HP 15c Manual

							Section 3: The Memory Stack, LAST X, and Data Storage 41 
 
Loading the Stack with a Constant. Because  the  number in the  T-register 
is replicated when the  stack drops, this number can be used as a constant in 
arithmetic operations. 
 
T c  c New constant 
generation. Z c  c 
Y c  c Drops to interact 
with X-register. X x  cx 
Keys:  *   
Fill  the  stack  with  a  constant  by  keying  it  into  the  display  and  pressing 
v three  times.  Key  in  your  initial  argument  and  perform  the 
arithmetic  operation.  The  stack  will  drop,  a  copy  of  the  constant  will  fall 
into the  Y-register, and a  new  copy of the  constant  will be  generated in the 
T-register. 
If the  variables change  (as in the  preceding example), be  sure  and clear  the 
display before  entering  the  new  variable. This disables the  stack  so that  the 
arithmetic  result  will  be  written  over  and  only  the  constant  will  occupy  the 
rest of the stack. 
If  you  do not have  different  arguments,  that  is,  the  operation  will  be 
performed upon a cumulative number, then do not clear the display—simply 
repeat the arithmetic operation. 
Example: A bacteriologist tests a certain strain 
of  microorganisms  whose  population  typically 
increases  by  15%  each  day  (a  growth  factor  of 
1.15).  If  she  starts  with  a  sample  culture  of 
1000,  what  will  be  the  bacteria  population  at 
the end of each day for four consecutive days? 
Keystrokes Display  
1.15 1.15 Growth factor. 
vv
v 
1.1500 Filling the stack. 
1000 1,000 Initial culture size.   
						

							42 Section 3: The Memory Stack, LAST X, and Data Storage 
 
 
Keystrokes Display  
* 1,150.0000 Population at the end of day 1. 
* 1,322.5000 Day 2. 
* 1,520.8750 Day 3. 
* 1,749.0063 Day 4. 
Storage Register Operations 
When  numbers  are  stored  or  recalled,  they  are  copied  between  the  display 
(X-register) and the data storage registers. At ―power-up‖ (initial turn-on or 
Continuous  Memory  reset)  the  HP-15C  has  21  directly  accessible  storage 
registers: R0 through R9, R.0 through R.9, and the Index register (RI) (see the 
diagram  of  the  registers on  the  inside  back  cover).  Six  registers,  R2 to  R7, 
are also used for statistics calculations. 
The  number  of  available  data  storage  registers  can  be  increased  or 
decreased.  The m function,  which  is  used  to  reallocate  registers  in 
calculator  memory,  is  discussed  in  appendix  C,  Memory  Allocation.  The 
lowest-numbered  registers  are  the  last  to  be  deallocated  from  data  storage, 
therefore  it  is  wisest  to  store  data  in  the  lowest-numbered  registers 
available.  
Storing and Recalling Numbers 
O (store).  When  followed by  a  storage  register  address  (0  through  9  or 
.0 through .9*), this  function  copies a  number from the  display (X-register) 
into  the  specified  data  storage  register.  It  will  replace  any  existing  contents 
of that register. 
l (recall). Similarly,  you  can  recall  data  from  a  particular  register  into 
the  display  by  pressing l followed  by  the  register  address.  This  brings 
a copy of  the  desired  data  into  the  display;  the  contents  of  the  storage 
register remain unaltered. 
X (X  exchange). Followed  by  0  through  .9,* this  function exchanges  the 
contents of  the  X-register  and  the  addressed  data  storage  register.  This  is 
useful to view storage registers without disturbing the stack. 
                                                           * All storage register operations can also be performed with the Index register (using V or %), which is covered in section 10, and with matrices, section 12.  
						

							Section 3: The Memory Stack, LAST X, and Data Storage 43 
 
The above are stack lift-enabling operations, so the number remaining in the 
X-register can  be  used  for  subsequent  calculations.  If  you  address  a 
nonexistent register, the display will show Error 3. 
Example: Springtime  is coming and  you  want to keep track of 24 crocuses 
planted in your garden. Store the number of crocuses blooming the first day 
and add to this the number of new blooms the second day. 
Keystrokes Display  
3 O 0 3.0000 Stores the number of first-day 
blooms in R0. 
 
Turn the calculator off. Next day, turn it back on again. 
 
l 0 3.0000 Recalls the number of crocuses that 
bloomed yesterday. 
5 + 8.0000 Adds todays new blooms to get the 
total blooming crocuses. 
Clearing Data Storage Registers 
Pressing ´ CLEAR Q (clear registers) clears the contents of all data 
storage  registers  to  zero.  (It  does  not  affect  the  stack  or  the  LAST  X 
register.)  To  clear  a  single  data  storage  register,  store  zero  in  that  register. 
Resetting Continuous Memory clears all registers and the stack. 
Storage and Recall Arithmetic 
Storage  Arithmetic.  Suppose  you  not  only  wanted  to  store  a  number,  but 
perform arithmetic  with it and store the result in the same register. You can 
do this directly – without using l – by using the following procedure. 
1. Have  your second operand (besides the one in storage) in the display 
(as the result of a calculation, a recall, or keying in). 
2. Press O. 
3. Press +, -, *, or ÷. 
4. Key in the register address (0 to 9, .0 to .9). (The Index register, 
discussed in section 10, can also be used.)  
						

							44 Section 3: The Memory Stack, LAST X, and Data Storage 
 
The number in the register is determined as follows: 
For storage arithmetic, 
new contents  
of register = old contents  
of register 
 
 
× 
 
number in  
display 
 
R0 r T t R0 r-x T t 
  Z z   Z z 
  Y y   Y y 
  X x   X x 
  Keys:  O-0    
Recall Arithmetic. Recall arithmetic allows you to perform arithmetic with 
the  displayed  value  and  a  stored  value without  lifting  the  stack, that  is, 
without  losing  any  values  from  the  Y-,  Z,  and  T-registers.  The  keystroke 
sequence  is  the  same  as  for  storage  arithmetic  using l in  place  of 
O. 
For recall arithmetic, 
new display = old display 
 
 
× 
 
contents of  
register 
 
R0 r T t R0 r T t 
  Z z   Z z 
  Y y   Y y 
  X x   X x-r 
  Keys:  l-0     
						

							Section 3: The Memory Stack, LAST X, and Data Storage 45 
 
Example: Keep a running count of your newly blooming crocuses for two 
more days. 
Keystrokes Display  
8 O 0 8.0000 Places the total number of blooms as of 
day 2 in R0. 
4 O + 0 4.0000 Day 3: adds four new blooms to those 
already blooming. 
3 O + 0 3.0000 Day 4: adds three new blooms. 
24 l - 0 9.0000 Subtracts total number of blooms 
summed in R0(15) from the total 
number of plants (24); 9 crocuses have 
not bloomed. 
l 0 15.0000 (The number in R0 does not change.) 
Overflow and Underflow 
If  an  attempted  storage  or  recall  arithmetic  operation  would  result  in 
overflow in a  data  storage  register, the  value  in the  affected register  will be 
replaced  with  ±9.999999999×1099 and  the  display  will  blink.  To  stop  the 
blinking (clear the overflow condition), press − or = or |  9. 
In case of underflow, the value in the register will be replaced with zero (no 
display  blinking).  Overflow  and  underflow  are  discussed  further  on  page 
61. 
Problems 
1. Calculate the value of x in the following equation. 
 
Answer: 4.5728. 
A possible keystroke solution is: 
4 v 5.2 - 8.33 * | K 7.46 - 0.32 * ÷ 3.15 
v 2.75 - 4.3 * 1.71 v 2.01 * - ÷ ¤ (2.01) (1.71)2.75)(3.15 4.3
0.32] 7.46)[(8.335.2)(4 8.33x
  
						

							46 Section 3: The Memory Stack, LAST X, and Data Storage 
 
2. Use  arithmetic  with  constants  to  calculate  the  remaining 
balance  of  a  $1000  loan  after  six  payments  of  $100  each  and 
an interest rate of 1% (0.01) per payment period. 
Procedure:  Load the  stack  with (1 + i),  where i = interest rate, 
and  key  in  the  initial  loan  balance.  Use  the  following  formula 
to find the new balance after each payment. 
New Balance = ((Old Balance)×(1 + i)) - Payment 
The first part of the key sequence would be: 
1.01 vvv 1000 
For each payment, execute: 
* 100 - 
Balance after six payments: $446.32. 
3. Store 100 in R5. Then: 
1. Divide the contents of R5 by 25. 
2. Subtract 2 from the contents of R5. 
3. Multiply the contents of R5 by 0.75. 
4. Add 1.75 to the contents of R5. 
5. Recall the contents of R5. 
Answer: 3.2500.  
						

							 
47 
Section 4 
Statistics Functions 
A word about the statistics functions: their use is based on an understanding 
of  memory  stack  operation  (Section  3). You  will  find  that  order  of  entry  is 
important for most statistics calculations. 
Probability Calculations 
The  input  for  permutation  and  combination  calculations  is  restricted  to 
nonnegative integers. Enter the y-value before the x-value. These functions, 
like  the  arithmetic  operators,  cause  the  stack  to  drop  as  the  result  is  placed 
in the X-register. 
Permutations.  Pressing ´p calculates  the  number  of  possible 
different arrangements of y different items taken in quantities of x items at a 
time.  No  item  occurs  more  than  once  in  an  arrangement,  and  different 
orders  of  the  same x items  in  an  arrangement are counted  separately.  The 
formula is 
 
Combinations.  Pressing |c calculates  the  number  of  possible sets 
of y different  items  taken  in  quantities  of x items  at  a  time.  No  item  occurs 
more than once in a set, and different orders of the same x items in a set are 
not counted separately. The formula is 
 
Examples:  How  many  different  arrangements  are  possible  of  five  pictures 
which can be hung on the wall three at a time? 
Keystrokes Display  
5 v 3 3 Five (y) pictures put up three (x) at a 
time. 
´p 60.0000 Sixty different arrangement possible. )!(
!,xy
yPxy  )!(!
!,xyx
yCxy  
						

							48 Section 4: Statistics Functions 
 
How many different four-card hands can be dealt from a deck of 52 cards? 
Keystrokes Display  
52 v 4  4 Fifty-two (y) cards dealt four 
(x) at a time. 
|c  270,725.0000 Number of different hands 
possible. 
The maximum size of x or y is 9,999,999,999. 
Random Number Generator 
Pressing ´# (random  number) will  generate  a  random  number 
(part  of  a  uniformly  distributed  pseudo-random  number  sequence)  in  the 
range 0 ≤ r 
						

							 Section 4: Statistics Functions 49 
 
Keystrokes Display  
l´
# 
0.2809 Recall last random number generated, 
which is the new seed. (The ´ may be 
omitted.) 
Accumulating Statistics 
The  HP-15C  performs  one- and  two-variable  statistical  calculations.  The 
data  is  first  entered  into  the  Y- and  X-registers.  Then  the z function 
automatically  calculates  and  stores  statistics  of  the  data  in  storage  registers 
R2 through  R7. These  registers  are  therefore  referred  to  as  the statistics 
registers. 
Before  beginning  to  accumulate  statistics  for  a  new  set  of  data,  press  
´ CLEAR ∑ to  clear  the  statistics  registers  and  stack.  (If  you  have 
reallocated  registers  in  memory  and  any  of  the  statistics  registers  no  longer 
exist, Error 3 will  be  displayed  when  you  try  to  use CLEAR ∑, z, or 
w Appendix C explains how to reallocate memory.) 
In  one-variable  statistical  calculations,  enter  each  data  point  (x-value)  by 
keying in x and then press z. 
In  two-variable  statistical  calculations,  enter  each  data  pair  (the x- and y-
values) as follows: 
1. Key y into the display first. 
2. Press v. The displayed y-value is copied into the Y-register. 
3. Key x into the display. 
4. Press z. The current number of accumulated data points, n, will be 
displayed. The x-value is saved in the LAST X register and y remains 
in  the  Y-register. z disable  stack  lift,  so  the  stack  will  not  lift 
when the next number is keyed in.  
						

							50 Section 4: Statistics Functions 
 
In  some  cases  involving x or y data  values  that  differ  by  a  relatively  small 
amount,  the  calculator cannot compute s, r, linear regression, or ŷ, and  will 
display Error 2. This will not happen, however, if you normalize the data by 
keying  in  only  the  difference  between  each  value  and  the  mean  or 
approximate  mean of the  values.  This difference  must be  added back to the 
calculations of  x, ŷ, and the y-intercept (L). For example, if your x-values 
were 665999, 666000, and 666001, you should enter the data as -1, 0, and 1; 
then add 666000 back to the relevant results. 
The statistics of the data are compiled as follows: 
 
Register Contents 
R2 n Number of data points accumulated (n also 
appears in the X-register). 
R3 Σx Summation of x-values. 
R4 Σx 2 Summation of squares of x-values. 
R5 Σy Summation of y-values. 
R6 Σy2 Summation of squares of y-values. 
R7 Σxy Summation of products of x- and y-values. 
You  can  recall  any  of  the  accumulated  statistics  to  the  display (X-register) 
by pressing l and the number of the data storage register containing the 
desired  statistic.  If  you  press l z, Σy and  Σx will  be  copied 
simultaneously  from  R3 and  R5 respectively,  into  the  X-register  and  the  Y-
register, respectively. (The sequence l z lifts the stack twice if stack 
lift is enabled, once if not, and then enables stack lift.) 
Example: Agronomist  Silas  Farmer  has 
developed  a  new  variety  of  high-yield  rice, 
and  has  measured  the  plants  yield  as  a 
function of fertilization. Use the z function 
to accumulate the data below to find the values 
for Σx, Σx2 Σy, Σy2,  and Σxy for  nitrogen 
fertilizer application (x) versus grain yield (y).