HP 15c Manual

 Section 2: Numeric Functions 31 
 
Rectangular Conversion. Pressing ´; (rectangular) converts a set of 
polar coordinates (magnitude r angle θ) into rectangular coordinates (x, y). θ 
must  be  entered  first  then r. Upon  executing ´;, x will  be  displayed 
first; press ® to display y. 
 
 
 
 
 
 
 
 
Keystrokes Display  
|D  Set to Degrees mode (no annunciator). 
5 v 5.0000 y-value. 
10 10 x-value. 
|: 11.1803 r. 
® 26.5651 θ; rectangular coordinates converted to 
polar coordinates. 
30 v 30.0000...

 
32 
Section 3 
The Automatic Memory Stack, 
LAST X, and Data Storage 
The Automatic Memory Stack 
and Stack Manipulation 
HP  operating  logic  is  based  on  a  mathematical  logic  known  as ―Polish 
Notation,‖  developed  by  the  noted  Polish  logician  Jan Łukasiewicz 
(Wookashyeveech) (1878-1956). Conventional algebraic notation places the 
algebraic  operators between the  relevant  numbers  or  variables  when 
evaluating  algebraic  expressions. Łukasiewicz’s  notation  specifies  the...

Section 3: The Memory Stack, LAST X, and Data Storage 33 
 
Any  number  that  is  keyed  in  or  results  from  the  execution  of  a  numeric 
function  is  placed  into  the  display  (X-register).  This  action  will  cause 
numbers  already  in  the  stack  to  lift,  remain  in  the  same  register,  or  drop, 
depending  upon  both  the  immediately  preceding  and  the  current  operation. 
Numbers in the stack are stored on a last-in, first-out basis. The three stacks 
drawn  below  illustrate...

34 Section 3: The Memory Stack, LAST X, and Data Storage 
 
shading indicates  that  the  contents  of  that  register  will  be  written  over 
when the next number is keyed in or recalled.) 
 
   lost  lost    lost 
T t  z  y  y  x 
Z z  y  x  x  1 
Y y  x  1  1  2 
X x  1  1  2  2 
Keys:  1  v  2  v  
 
     lost   
T x  x  1  1 
Z 1  1  2  2 
Y 2  2  3  3 
X 2  3  3  4 
Keys:  3  v  4  
 
) (roll down), ( (roll up), and ® (X exchange Y). ) and ( 
roll the  contents of the  stack registers up or down...

Section 3: The Memory Stack, LAST X, and Data Storage 35 
 
The LAST X Register and K 
The  LAST  X  register,  a  separate  memory  register,  preserves  the  value  that 
was  last  in  the  display before  execution  of  a  numeric  operation.* Pressing 
|K (LAST  X) places  a  copy  of  the  contents  of  the  LAST  X  register 
into the display (X-register). For example: 
 
     lost 
T t  t  z 
Z z  z  y 
Y y  y  16 
X 4  16  4 
Keys:  |x  |K  
LAST X: /  4  4 
The K feature  saves  you  from...

36 Section 3: The Memory Stack, LAST X, and Data Storage 
 
 
Keystrokes  Display  
* 287.0000 Reverses the function that 
produced the wrong answer. 
13.9 + 20.6475 The correct answer. 
Calculator Functions and the Stack 
When  you  want  to  key  in  two  numbers,  one  after  the  other,  you  press 
v between  entries  of  the  numbers.  However,  when  you  want  to  key 
in  a  number  immediately  following  any  function  (including  manipulations 
like )),  you  do  not  need  to  use v.  Why?...

Section 3: The Memory Stack, LAST X, and Data Storage 37 
 
 
     lost   
T z  z  z  z 
Z z  z  z  z 
Y y  y  y  y 
X 7  0  6  y6 
Keys:  |`  6  Y  
Order of Entry and the v Key 
An  important  aspect  of  two-number  functions  is  the  positioning  of  the 
numbers in the stack. To execute an arithmetic function, the numbers should 
be  positioned  in  the  stack  in  the  same  way  that  you  would  vertically 
position them on paper. For example: 
98  98  98  98 
-15  +15  x15  15 
As  you  can...

38 Section 3: The Memory Stack, LAST X, and Data Storage 
 
Nested Calculations 
The  automatic  stack  lift  and  stack  drop  make  it  possible  to  do  nested 
calculations  without  using  parentheses  or  storing  intermediate  results.  A 
nested  calculation  is  solved  simply as  a  series  of  one- and  two-number 
operations. 
Almost  every  nested  calculation  you  are  likely  to  encounter  can  be  done 
using  just  the  four  stack  registers.  It  is  usually  wisest  to  begin  the...

Section 3: The Memory Stack, LAST X, and Data Storage 39 
 
 
T y  y  y  y 
Z y  x  y  x 
Y x  13  x  65 
X 13  5  65  4 
Keys:  5  *  4  
 
T y  y  y  y 
Z x  y  x  y 
Y 65  x  69  x 
X 4  69  3  207 
Keys:  +  3  *  
 
Arithmetic Calculations With Constants 
There  are  three  ways  (without  using  a storage  register)  to  manipulate  the 
memory stack to perform repeated calculations with a constant: 
1. Use the LAST X register. 
2. Load the stack with a constant and operate upon different 
numbers....

40 Section 3: The Memory Stack, LAST X, and Data Storage 
 
Example: Two close stellar neighbors of Earth 
are Rigel  Centaurus (4.3 light-years away) and 
Sirius (8.7 light-years away).  Use the  speed of 
light, c (3.0×108 meters/second,  or  9.5×1015 
meters/year),  to  figure  the  distances  to  these 
stars in meters. (The stack diagrams show only 
one decimal place.) 
 
 
T t  z  y  y 
Z z  y  x  x 
Y y  x  4.3  4.3 
X x  4.3  4.3  9.5   15 
Keys:  4.3  v 9.5 ‛ 15 
LAST X: /  /  /  / 
        
T y...