Memory Circuit 18, Arithmetic and Register Circuit 20, Clock Driver 22, Display Unit 14, Keyboard 12, LED Display, Selected Instruction Sets and their operation are described in detail in commonly owned, and allowed U.S. Pat. Ser. No. 3,863,060 entitled &#34;General Purpose Calculator with Capability for Performing Interdisciplinary Business Calculations&#34; filed on Oct. 30, 1972, by France Rode, et al. Said patent is fully incorporated herein by reference. 
     Referenced U.S. Pat. Ser. No. 3,863,060 describes a nonprogrammable business calculator having seven registers A-F and M, as shown for example in FIG. 11 of said patent. In contrast, the preferred embodiment of the instant application has 37 56-bit registers. Each of these registers is capable of containing 14 BCD digits. The 37 registers (A-F, M, and 30 storage registers) can be divided into four groups: the working registers A, B and C with C also being the bottom register of a four register operational stack; the next three registers D, E and F in the stack; 30 separate storage registers within data storage 25 and the M register which is put to use to maintain status information in addition to that maintained by 12 status bits internal to the control and timing circuit 16. The structure and operation of a stack formed by registers C, D, E and F are fully described in reference U.S. Pat. Ser. No. 3,863,060 and further described in U.S. Pat. No. 3,781,820 entitled PORTABLE ELECTRONIC CALCULATOR filed on May 30, 1972, by David S. Cochran, et al. and issued on Dec.  25, 1973. Registers C, D, E and F represent an operational stack. Registers A and B are the working registers throughout which various algorithms are implemented. The A and B registers also provide the information which is decoded into signals for the display drivers of display unit 14. The M register is of the same structure as the single storage register employed in U.S. Patent Application Ser. No. 3,863,060 but in the preferred embodiment the data storage registers within data storage circuit 25 provide ample supplementary storage and the M register manages status information in addition to that maintained by 12 status bits internal to Control and Timing Circuit 16. The M register stores information such as which angular format is in effect, which display format is in effect and the state of programming affairs, for example, whether the function is being executed from the keyboard as a result of executing a run stop command or as a result of a single step instruction as further described hereinafter. Digit positions 4 and 3, the least significant mantissa digits of the M register, contain the two digits of the current line number of program memory. 
     Referring to FIG. 3 there is shown a representation of the contents of seven registers 23 through 29 within data storage 25. If a key other than BST 3, SST 4, or GTO 5 is pressed, a microprogram stored in ROM 18 transfers control to a portion of the read-only memory which generates a two digit key code which is built up into the exponent field of the C register. These key codes match the matrix location of the key on the keyboard. An indexing scheme for directly associating displayed key codes with the physical position of non-numeric or the identity of digit keys contained on a key-board is fully described in U.S. Pat. No. 3,855,461 entitled CALCULATOR WITH KEY CODE ASSOCIATION AND DISPLAY FEATURES by Richard Kent Stockwell, et al. issued on Dec. 17, 1974. In the preferred embodiment the key codes generally match the matrix location of the key on the keyboard in a row-column configuration. The key code list for the preferred embodiment is: 
     
         ______________________________________Key         Key Code    Key      Key Code______________________________________Σ+    11          -        48y.sup.x     12          +        381/x         13          ×  28%           14          ÷    18 ##STR1##    21          .        16 ##STR2##    22          R/S      15 ##STR3##    23          0        00FIX         24          1        01f           31          2        02g           32          3        03STO         33          4        04RCL         34          5        05 ##STR4##    41          6        06CHS         42          7        07EEX         43          8        08CLX         44          9        09______________________________________ 
    
     The f and g keys are prefix keys whose function is as described in referenced U.S. Pat. No. 3,855,461. 
     Exceptions to the row-column matrix key code are the digit keys which have key codes matching the digit and the keys -, +, ×, ÷, ., and R/S key 6. 
     Following the build up of the key code the position of multi-position switch 2 is implemented by a microcode in ROM 18 and the flow of the program is as shown in FIG. 4. 
     Referring to FIG. 4, in the routine to display the key codes, the nines complement of the key code is taken before it is displayed if the least significant digit is greater than or equal to 5 and the most significant digit is not equal to 0. This maintains the matrix row-column rule and key codes 50-99 are reserved for merged GO TO&#39;s as described hereafter. 
     Referring to FIG. 5, a flag is set and the next two digits which are pressed become the destination of a branch instruction in a program when the GO TO key 5 is pressed. If switch 2 is in a run position these two digits immediately replace the old line number digits stored in the M register. If switch 2 is in a program position, 50 is added to the two digits and the new key code is placed in program memory. For example GO TO 00 has key code 50; GO TO 05 has key code 55; GO TO 46 has key code 96; etc. 
     The routine to display the key codes subtracts 50 from the key code and supplements the display by lighting a minus sign in the exponent sign field if the most significant digit is greater than or equal to 5, thereby indicating a branch instruction with the minus sign. 
     In the process of decoding a key code, if 1 has been subtracted from the tens digit 5 times and a carry has not been detected, the key code is a GO TO and the remaining key code is the destination line number which immediately replaces the old line number digits in the M register. 
     Referring to FIG. 4, the program is begun by setting status information in the M register by actuating the R/S key 6 from the keyboard. The key code associated with the prevailing line number is secured from program memory, placed in the exponent field of the M register and the function is decoded and executed. 
     When the SST key 4 is pressed a flag is set in the M register. If switch 2 is in program position, the line number is increased by one and control branches to a routine which generates the program mode display. Only the key code associated with the prevailing line number is executed if switch 2 is in run mode. 
     The line number is decreased by one and control branches to the routine which generates the program mode display when the BST key 3 is pressed while switch 2 is in the program position. If switch 2 is in run mode the line number in the M register is zeroed. This enables a user to transfer control to line 00 by pressing only one key while in the run mode. 
     Whenever a line number becomes 50 or 99 by adding 1 to 49 or subtracting 1 from 00, it is readjusted to 00 by the program. Also any time program control is transferred to line 00 in a running program, program execution stops. 
     Each state of program memory contains a 50 when the calculator is turned on, representing a GO TO 00. This enables a user upon keying in a simple program to have control automatically branch to line 00 after completion of the last program step. The program stops and is ready to be run again. This precludes the requirement for an END key or a RETURN key or some other program terminator key. 
     Referring to FIG. 1, a user programs a conditional branch instruction by actuating an f key 7 or a g key 8 from the keyboard. Status bits generated by actuating an f key 7 or a g key 8 create flags which preclude the calculator from completing a branch if conditions corresponding to the key actuated are not met. For example, actuation of the f prefix key 7 followed by actuation of GTO key 5 corresponds to X less than or equal to Y and actuation of the g prefix key 8 followed by actuating GTO key 5 corresponds to X = Y. The branch will be completed only if a condition indicated is true. When the condition is not true, the line number indexes by one if the calculator is executing a program or if a user is actuating a single step series. If a conditional branch is attempted from the keyboard and the condition is not true, then the line number remains unchanged. 
     A user begins to program the calculator by sliding the switch 2 to PRGM. A user will see 00. in the display. 
     Pressing SST key 4 displays 01. -00 
     Pressing SST key 4 again displays 02. -00 
     Pressing SST key 4 again displays 03. -00 The number on the left is a program step number (or line number). SST stands for single step, and by repeatedly pressing SST key 4 a user steps through the contents of the program memory one line at a time. 
     Pressing BST key 3 displays 02. -00 
     Pressing BST key 3 again displays 01. -00 
     Pressing BST key 3 again displays 00. BST stands for backstep. 
     The preferred embodiment has fifty addressable line numbers labeled 00. to 49. If the first digit of the GTO address is 5 or greater, the GTO is ignored. 
     All lines initially have -00 in them except line 00 since the -00 is the actual program instruction contained in each line. Line 00. is the &#34;top of the memory&#34;, and as such cannot contain an instruction. A user can easily transfer control to line 00. with the GTO (GO TO) key 5. 
     Assume a user wishes to write a program that computes the length of the hypotenuse of a right triangle using the Pythagorian Theorem. The theorem says that C 2  = a 2  + b 2  or c = ⊖a 2  + b 2 . The user translates this formula into keystrokes taking advantage of the operational stack. 
     Referring to FIG. 1 and assuming that a and b are in the X and Y registers, the correct keystrokes are ##STR5## The f and g keys actuated in this sequence perform the function of prefix keys as fully described in commonly owned U.S. Patent Application Ser. No. 425,341 entitled &#34;Calculator Having Merged Key Codes&#34; filed on Dec. 17, 1973, by Thomas E. Osborne, et al. 
     A user keys these steps in the program memory with the switch in PRGM mode and the program pointer (line number in the display) at 00. 
     
         ______________________________________Key Depressed          Display______________________________________Press g                01. 32Press CHS              02. 42 ##STR6##               03. 22Press g                04. 32Press CHS              05. 42Press +                06. 61Press f                07. 31Press CHS              08. 42______________________________________ 
    
     The numbers 32, 42, etc., following the displayed line number are the two digit key codes associated with the series of keys pressed: 32 for g, 42 for CHS, etc. A user easily makes the association by locating the key on the keyboard assuming that the code is rc (row column) as hereinbefore described. In other words, g is 32, third row (from the top), second column (from the left). The exception to this rule is the digit keys, which have the code Od (d = digit). 0 is 00, 1 is 01, etc. 
     A user terminates the program with a R/S. Pressing R/S displays 09. 84. 
     R/S stands for RUN/STOP. When pressed from the keyboard (in RUN mode) the program begins running. When the R/S key code is encountered in a running program, the program stops, and the calculator displays the contents of the X register. When R/S is pressed program execution begins with the line at which the program pointer is located. 
     A user knows where the program pointer is by switching to PRGM. For example, by switching to PRGM 09. 84. is displayed thereby indicating the program pointer is at line 09. To execute the program a user must get to the top of memory. By switching to RUN and pressing GTO 0 0, keying in some data, as, for example, 3 ENTER↑ 4 and pressing R/S a user will see 5.00, the hypotenuse of a 3-4-5 right triangle. 
     Flipping switch 2 to PRGM a user sees 09. 84 thereby displaying, respectively, the line where the program stopped and where the point currently is. 
     If a user wants to run the program again he must get to top of memory again. Flipping to RUN, pressing GTO 0 0, keying in new data, 5 ENTER↑ 12 R/S a user sees 13.00, the hypotenuse of a 5-12-13 right triangle. 
     A user does not have to press GTO 0 0 every time he wants to run a program with new data. Using the GTO key is only one way of doing it. Another way is to press BST in RUN mode. Pressing BST in run mode does two things: 
     a. It moves the program pointer to line 00. 
     b. It clears any prefix keys which may have been pressed. 
     This is convenient, if, for example, a user has inadvertently pressed a prefix key. The easiest way of getting back to the top of program memory after a user has finished executing is to include a programmed GTO 0 0 instruction at the end of the program and let the program move the pointer. 
     When a program is keyed into the calculator the contents of each line are replaced with a new key code one line at a time, each key code being placed into a line one line downstream from the one in the display when a key is pressed so a user can see each step as he keys in his program. 
     Therefore, in order to change, for example, line 37 a user presses GTO 3 7 in RUN mode. By flipping switch 2 to PRGM, 37. -00 is displayed. To change line 37 to a R/S, for example, R/S is pressed and 37. 84. is displayed. If a user wishes to change the program to transfer control to line 37 after it has computed the hypotenuse example given hereinabove, for example he does the following: 
     Flips to RUN. Presses GTO 0 9. 
     Flips to PRGM. Sees 09. 84, the old R/S instruction. 
     Presses BST and sees 08. 42. 
     To make line 09 a GTO 37, a user 
     presses GTO and sees 09 - 
     presses 3 and sees 09 -3 
     presses 7 and sees 09 -37 
     Line 09 now contains the complete 3 KEYSTROKE instruction GTO 37. The sign indicates that the instruction is a GO TO and the 37 is the line number of the destination. 
     The -00&#39;s originally observed are one line GTO 00 instructions. When a user first turns the calculator on every instruction is a GTO 00. When a user writes his first program, the last line will always be followed by a GO TO 00. This transfers control to the top of memory automatically. 
     Executing line 00. in a program causes the calculator to stop. Line 00. acts as if it has a permanent R/S instruction programmed in it. 
     The program example as now written computes a hypotenuse, jumps to line 37, and stops (because line 37 contains a R/S). 
     To change the GTO 37 in line 09 to GTO 00 a user switches to RUN, presses GTO 0 8, switches to PRGM, presses GTO 0 0 and sees 09. -00. A user runs his program as many times as he wants with fresh data just by keying in data, R/S, data, R/S, data R/S, etc. 
     With switch 2 in RUN mode program execution always begins with the number at which the pointer is pointing unless the program step contained in this line is a R/S (84). In that case execution begins at the next line so a user can program a R/S into his program, for purposes of new data entry or to review intermediate calculations, and then get started again by pressing R/S. This exception also applies to line 00. 
     A user can single step through his program in RUN modes. Assume a user is at the top of program memory (line 00). A user can key in some new data and single step through as follows: 
     Key in 9 ENTER↑ 12. 
     Press SST See 12.00 A user moves to 01. 
     Press SST See 12.00 A user executes g 
     Press SST See 144.00 A user executes x 2  (g CHS) 
     Continue pressing SST see 
     9.00 
     9.00 
     81.00 
     225.00 
     225.00 
     15.00 
     15.00 is the answer and the program pointer is at line 09. One more SST will execute line 09. -00. A user is now at line 00. 
     The activities of the calculator in PRGM modes may be summarized. Pressing SST will increment the program pointer and display that line number and key code. If the pointer is at line 00, pressing BST will leave it at line 00. 
     Pressing any other key but GTO will cause the pointer to increment, the key code associated with that key to be stored in program memory at the incremented line, and that line and key code to be displayed. If the program pointer is at line 49 when a new key is pressed, the pointer moves to line 00 and the new key is ignored. 
     Pressing GTO does NOT move the program pointer, but the step number in the display WILL increment and only the - sign will light in the key code field. 
     If the GTO is followed by legitimate digit keys (i.e., 23, 47,00) these digits will light in the key code field one at a time and only then will the program pointer increment, storing the merged GO TO statement into memory. If the GTO is followed by an illegitimate key (i.e., 5, R↓ EEX), the GTO is ignored and the key code for the subsequent key is stored in program memory and displayed. 
     The calculator can be commanded to perform a requested GO TO only if a certain relational condition between the contents of the X and Y registers is true. The allowable conditions are x≦y and x=y. If the GTO is immediately preceded by an f (either from the keyboard or from the prior step in program memory) the GTO will only be performed if x is equal to or less than y. Likewise if the GTO is immediately preceded by a g, the GTO will only be performed if x is equal to y. 
     As an example of this, the following is a program which will order the contents of the operational stack so that the largest number is in T, next largest in Z, next in Y, and smallest in X. 
     
         ______________________________________00.         11. 4      22. 3      33. GTO 1201. STO     12. RCL    23. GTO 12 34. RCL02. 1       13. 4      24. RCL    35. l ##STR7##    14. RCL    25. 2      36. f04. STO     15. 3      26.f       37. GTO 0005. 2       16. f      27. GTO 34 38. STO ##STR8##    17. GTO 24                   28. STO    39. 2 07. STO     18. STO    29. 3                              ##STR9## 08. 3       19. 4                   ##STR10##  41. STO ##STR11##        ##STR12##  31. STO    42. 110. STO     21. STO    32. 2      43. GTO 12______________________________________ 
    
     If an illegal operation is attempted in a running program, the calculator will stop execution, the contents of the X register will flash and the program pointer will remain at the line number which contains the illegal operation. 
     There are 4 ways that a running program will stop execution. 
     1. Encountering a R/S after the first executed line. 
     2. Transferring program control to line 00, either by executing a GTO 00 or flowing through line 49. 
     3. Encountering an illegal operation as described hereinafter. 
     4. If the user presses any key during execution which is handy if a user gets caught in an endless loop. Illegal operations include, for example: 
     1. Pressing ÷with x = 0. 
     2. Pressing 1/x with x = 0. 
     The contents of the x register is flashed, which in general is the illegal argument causing the error. The calculator restores the stack and the data storage registers to their conditions before the illegal operation was attempted. A user presses any key to stop the flashing. 
     Two digits are displayed to the right of the decimal point when a user switches on the calculator even though numbers are always maintained internally to ten significant digits. 
     Referring to FIG. 1, a user specifies a fixed decimal display by actuating FIX key 9 followed by a digit key 0-9. A user specifies scientific notation display by actuating prefix key f 7 and a digit key 0-9 that determines the number of digits displayed to the right of the decimal point. 
     Referring to FIG. 6B a flow diagram for implementing display format is shown. If a number is too large or too small for a &#34;FIX&#34; format specified by a user, the calculator automatically displays the number in scientific notation displaying 10 significant digits. Values having a magnitude greater than or equal to ±9.999999999 × 10 99  are approximated by ±9.999999999 × 10 99 . Values having a magnitude less than 10 -   99  are approximated by zero. 
     Referring to FIG. 6A, the number to be displayed is shown in normalized form, 14 bits representing sign, matissa and magnitude. Referring to FIG. 6B, a flow chart of the display generating routing assumes a number to be displayed is in this normalized form and has a decimal point between digits eleven and twelve. The exponent in 10&#39;s complement form is in digit positions 0, 1, 2 and the sign is in digit position 13, 0 being + and 9 being -. 
     The number of digits to be displayed to the right of the decimal point (0-9) is stored in the M register digit position 6. A &#34;0&#34; is in digit position 7 if the calculator is in a fixed point format and a &#34;1&#34; is in digit position 7 if the calculator is in a scientific notation format. 
     A listing of routines and subroutines of instructions employed by the calculator and of all of the constants employed by these routines and subroutines is given below. Listings for implementing additional features are shown in referenced U.S. Pat. Ser. No. 3,863,060 and in U.S. Pat. Application Ser. No. 364,570 entitled &#34;Improved Scientific Calculator&#34; filed May 29, 1973, by Peter D. Dickinson, et al. 
     Routines, subroutines, and constants are stored in QUAD ROM&#39;s 1 through 3 of ROM 18. Each line in each QUAD ROM is separately numbered in the first column from the left-hand side of the page. This facilitates reference to different parts of the listing. Each address in QUAD ROM&#39;s 1, 2 and 3 is represented in octal form by five digits in the second column from the left-hand side of the page. The first two digits identify which QUAD ROM and the next three digits represent an eight-bit address. QUAD ROM 1 is identified by the first two digits being 00, 01, 02, or 03; QUAD ROM 2 is identified by the first two digits being 04, 05, 06, or 07, and QUAD ROM 3 is identified by the first two digits being 10, 11, 12 or 13. The instruction or constant stored in each address of QUAD ROM&#39;s 1, 2 and 3 is represented in binary form in the third column from the left-hand side of the page. Branching addresses are represented in octal form by four digits in the fourth column from the left-hand side of the page. Explanatory comments are given in the remaining columns. ##SPC1## ##SPC2## ##SPC3## ##SPC4## ##SPC5## ##SPC6## ##SPC7## ##SPC8##