HP 15c Manual

							 Section 6: Programming Basics 71 
 
The program to calculate this information uses these formulas and data: 
base area = r2. 
volume = base area × height = r2h. 
surface area = 2 base areas + side area = 2r2 + 2rh. 
 
Radius, r Height, h Base Area Volume Surface Area 
2.5cm 8.0 cm ? ? ? 
4.0 10.5 ? ? ? 
4.5 4.0 ? ? ? 
TOTALS   ? ? ? 
Method: 
1. Enter an r value into the calculator and save it for other calculations. 
Calculate  the  base  area  (r2),  store  it  for  later  use,  and  add  the  base 
area to a register which will hold the sum of all base areas. 
2. Enter h and  calculate  the  volume  (r2h). Add  it  to  a  register  to  hold 
the sum of all volumes. 
3. Recall r.  Divide  the  volume  by r and  multiply  by  2  to  yield  the  side 
area.  Recall  the  base  area,  multiply  by  2,  and  add  to  the  side  area  to 
yield the surface areas. Sum the surface areas in a register. 
Do not enter  the  actual data  while  writing  the  program – just provide  for 
their  entry.  These  values  will  vary  and  so  will  be  entered  before  and/or 
during each program run. 
Key  in  the  following  program  to  solve  the  above  problem.  The  display 
shows  line  numbers  and  keycodes  (the  row  and  column  location  of  a  key), 
which will be explained under Further Information. 
Keystrokes Display  
| ¥ 000- Sets calculator to Program 
mode (PRGM displayed). 
´ CLEAR M 000- Clears program memory. Starts 
at line 000.  
						

							72 Section 6: Programming Basics 
 
 
Keystrokes Display   
´bA 001-42,21,11  Assigns this program the label 
―A‖. 
O 0 002-   44  0  Stores the contents of X-register 
into R0. r must be in the X-
register before running the 
program. 
|x 003-   43 11  Squares the contents of the X-
register (which will be r). 
|$ 004-   43 26   
* 005-      20  r2, the BASE AREA of a can. 
O 4 006-   44  4  Stores the BASE AREA in R4. 
O + 1 007-44,40, 1  Keeps a sum of all BASE 
AREAS in R1. 
¦ 008-      31  Stops to display BASE AREA 
and allow entry of the h value. 
* 009-      20  Multiplies h by the BASE 
AREA, giving VOLUME. 
´ © 010-   42 31  Pauses briefly to display 
VOLUME. 
O + 2 011-44,40, 2  Keeps a sum of all can 
VOLUMES in R2. 
l 0 012-   45  0  Recalls r. 
÷ 013-      10  Divides VOLUME by r. 
2 014-       2   
* 015-      20  2 rh, the SIDE AREA of a can. 
l 4 016-   45  4  Recalls the BASE AREA of the 
can. 
2 017-       2  Multiplies base area by two (for 
top and bottom). * 018-      20  
						

							 Section 6: Programming Basics 73 
 
 
Keystrokes Display  
+ 019–      40 SIDE AREA + BASE AREA 
= SURFACE AREA. 
O + 3 020–44,40, 3 Keeps a sum of all SURFACE 
AREAS in R3. 
| n 021–   43 32 Ends the program and returns 
program memory to line 000. 
Now, lets run the program: 
Keystrokes Display  
| ¥  Sets calculator to Run mode. 
(PRGM cleared.) 
´ CLEAR Q  Clears all storage registers. The 
display does not change. 
2.5 2.5 Enter r of the first can. 
´ A  
(or: G A) 
19.6350 Starts program A. BASE AREA 
of first can. 
(running flashes during 
execution.) 
8 8 Enter h of first can. Then restart 
program. 
¦ 157.0796 VOLUME of first can. 
 164.9336 SURFACE AREA of first can. 
4 4 Enter r of the second can. 
¦ 50.2655 BASE AREA of second can. 
10.5 10.5 Enter h of second can. 
¦ 527.7876 VOLUME of second can. 
 364.4247 SURFACE AREA of 
second can. 
4.5 4.5 Enter r of the third can. 
¦ 63.6173 BASE AREA of third can.  
						

							74 Section 6: Programming Basics 
 
 
Keystrokes Display  
4 4 Enter h of third can. 
¦ 254.4690 VOLUME of third can. 
 240.3318 SURFACE AREA of third can. 
l 1 133.5177 Sum of BASE AREAS. 
l 2 939.3362 Sum of VOLUMES. 
l 3 769.6902 Sum of SURFACE AREAS. 
The  preceding  program  illustrates  the  basic  techniques  of  programming.  It 
also  shows  how  data  can  be  manipulated  in  Program  and  Run  modes  by 
entering,  storing,  and  recalling  data  (input  and  output)  using v, 
O, l, storage register arithmetic, and programmed stops. 
Further Information 
Program Instructions 
Each  digit,  decimal  point,  and  function  key  is considered  an instruction 
and is  stored  in  one line of  program  memory.  An  instruction  may  include 
prefixes  (such  as ´, O, t and b) and  still  occupy  only  one 
line. Most instructions require one byte of program memory; however, some 
require  two.  For  a  complete  list  of  two-byte  instructions,  refer  to 
Appendix C. 
Instruction Coding 
Each  key  on  the  HP-15C  keyboard – except for  the  digit  keys  0  through  
9 – is  identified  in  Program  mode  by  a  two-digit  ―keycode‖  that 
corresponds to the keys position on the keyboard. 
Instruction Code  
O + 1 006-44,40, 1 Sixth program line. 
´ e V XXX-42, 5,25 e is just ―5‖.=
The  first  digit  of= a  keycode  refers= to= the  row  (1= to= 4  from= top  to= bottom),=
and  the  second= digit  refers= to= the  column= (1,  OI=9,= 0  from= left= to= right). 
Exception: the keycode for a digit key is simply that digit.= 
						

							 Section 6: Programming Basics 75 
 
Keycode 25: second row, fifth key. 
Memory Configuration 
Understanding  memory  configuration  is  not  essential  to  your  use  of  the 
HP-15C.  It  is  essential,  however,  for  obtaining  maximum  efficiency  in 
memory and programming use. The more you program, the more useful this 
knowledge  will  be.  Memory  configuration  and  allocation  is  thoroughly 
explained in appendix C, Memory Allocation. 
Should you ever get an Error 10, you have run up against limitations of the 
HP-15C  memory.  If  you  learn  how  to  reallocate  memory,  you  can  greatly 
increase your ability to store information in the HP-15C. 
The  HP-15C  memory  consists  of  67  registers  (R0 to  R65 and  the  Index 
register) divided between data  storage  and programming/advanced  function 
capability. The initial configuration is: 
 46  registers  for  both  programming  and  the  advanced  functions 
(_, f, the  imaginary stack, and > functions). At seven 
bytes  of  memory  per  register,  this  is  worth  322  program  bytes  if  no 
memory is dedicated to advanced functions. 
 21  registers  for  data  storage  (R0 to  R9,  R.0 to  R.9,  and  the  Index 
register). 
   
						

							76 Section 6: Programming Basics 
 
 
Memory  is  reallocated  by  telling  the  calculator  which  data  storage  register 
shall be the highest data register; all other registers are left for programming 
and advanced functions. 
Keystrokes Display  
60 ´ m %* 60.0000 R60 and below allocated to data 
storage; five (R61 to R65) remain 
for programming. 
                                                           * The optional omission of the ´ keystroke after another prefix key is explained on page 78, Abbreviated Key Sequences. 
Initial Memory Configuration 
 
   
						

							 Section 6: Programming Basics 77 
 
 
Keystrokes Display  
1 ´ m % 1.0000 R1 and R0 allocated for data 
storage; R2 to R65 available for 
programming and advanced 
functions. 
19 ´ m% 19.0000 Original allocation: R19 (R.9) and 
below for data storage; R20, to 
R65 for programming and 
advanced functions.* 
lm% 19.0000 Displays the current highest data 
register. 
The m and W (memory  status) functions  are  described  in  detail  in 
appendix C. 
Keep  in  mind  that  an  error  message  will  result (given  the  above  memory 
configuration) if 
1. You  try  to  address  a  register  higher  than  R19 (R.9),  which  initially  is 
the highest register allocated to data storage (Error 3). 
2. You have  322 occupied program bytes and try to load more  program 
lines (Error 4). 
3. You  try  to  run  an  advanced  function  with  insufficient  available 
memory (Error 10). 
Program Boundaries 
End. Not every program needs to end with a n or ¦ instruction. If 
you  are  at  the  end  of  occupied  program  memory,  there  is  an automatic 
n instruction,  so  you  do  not  need  to  enter  one.  This  can  save  you  one 
line  of  memory.  On  the  other  hand,  a  program  can  ―end‖  by  simply 
transferring execution to another routine using t (section 7). 
Labels. Labels  in  a  program  (or  subroutine)  are  markers  telling  the 
calculator where to begin execution. Following an ´ label or G label 
instruction, the calculator will search downward in program memory for the 
                                                           * For memory allocation and indirect addressing, registers R.0 through R.9 are referred to as R10 through R19.  
						

							78 Section 6: Programming Basics 
 
corresponding  label.  If  need  be,  the  search  will  wrap  around  at  the  end  of 
program  memory  and  continue  at  line  000.  When  it  encounters  an 
appropriate label, the search stops and execution begins. 
If  a  label  is  encountered  as  part  of  a  running  program,  it  has  no  effect,  that 
is,  execution  simply  continues.  Therefore,  you  can  label  a  subordinate 
routine within a program (more on subroutines in section 9). 
Since the calculator searches in only one direction from its present position, 
it  is  possible  (though  not  advisable)  to  use  duplicate  program  labels. 
Execution will begin at the first appropriately labeled line encountered. 
 
If  an ´ A entry  starts  the  search 
for ―A‖ here,=
it= then= proceeds= downward= through 
memory,  wraps  around= to= line= 000,=
and stops  at  label  ―A‖.  Execution  then 
starts= and  continues  (ignoring  any 
other labels) until a halt instructionK=
000- 
(stop) 
´bA 
 
´b3 
 
¦ 
end of memory 
Unexpected Program Stops 
Pressing  Any  Key. Pressing  any  key  will  halt  program  execution. It  will 
not halt  in  the  middle  of  an  operation.  This  instruction  will  be  completed 
before the program stops. 
Error  Stops. Program execution is immediately  halted  when the  calculator 
attempts an improper operation that results in an Error display. 
To  see  the  line  number  and  keycode  of  the  error-causing  instruction  (the 
line  at  which  the  program  stopped), press  any  one  key  to  remove  the Error 
message, then switch to Program mode. 
If the display is flashing when a program stops, an overflow condition exists 
(page 61). Press − =, or |  9 to stop the blinking. 
Abbreviated Key Sequences 
In  certain  cases,  an ´ prefix  you  might  expect  to  include  in  a  key 
sequence  is  not  needed.  The  rule  for  using  an abbreviated  key  sequence is: 
the ´ prefix  key  is  unnecessary  after  any  other  prefix  key.  (Page  19 
contains a list of prefix keys.)  
						

							 Section 6: Programming Basics 79 
 
For  example, ´b´A becomes ´bA, ´m´% 
becomes ´m%,  and O´# becomes O#. 
The removal of the ´ is not ambiguous because the ´-shifted function 
is the only logical one in these cases. The keycodes for such instructions do 
not include the extraneous ´ even if you do key it in. 
User Mode 
User  mode  is  a  convenience  to  save  keystrokes  when  addressing  (calling 
up) programs for execution. Pressing ´U will exchange the  primary 
functions  and ´-shifted  functions  of  the A through E keys  only.  In 
User mode (USER annunciator displayed): 
 
´ shift  
Primary 
 A B C D E 
¤  @ y ∕ 
| shift x2 LN LOG 

Press | U again to deactivate User mode. 
Polynomial Expressions and Horners Method 
Some expressions, such as polynomials, use the same variable several times 
for their solution. For example, the expression 
f(x) = Ax4 + Bx3 + Cx2 + Dx + E 
uses  the  variable x four  different  times.  A  program  to  solve  such  an 
equation  could  repeatedly  recall  a  stored  copy  of x from  a  storage  register. 
A  shorter  programming  method,  however,  would  be  to  use  a  stack  which 
has  been  filled  with  the  constant  (refer  to  Loading  the  Stack  with  a 
Constant, page 41). 
Horners Method is a useful means of rearranging polynomial expressions to 
cut  calculation  steps  and  calculation  time.  It  is  especially  expedient  in 
_ and f, two rather long-running functions that use subroutines. 
This method involves rewriting a polynomial expression in a nested fashion 
to eliminate exponents greater than 1: 
Ax4 + Bx3 + Cx2 + Dx + E 
(Ax3 + Bx2 + Cx + D)x + E 
((Ax2 + Bx + C)x + D)x + E 
(((Ax + B)x + C)x + D)x + E  
						

							80 Section 6: Programming Basics 
 
Example: Write  a  program  for 5x4 + 2x3 as (((5x + 2)x)x)x, then  evaluate 
for x = 7 
Keystrokes Display  
| ¥ 000- Assumes position in memory 
is line 000. If it is not, clear 
program memory. 
´ b B 001-42,21,12  
5 002-       5  
* 003-      20 5x. 
2 004-       2  
+ 005-      40 5x + 2. 
* 006-      20 (5x + 2)x. 
* 007-      20 (5x + 2)x2. 
* 008-      20 (5x + 2)x3. 
| n 009-   43 32  
| ¥  Returns to Run mode, Prior 
result remains in display. 
7 v v 
v 
  
7.0000 Loads the stack (X-, Y-, Z-, 
and T-registers) with 7. 
´ B 12,691.0000  
Nonprogrammable Functions 
When  the  calculator  is  in  Program  mode,  almost  every  function  on  the 
keyboard  can  be  recorded  as an  instruction  in  program  memory.  The 
following functions cannot be stored as instructions in program memory. 
 
´ CLEAR u | ‚ Â 
´ CLEAR M | W − 
´ % | ¥ =/. 
´ U t “ nnn =/­