HP 15c Manual

							 Section 1: Getting Started 21 
 
 
Clearing Sequence Effect 
 ´ CLEAR M  
In Run mode: Repositions program memory to line 000. 
In Program mode: Deletes all program memory. 
 ´ CLEAR Q Clears all data storage registers. 
 ´ CLEAR u* Clears any prefix from a partially entered 
key sequence. 
* Also temporarily displays the mantissa. 
Display Clearing: ` and − 
The HP-15C has two types of display clearing operations: ` (clear X) 
and − (back arrow). 
In Run mode:  
 ` clears the display to zero. 
 − deletes  only  the  last  digit  in  the  display if  digit  entry  has  not 
been  terminated by v or  most  other  functions.  You  can  then 
key in a new digit or digits to replace the one(s) deleted. If digit entry 
has been terminated, then − acts like `. 
Keystrokes Display  
12345 12,345 Digit entry not terminated. 
− 1,234 Clears only the last digit. 
9 12,349  
¤ 111.1261 Terminates digit entry. 
− 0.0000 Clears all digits to zero. 
In Program mode: 
 ` is  programmable:  it  is stored  as a  programmed  instruction, 
and will not delete the currently displayed instruction. 
 − is not programmable,  so  it  can  be  used  for  program  correction. 
Pressing − will delete the entire instruction currently displayed.  
						

							22 Section 1: Getting Started 
 
Calculations 
One-Number Functions 
A one-number function performs an operation using only the number in the 
display.  To  use  any  one-number  function,  press  the  function  key after the 
number has been placed in the display. 
Keystrokes Display 
45 45 
|o 1.6532 
Two-Number Functions and v 
A  two-number  function  must  have  two  numbers  present  in  the  calculator 
before executing  the  function. +, -, * and ÷ are  examples  of 
two-number functions. 
Terminating  Digit  Entry. When keying  in two  numbers  to  perform  an 
operation, the calculator needs a  signal that digit entry  is terminated for the 
first number. This is done by pressing v to separate the two numbers. 
If,  on  the  other  hand,  one  of  the  numbers  is  already  in  the  calculator  as  the 
result of a previous operation,  you do not need  to use  the v key.  All 
functions  except  the  digit  entry  keys  themselves* have  the  effect  of 
terminating digit entry. 
Notice that, regardless of the  number, a decimal point always appears and a 
set  number  of  decimal  places  are  displayed  when  you  terminate  digit  entry 
(as by pressing v). 
Chain Calculations. In the following calculations, notice that: 
 The v key  is  used  only  for  separating  the sequential entry  of 
two numbers. 
 The operator is keyed in only after both operands are in the calculator. 
 The  result  of  any  operation  may  itself  become  an  operand.  Such 
intermediate  results  are  stored  and  retrieved  on  a  last-in,  first-out 
basis. New digits keyed in following an operation are treated as a new 
number. 
                                                           * The digit keys, +, “, ‛, and −.  
						

							 Section 1: Getting Started 23 
 
Example: Calculate (9 + 17  4) ÷ 4. 
Keystrokes Display  
9 v 9.0000 Digit entry terminated. 
17 + 26.0000 (9 + 17). 
4 - 22.0000 (9 + 17 –=4)K=
4 ÷ 5.5000 (9 + 17 –=4) 
						

							 
24 
Section 2 
Numeric Functions 
This  section  discusses  the  numeric  functions  of  the  HP-15C  (excluding 
statistics  and  advanced  functions).  The  nonnumeric  functions  are  discussed 
separately  (digit  entry  in  section  1,  stack  manipulation  in  section  3,  and 
display control in section 5). 
The  numeric  functions  of  the  HP-15C  are  used  in  the  same  way  whether 
executed from the keyboard or in a program. Some of the functions (such as 
a) are, in fact, primarily of interest for programming. 
Remember  that the  numeric  functions,  like  all  functions  except  digit  entry 
functions,  automatically  terminate  digit  entry.  This  means  a  numeric 
function does not need to be preceded or followed by v. 
Pi 
Pressing | $ places  the  first  10  digits  of π into  the  calculator. $ 
does not need to be separated from other numbers by v. 
Number Alteration Functions 
The  number  alteration  functions  act upon  the  number  in  the  display 
(X-register). 
Integer  Portion. Pressing | ‘ replaces  the  number  in  the  display 
with the nearest integer of lesser or equal magnitude. 
Fractional Portion. Pressing ´ q replaces the number in the display 
with  its  fractional  part  (that  is,  the  difference  between  the  number  and  its 
integer part). 
Rounding. Pressing | & rounds  all  10  internally  held  digits  of  the 
mantissa  of  the  displayed  value  to  the  number  of  digits  specified  by  the 
current •, i, or ^ display format. 
Absolute  Value. Pressing | a yields  the  absolute value  of  the 
number in the display. 
  
						

							 Section 2: Numeric Functions 25 
 
Keystrokes Display  
123.4567 |‘  123.0000  
|K “ |‘ -123.0000 Reversing the sign does 
not alter digits. 
|K ´q -0.4567  
1.23456789 “   
|& -1.2346  
´ CLEAR u 
(release) 
 1234600000 Temporarily displays all 
-1.2346 digits in the mantissa. 
|a  1.2346  
One-Number Functions 
One-number math functions in the HP-15C operate only upon the number in 
the display (X-register). 
General Functions 
Reciprocal. Pressing ∕ calculates  the  reciprocal  of  the  number  in  the 
display. 
Factorial  and  Gamma. Pressing ´ ! calculates  the  factorial  of  the 
displayed value, where x is an integer 0≤x≤69. 
You  can  also  use ! to  calculate  the  Gamma  function,  Γ(x), used  in 
advanced mathematics and statistics. Pressing ´ ! calculates Γ(x + 1), 
so you must subtract 1 from your initial operand to get Γ(x). For the Gamma 
function, x is not restricted to nonnegative integers. 
Square  Root. Pressing ¤ calculates  the  positive  square  root  of  the 
number in the display. 
Squaring. Pressing | x calculates  the  square  of  the  number  in  the 
display. 
 
Keystrokes Display  
25 ∕ 0.0400  
8 ´ ! 40,320.0000 Calculates 8! or Γ(9).=
3.9 ¤ 1.9748  
12.3 | x 151.2900   
						

							26 Section 2: Numeric Functions  
 
Trigonometric Operations 
Trigonometric  Modes. The  trigonometric  functions  operate  in  the 
trigonometric  mode  you  select.  Specifying  a  trigonometric  mode  does  not 
convert  any  number already  in  the  calculator  to  that  mode;  it  merely  tells 
the  calculator  what  unit  of  measure  (degrees,  radians,  or  grads)  to  assign  a 
number for a trigonometric function. 
Pressing | D sets  Degrees  mode.  No  annunciator  appears  in  the 
display. Degrees are in decimal, not minutes-seconds form. 
Pressing | R sets  Radians  mode.  The RAD annunciator  appears  in 
the  display. In  Complex  mode, all  functions (except : and ;) assume 
values are in radians, regardless of the trigonometric annunciator displayed. 
Pressing |  g sets  Grads  mode.  The GRAD annunciator  appears  in 
the display. 
Continuous Memory  will  maintain the  last  trigonometric  mode  selected.  At 
power  up  (initial  condition  or  when  Continuous  Memory  is  reset),  the 
calculator is in Degrees mode, 
Trigonometric Functions. Given x in the display (X-register): 
 
Pressing Calculates 
[ sine of x 
|, arc sine of x 
\ cosine of x 
|{ arc cosine of x 
] tangent of x 
|/ arc tangent of x 
Before  executing  a  trigonometric  function,  be  sure  that  the  calculator  is  set 
to the desired trigonometric mode (Degrees, Radians, or Grads). 
Time and Angle Conversions 
Numbers representing time  (hours) or angles (degrees) can be  converted by 
the HP-15C between a decimal-fraction and a minutes-seconds format: 
  
						

							 Section 2: Numeric Functions 27 
 
Hours.Decimal Hours  Hours.Minutes Seconds Decimal Seconds 
(H.h)  (H.MMSSs) 
Degrees.Decimal Hours  Degrees.Minutes Seconds Decimal Seconds 
(D.d)  (D.MMSSs) 
Hours/Degrees-Minutes-Seconds  Conversion. Pressing ´ h 
converts  the  number  in  the  display  from  a  decimal  hours/degrees  format  to 
an hours/degree-minutes-seconds-decimal seconds format. 
For example, press ´ h to convert 
 
Press ´ u to display the value to all possible decimal places: 
 
Decimal  Hours  (or  Degrees)  Conversion. Pressing | À converts the 
number  in  the  display  from  an  hours/degrees-minutes-seconds-decimal 
seconds format to a decimal hours/degrees format. 
Degrees/Radians Conversions 
The d and r functions  are  used  to  convert  angles  to  degrees 
or  radians  (D.dR.r). The  degrees must  be  expressed  as  decimal  numbers, 
and not in a minutes-seconds format. 
Keystrokes Display  
40.5 ´ r 0.7069 Radians. 
| d 40.5000 40.5 degrees (decimal fraction). 
1 1 4 0 4 2 0 0 0 0  
to the hundred-thousandth of a second. 
seconds 
hours 
1 . 1 4 0 4 1.2 3 4 5 
minutes 
hours 
to  
						

							28 Section 2: Numeric Functions  
 
Logarithmic Functions 
Natural  Logarithm. Pressing |Z calculates  the  natural  logarithm  of 
the number in the display; that is, the logarithm to the base e. 
Natural  Antilogarithm. Pressing  calculates  the  natural  antilogarithm 
of the number in the display; that is, raises e to the power of that number. 
Common  Logarithm. Pressing | o calculates  the  common 
logarithm of the number in the display; that is, the logarithm to the base 10. 
Common  Antilogarithm. Pressing @ calculates  the  common 
antilogarithm of the number in the display; that is, raises 10 to the power of 
that number. 
Keystrokes Display  
45 |Z 3.8067 Natural log of 45. 
3.4012  30.0001 Natural antilog of 3.4012. 
12.4578 | o 1.0954 Common log of 12.4578. 
3.1354 @ 1,365.8405 Common antilog of 
3.1354. 
Hyperbolic Functions 
Given x in the display (X-register): 
 
Pressing Calculates 
´P[ hyperbolic sine of x 
|H[ inverse hyperbolic sine of x 
´P\ hyperbolic cosine of x 
|H\ inverse hyperbolic cosine of x 
´P] hyperbolic tangent of x 
|H] inverse hyperbolic tangent of x   
						

							 Section 2: Numeric Functions 29 
 
Two-Number Functions 
The HP-15C performs two-number math functions using two values entered 
sequentially  into  the  display.  If  you  are keying  in both  numbers,  remember 
that  they  must  be  separated  by v or  any  other  function – like | 
‘ or ∕ – that terminates digit entry. 
For a two-number function, the first value entered is considered the y-value 
because  it  is  placed  into  the  Y-register  for  memory  storage.  The  second 
value  entered  is considered  the x-value  because  it  remains  in  the  display, 
which is the X-register. 
The  arithmetic  operators, +, -, *, and ÷, are  the four basic two-
number functions. Others are given below. 
The Power Function 
Pressing Y calculates  the  value  of y raised  to the x power.  The  base 
number, y, is keyed in before the exponent, x. 
 
To Calculate Keystrokes Display 
21.4 2 v 1.4 Y  2.6390 
2-1.4 2 v 1.4 “ Y  0.3789 
(-2)3 2 “ v 3 Y -8.0000 
 or 21/3 2 v 3 ∕ Y  1.2599 
Percentages 
The  percentage  functions, k and ∆,  preserve  the  value  of  the  original 
base  number  along  with  the  result  of  the  percentage  calculation.  As  shown 
in  the  example  below,  this  allows  you  to  carry  out  subsequent  calculations 
using the base number and the result without re-entering the base number. 
Percent. The k function  calculates  the  specified  percentage  of  a  base 
number. 32  
						

							30 Section 2: Numeric Functions  
 
For example, to find the sales tax at 3% and total cost of a $15.76 item: 
Keystrokes Display  
15.76 v 15.7600 Enters the base number (the price). 
3 |k 0.4728 Calculates 3% of $15.76 (the tax). 
+ 16.2328 Total cost of item ($15.76 + $0.47). 
Percent  Difference. The ∆ function  calculates  the  percent difference 
between two  numbers. The  result expresses the  relative  increase  (a  positive 
result)  or  decrease  (a  negative  result)  of  the  second  number  entered 
compared to the first number entered. 
For example, suppose the $15.76 item only cost $14.12 last year. What is 
the percent difference in last year’s price relative to this year’s? 
Keystrokes Display  
15.76 v  15.7600 This years price (our base number) 
14.12 |∆ -10.4061 Last years price was 10.41% less 
than this years price. 
Polar and Rectangular Coordinate Conversions 
The : and ; functions are provided in the 
HP-15C  for  conversions  between  polar 
coordinates  and  rectangular  coordinates.  The 
angle θ is assumed  to be in  the  mode,  whether 
degrees  (in  a  decimal  format, not  a  minutes-
seconds  format), radians,  or  grads. θ is 
measured as shown in the illustration at right. 
Polar  Conversion. Pressing |: 
(polar) converts  a  set  of  rectangular  coordinates (x,  y) to  polar  coordinates 
(magnitude r,  angle θ).  The y-value must  be  entered  first,  the x-value 
second.  Upon  executing |: r will  appear  in  the  display.  Press ® 
(X exchange Y) to  bring θ out  of  the  Y-register  and  into  the  display  (X-
register). θ will be  returned as a  value  between -180° and 180°,  between -π 
and π radians, or between -200 and 200 grads.