HP 15c Manual

							 Section 10: The Index Register and Loop Control 111 
 
False (nnnnn > xxx)  True (nnnnn  xxx) 
 instruction  
 ´sV  
loop t. 1  
 Instruction exit loop 
For e: given nnnnn.xxxyy, decrement nnnnn to nnnnn - yy, compare 
it to xxx, and skip the  next program line if the  new value  satisfies nnnnn ≤ 
xxx. This  allows  you  to  exit  a  loop  at  this  point  when nnnnn becomes  less 
than or equal to xxx. 
For example, loop iterations will alter these control numbers as follows: 
Iterations 
Operation 0 1 2 3 4 
I 0.00602 2.00602 4.00602 6.00602 8.00602 
     (skip next 
line) 
e 6.00002 4.00002 2.00002 0.00002  
    (skip next 
line) 
 
Examples 
Examples: Register Operations 
Storing and Recalling 
Keystrokes Display  
´ CLEAR Q  Clears all storage registers. 
12.3456 12.3456  
O V 12.3456 Stores in RI. 
7 ¤ 2.6458  
O% 2.6458 Storage  in  R.2 by  indirect  addressing 
(RI = 12.3456). 
lV 12.3456 Recalls contents of RI.  
						

							112 Section 10: The Index Register and Loop Control 
 
Keystrokes Display  
l % 2.6458 Indirectly recalls contents of R.2. 
´ X .2 2.6458 Check: same contents recalled by 
directly addressing R.2. 
Exchanging the X-Register 
Keystrokes Display  
´ X V 12.3456 Exchanges  contents  of  RI and  X-
register. 
l V 2.6458 Present contents of RI. 
´ X% 0.0000 Exchanges contents of  R2 (which is 
zero) with X. 
l % 2.6458  
´ X 2 2.6458 Check: directly address R2. 
Storage Register Arithmetic 
Keystrokes Display  
10 O + V 10.0000 Adds 10 to RI. 
l V 12.6458 New contents of RI (= old + 10). 
| $ O ÷ 
% 
3.1416 Divides contents of R.2 by .
l% 0.8422 New contents of R.2. 
´ X.2 0.8422 Check: directly address R.2. 
Example: Loop Control with e 
Remember  the  program  in  section  8  which  used  a  loop  to  calculate 
radioactive decay? (Refer to page 93.) This program used a test condition (x 
≥ y?) to exit the loop when the calculated result passed the given limit (50). 
As weve seen in this section, theres another way to control loop execution: 
through  a  stored  loop  counter  that  is  monitored  by  the I or e 
function.  
						

							 Section 10: The Index Register and Loop Control 113 
 
Here  is  a  revision  of  the original  radioisotope  decay  program.  This  
time,  we  will  limit  the  program  to  three  executions  of  the  loop  rather  
than setting  a  specific  limit  value.  This  example  uses e with  a  
loop control number in R2 of  
3.0 0 0 0 1. 
     initial loop counter          decrement value 
      test (goal) value 
Make  the  following  changes  to  the  program  (assuming  it  is  in  memory).  A 
loop counter will be stored in R2 and a line number in the Index register. 
Keystrokes Display  
| ¥ 000- Program mode. 
t“013 013-43,30, 9 The  second  of  the  two  loop 
test condition lines. 
−− 011-   42 31 Delete lines 013 and 012. 
´e 2 012-42, 5, 2 Add  your  loop  counter 
function  (counter  stored  in 
R2). 
t V 013-   22 25 Go  to  given  line  number 
(015). 
Now when the loop counter (stored in R2) has reached zero, it will skip line 
013 and go on to 014, the n instruction, thereby ending the program. If 
the loop counter has not yet decreased to zero, execution continues with line 
013. This branches to line 015 and continues the program and the looping. 
To run the program, put t1 (day 1) in R0, N0 (initial isotope  batch) in R1 the 
loop counter in R2, and the line number for branching in the Index register. 
Keystrokes Display  
| ¥  Run mode. 
2 O 0 2.00000 t1. 
100 O 1 100.0000 N0. 
3.000001 O 2 3.0000 Loop counter. (This instruction could also be 
programmed.) 
    
						

							114 Section 10: The Index Register and Loop Control 
 
Keystrokes Display 
15 “ O 
V ´ A 
-15.0000 Branch line number. 
 2.0000 Running  program  loop  counter  
= 3. 
  84.0896  
  5.0000 Loop counter = 2. 
  64.8420  
  8.0000 Loop counter = 1. 
  50.0000  
  50.0000 Loop counter = 0; program ends. 
Example: Display Format Control 
The  following  program  pauses  and  displays  an  example  of • display 
format for each possible decimal place. It utilizes a loop containing a s 
instruction to automatically change the number of decimal places. 
Keystrokes 
 
|¥  
´CLEAR M  
´ b B  
9 nnnnn = 9. Therefore, xxx = 0 and by default yy 
= 1 (yy cannot be zero). 
O V  
´ b 0  
´ • V  
l V  
´ © Displays current value of nnnnn. 
´ e V Value in RI is decremented and tested. Skip a line 
if nnnnn  test value. 
t 0 Continue loop if nnnnn > test value (0). 
| T 1 Tests whether value in display is greater than 0, so 
loop  will  continue  when nnnnn has  reached  0  but 
display still only shows 1.0. t 0 
| n   
						

							 Section 10: The Index Register and Loop Control 115 
 
To  display  fixed  point notation  for  all  possible  decimal  places  on  the 
HP-15C: 
Keystrokes Display  
| ¥  Run mode. 
´ B 9.000000000  
 8.00000000  
 7.0000000  
 6.000000  
 5.00000  
 4.0000  
 3.000  
 2.00  
 1.0  
 0. Display at ´©instruction. 
 0. Display when program halts. 
Further Information 
Index Register Contents 
Any  value  stored  in  the  Index  register  can  be  referenced  in  three  different 
ways: 
 Using V like  any  other  storage  register.  The  value  in  RI can  be 
manipulated as it is: stored, recalled, exchanged, added to, etc. 
 Using V as  a  control  number.  The  absolute  value  of  the  integer 
portion in RI is a separate entity from the fractional portion. For indirect 
branching,  flag  control,  and  display  format  control  with V,  only  this 
portion is used. For loop control, the fractional portion is also used, but 
separately from the integer portion.* 
 Using % as  a  reference  to  the  contents  of  another  storage  register. 
The % key uses the indirect addressing system shown in the tables on 
pages 107 and 108. (In turn, the contents of that second register may be 
used as a loop control number, in the fashion described above.) 
                                                           *  This is also true for the value in any storage register used for indirect loop control.  
						

							116 Section 10: The Index Register and Loop Control 
 
I and e 
For  the  purpose  of  loop  control,  the  integer  portion  (the  counter  value)  of 
the stored control number can be up to five digits long (nnnnn.xxxyy). The 
counter value (nnnnn) is zero if not specified otherwise. 
xxx, in  the  decimal  portion  of  the  control  number,  must  be  specified  as  a 
three-digit  number.  (For  example,  ―5‖  must  be  ―005‖.) xxx is  zero  if  not 
specified  otherwise.  Whenever I or e is  encountered,  nnnnn  is 
compared internally to xxx, which represents the end level for incrementing 
or decrementing. 
yy must be specified as a two-digit number. yy cannot be zero, so if left (or 
specified)  as 00, the  value  for yy defaults  to 1. The  value nnnnn is  altered 
by the  amount of yy each time  the  loop runs through I or e. Both 
yy and xxx are reference values, which do not change with loop execution. 
Indirect Display Control 
While you can use the Index register to format the display manually (that is, 
from  the  keyboard),  this  function  is  most  commonly  used  in  programming. 
This  capability  is  especially  valuable  for  the f function,  for  which 
accuracy  can  be  stipulated  by  specifying  the  number  of  digits  to  be 
displayed (as described in section 14). 
There  are,  as  usual,  certain  display  limitations  to  keep  in  mind.  Recall  that 
any  display  format  function  merely  alters  the  number  of  decimal  places  to 
which the display is rounded. In its memory, the calculator always retains a 
number  in  scientific  notation  as  a  10-digit  mantissa  with  a  two-digit 
exponent. 
The integer portion of the number in the Index register specifies the number 
of decimal  places to  which the  display is rounded. A  number less than zero 
defaults  to  zero  (zero  decimal  places  displayed  in • format),  while  a 
number greater than 9 defaults to 9 (9 decimal places displayed in •).* 
* Note that in i and ^ format modes, the maximum display is a seven-digit mantissa with a two-digit exponent. However, a format number greater than six (and less than or equal to nine) will alter the decimal place at which rounding occurs. (Refer to page 58-59.)  
						

							 Section 10: The Index Register and Loop Control 117 
 
An  exception  is  in  the  case  of f where  the  display  format  number  in  RI 
may range  from -6 to +9. (This is discussed in appendix E  on page  247.) A 
number  less  than  zero  will  not  affect  the  display  format,  but  will  affect 
accuracy with this function.  
						

							 
118  
						

							 
 
 
 
 
Part lll 
HP-15C 
Advanced Functions 
						

							 
120 
Section 11 
Calculating With 
Complex Numbers 
The  HP-15C  enables  you  to  calculate  with  complex  numbers,  that  is, 
numbers of the form 
a + ib, 
where     a is the real part of the complex number, 
b is the imaginary part of the complex number, and 
. 
As  you  will  see,  the  beauty  of  calculating  with  the  HP-15C  in  Complex 
mode  is  that  once  the  complex  numbers  are  keyed  in,  most  operations are 
executed in the same manner as with real numbers. 
The Complex Stack and Complex Mode 
Calculations  with  complex  numbers  are 
performed  using  a  complex  stack  composed 
of two parallel  four-register  stacks  (and  two 
LAST  X  registers).  One  of  these  parallel 
stacks – referred  to  as  the real stack – 
contains  the  real  parts  of  complex  numbers 
used  in  calculations.  (This  is  the  same  stack 
used  in  ordinary calculations.)  The  other 
stack – referred  to  as  the imaginary stack – 
contains  the  imaginary  parts  of  complex 
numbers used in calculations. 
Creating the Complex Stack 
The  imaginary  stack  is  created  (by  converting  five  storage  registers  as 
described  in  appendix  C)  when  you  activate  Complex  mode;  it  does  not 
exist when the calculator is not in Complex mode. 1i