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HP 33S Scientific Calculator

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HP 33SHewlett Packard F2216A F2216A**Hp**Hp33S Scientific Calculator**New

Pocket - Scientific - HP

Powerful/advanced pocket-size programmable scientific calculator. 32K user memory. Letter+4 program line labels. Cursor keys to navigate menus. Works in both RPN and algebraic modes. Features: keystroke programming, solve function, stats one and two variable, base-n function, 27 independent memories, trig, polar-rectang.

Brand: HP
Part Numbers: F2216A, HP33S
UPC: 082916014555
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User reviews and opinions

Comments to date: 3. Page 1 of 1. Average Rating:
wwwolf 7:57pm on Monday, November 1st, 2010 
For its price, one hell of a unit !! After 6 months NONE yet. Compactness, price, remote control, simplicity of use Not very good at high end of volume
lola5043 8:39am on Monday, September 13th, 2010 
Great Sound for a Micro System Rather than repeat what the other reviewers have said I will talk about some of the other points about this system that...
trall 7:29am on Monday, June 28th, 2010 
I have been pleased with the set until the above problem occured still trying to get help to sort it. Comments please.

Comments posted on are solely the views and opinions of the people posting them and do not necessarily reflect the views or opinions of us.





Left shift is active. Right shift is active. Reverse Polish Notation mode is active. Algebraic mode is active. Programentry is active. Equationentry mode is active, or the calculator is evaluating an expression or executing an equation. Indicates which flags are set (flags 5 through 11 have no annunciator. Radians or Grad angular mode is set. DEG mode (default) has no annunciator. Indicates the active number base. DEC (base 10, default) has no annunciator.

1, 2 1, C 12 6

HP 33s Annunciators (continued) Annunciator


The or keys are active to scroll the display, i.e. there are more digits to the left and right. (Equationentry and Programentry mode arent included) Use to see the rest of a decimal number; use the left and rightcursor keys ( , ) to see the rest of an equation or binary number. Both these annunciators may appear simultaneously in the display, indicating that there are more characters to the left and to the right. Press either of the indicated cursor keys ( or ) to see the leading or trailing characters. When an entry or equation has more than one display, you can press or followed by to skip from the current display to the first one. To skip to the last display, press or followed by. In the CONST and SUMS menus, you can press and to access the next menu page.
The and keys are active for stepping through an equation list or program lines. The alphabetic keys are active. Attention! Indicates a special condition or an error. Battery power is low.

1, 6, 12

Getting Started 113

Keying in Numbers

You can key in a number that has up to 12 digits plus a 3digit exponent up to 499. If you try to key in a number larger than this, digit entry halts and the annunciator briefly appears. If you make a mistake while keying in a number, press ~ to backspace and delete the last digit, or press to clear the whole number.

Making Numbers Negative

z key changes the sign of a number.
To key in a negative number, type the number, then press
To change the sign of a number that was entered previously, just press z. (If the number has an exponent, z affects only the mantissa the nonexponent part of the number.)

Exponents of Ten

Exponents in the Display Numbers with exponents of ten (such as 4.2 105) are displayed with an preceding the exponent (such as ). A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form. For example, in FIX 4 format for four decimal places, observe the effect of the following keystrokes:


Shows number being entered. Rounds number to fit the display format. Automatically uses scientific notation because otherwise no significant digits would appear.

\, @,

2. Press the function key. (For a shifted function, press the appropriate shift key first.) For example, calculate 1/32 and change its sign.
148.84. Then square the last result and
Operand. Reciprocal of 32. Square root of 148.84. Square of 12.2. Negation of 148.8400.


The onenumber functions also include trigonometric, logarithmic, hyperbolic, and partsofnumbers functions, all of which are discussed in chapter 4.

TwoNumber Functions

In RPN mode, to use a twonumber function (such as , , , , ), b, `, ', x, {, m or p): 1. Key in the first number. 2. Press
3. Key in the second number. (Do not press
to separate the first number from the second.)
4. Press the function key. (For a shifted function, press the appropriate shift key first.)
In RPN mode, type in both numbers (separate them by selecting ) before selecting a function key.

Getting Started 117

For example,

To calculate:

12 + Percent change from 8 to 12


The order of entry is important only for noncommutative functions such as , , ), b, `, ', x, {, m, p. If you type numbers in the wrong order, you can still get the correct answer (without retyping them) by pressing w to swap the order of the numbers on the stack. Then press the intended function key. (This is explained in detail in chapter 2 under "Exchanging the X and YRegisters in the Stack.")
Controlling the Display Format
Periods and Commas in Numbers
To exchange the periods and commas used for the decimal point (radix mark) and digit separators in a number: 1. Press
to display the MODES menu.
2. Specify the decimal point (radix mark) by pressing {} or {}. For example, the number one million looks like: if you press {} or if you press {}.

Number of Decimal Places

All numbers are stored with 12digit precision, but you can select the number of decimal places to be displayed by pressing (the display menu). During some complicated internal calculations, the calculator uses 15digit precision for intermediate results. The displayed number is rounded according to the display format. The DISPLAY menu gives you four options:

You can type almost any number as a fraction on the keyboard including an improper fraction (where the numerator is larger than the denominator). However, the calculator displays if you disregard these two restrictions: The integer and numerator must not contain more than 12 digits total. The denominator must not contain more than 4 digits.
Turns on Fractiondisplay mode. Enters 1.5; shown as a fraction. Enters 1 3/4. Displays x as a decimal number. Displays x as a fraction.
If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.) The next topic includes more examples of valid and invalid input fractions. You can type fractions only if the number base is 10 the normal number base. See chapter 10 for information about changing the number base.

Fractions in the Display

In Fractiondisplay mode, numbers are evaluated internally as decimal numbers, then they're displayed using the most precise fractions allowed. In addition, accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12digit decimal value. (Most statistics registers are exceptions they're always shown as decimal numbers.)

Display Rules

The fraction you see may differ from the one you enter. In its default condition, the calculator displays a fractional number according to the following rules. (To change the rules, see "Changing the Fraction Display" later in this chapter.) The number has an integer part and, if necessary, a proper fraction (the numerator is less than the denominator). The denominator is no greater than 4095. The fraction is reduced as far as possible.


These are examples of entered values and the resulting displays. For comparison, the internal 12digit values are also shown. The and annunciators in the last column are explained below.

Entered Value

2 3/15/32

54/ 12

Internal Value
2.37500000000 14.4687500000 4.50000000000 9.60000000000 2.83333333333 0.00183105469 (Illegal entry) (Illegal entry)

Displayed Fraction

6 18/5

34/ 15/ 12 8192

12345678 12345/3/16384

# eA A

Changing the Fraction Display
In its default condition, the calculator displays a fractional number according to certain rules. (See "Display Rules" earlier in this chapter.) However, you can change the rules according to how you want fractions displayed: You can set the maximum denominator that's used.
You can select one of three fraction formats. The next few topics show how to change the fraction display.
Setting the Maximum Denominator
For any fraction, the denominator is selected based on a value stored in the calculator. If you think of fractions as a b/c, then /c corresponds to the value that controls the denominator. The /c value defines only the maximum denominator used in Fractiondisplay mode the specific denominator that's used is determined by the fraction format (discussed in the next topic). To set the /c value, press n , where n is the maximum denominator you want. n can't exceed 4095. This also turns on Fractiondisplay mode.
. To restore the default value or 4095, press 0 . (You also restore the
To recall the /c value to the Xregister, press 1 default if you use 4095 or greater.) This also turns on Fractiondisplay mode. The /c function uses the absolute value of the integer part of the number in the Xregister. It doesn't change the value in the LAST X register.
Choosing a Fraction Format
The calculator has three fraction formats. Regardless of the format, the displayed fractions are always the closest fractions within the rules for that format.
Most precise fractions. Fractions have any denominator up to the /c value, and they're reduced as much as possible. For example, if you're studying math concepts with fractions, you might want any denominator to be possible (/c value is 4095). This is the default fraction format. Factors of denominator. Fractions have only denominators that are factors of the /c value, and they're reduced as much as possible. For example, if you're calculating stock prices, you might want to see and ( /c value is 8 ). Or if the /c value is 12, possible denominators are 2, 3, 4, 6, and 12. Fixed denominator. Fractions always use the /c value as the denominator they're not reduced. For example, if you're working with time measurements, you might want to see ( /c value is 60 ).
To select a fraction format, you must change the states of two flags. Each flag can be "set" or "clear," and in one case the state of flag 9 doesn't matter.
To Get This Fraction Format:

Change These Flags: 8 9

Clear Set
Most precise Factors of denominator Fixed denominator

Example: Evaluating an Equation with ENTER.
Use the equation from the beginning of this chapter to find the volume of a 35mm diameter pipe that's 20 meters long.
Displays the desired equation. Starts evaluating the assignment equation so the value will be stored in V. Prompts for variables on the righthand side of the equation. The current value for D is 2.5000. Stores D, prompts for L, whose current value is 16.0000. Stores L in millimeters; calculates V in cubic millimeters, stores the result in V, and displays V.

d ( as required)

Changes cubic millimeters to liters (but doesn't change V).

Using XEQ for Evaluation

If an equation is displayed in the equation list, you can press t to evaluate the equation. The entire equation is evaluated, regardless of the type of equation. The result is returned to the Xregister.
Example: Evaluating an Equation with XEQ.
Use the results from the previous example to find out how much the volume of the pipe changes if the diameter is changed to 35.5 millimeters.
Displays the desired equation.
Starts evaluating the equation to find its value. Prompts for all variables.
Keeps the same V, prompts for D. Stores new D, Prompts for L. Keeps the same L; calculates the value of the equation the imbalance between the left and right sides. Changes cubic millimeters to liters.
The value of the equation is the old volume (from V) minus the new volume (calculated using the new D value) so the old volume is smaller by the amount shown.
Responding to Equation Prompts
When you evaluate an equation, you're prompted for a value for each variable that's needed. The prompt gives the variable name and its current value, such as .
To leave the number unchanged, just press
To change the number, type the new number and press. This new number writes over the old value in the Xregister. You can enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press. For example, you can press ). To calculate with the displayed number, press typing another number.


To cancel the prompt, press. The current value for the variable remains in the Xregister. If you press during digit entry, it clears the number to zero. Press again to cancel the prompt. To display digits hidden by the prompt, press

x + iy.

It has operations for complex arithmetic (+, , , ), complex trigonometry (sin, cos, tan), and the mathematics functions z, 1/z, z1z 2 , ln z, and e z. (where z1 and z2 are complex numbers).
To enter a complex number: 1.

Type the imaginary part.

3. Type the real part.
Complex numbers in the HP 33s are handled by entering each part (imaginary and real) of a complex number as a separate entry. To enter two complex numbers, you enter four separate numbers. To do a complex operation, press c before the operator. For example, to do (2 + i 4) + (3 + i 5), press 4
The result is 5 + i 9. (The first line is the imaginary and the second is the real part.)

The Complex Stack

In RPN mode, the complex stack is really the regular memory stack split into two double registers for holding two complex numbers, z1x + i z1y and z2x + i z2y:
Since the imaginary and real parts of a complex number are entered and stored separately, you can easily work with or alter either part by itself.

Complex function

(displayed) (displayed)

imaginary part real part

Complex input z or z 1and z 2

Complex result, z

Always enter the imaginary part (the ypart) of a number first. The real portion of the result (zx) is displayed on the second line; the imaginary portion (zy) is displayed on the first line. (For twonumber operations, the first complex number, z1, is replicated in the stack's Z and T registers.)

Complex Operations

Use the complex operations as you do real operations, but precede the operator with c.
To do an operation with one complex number: 1.
Enter the complex number z, composed of x + i y, by keying in y
2. Select the complex function.
Functions for One Complex Number, z To Calculate:
Change sign, z Inverse, 1/z Natural log, ln z Natural antilog, ez Sin z Cos z Tan z

cz c, c& c# ck cn cq

To do an arithmetic operation with two complex numbers: 1.
Enter the first complex number, z1 (composed of x1 + i y1), by keying in y1 x1. (For z1z2 , key in the base part, z1, first.)
2. Enter the second complex number, z2, by keying in y2 x2. (For key in the exponent, z2, second.) 3. Select the arithmetic operation:

y3 + b2y2 + b1y + b0 = 0

where b2 = a2

b1 = a3a1 4a0

1520 Mathematics Programs

b0 = a0(4a2 a32) a12.

Let y0 be the largest real root of the above cubic. Then the fourthorder polynomial is reduced to two quadratic polynomials:
x2 + (J + L)x + (K + M) = 0 x2 + (J L)x + (K M) = 0

where J = a3/2

K = y0 /2 L= M=
J 2 a2 + y 0 (the sign of JK a1/2)

K 2 a0

Roots of the fourth degree polynomial are found by solving these two quadratic polynomials. A quadratic equation x2 + a1x + a0 = 0 is solved by the formula

x1,2 =

a1 a ( 1 )2 a2
If the discriminant d = (a1/2)2 ao 0, the roots are real; if d < 0, the roots are complex, being u iv = (a1 2) i d.
Mathematics Programs 1521
Defines the beginning of the polynomial root finder routine. Prompts for and stores the order of the polynomial. Uses order as loop counter.
Checksum and length: 5CC4 9
Starts prompting routine. Prompts for a coefficient. Counts down the input loop. Repeats until done. Uses order to select root finding routine. Starts root finding routine.
Checksum and length: 588B 21
Evaluates polynomials using Horner's method, and synthetically reduces the order of the polynomial using the root. Uses pointer to polynomial as index. Starting value for Horner's method.
Checksum and length: 0072 24
Starts the Horner's method loop. Saves synthetic division coefficient. Multiplies current sum by next power of x. Adds new coefficient. Counts down the loop. Repeats until done.
Checksum and length: 2582 21
Starts solver setup routine. Stores location of coefficients to use.
1522 Mathematics Programs
First initial guess. Second initial guess. Specifies routine to solve. Solves for a real root. Gets synthetic division coefficients for next lower order polynomial. Generates DIVIDE BY 0 error if no real root found.
Checksum and length: 15FE 54


Starts quadratic solution routine. Exchanges a0 and a1.
a1/2. Saves a1/2. Stores real part if complex root. (a1/2)2.
(a1/2)2 ao. Initializes flag 0. Discriminant (d) < 0 Sets flag 0 if d < 0 (complex roots).

A: You must clear a portion of memory before proceeding. (See appendix B.) Q: Why does calculating the sine (or tangent) of radians display a very small number instead of 0? A: cannot be represented exactly with the 12digit precision of the calculator. Q: Why do I get incorrect answers when I use the trigonometric functions? A: You must make sure the calculator is using the correct angular mode ( { }, { }, or { } ). Q: What does an annunciator in the display mean? A: It indicates something about the status of the calculator. See "Annunciators" in chapter 1. Q: Numbers show up as fractions. How do I get decimal numbers? A: Press

Environmental Limits

To maintain product reliability, observe the following temperature and humidity limits: Operating temperature: 0 to 45 C (32 to 113 F). Storage temperature: 20 to 65 C (4 to 149 F). Operating and storage humidity: 90% relative humidity at 40 C (104 F) maximum.

Changing the Batteries

The calculator is powered by two 3-volt lithium coin batteries, CR2032. Replace the batteries as soon as possible when the low battery annunciator ( ) appears. If the battery annunciator is on, and the display dims, you may lose data. If data is lost, the message is displayed.
Once you've removed the batteries, replace them within 2 minutes to avoid losing stored information. (Have the new batteries readily at hand before you open the battery compartment.) To install batteries: 1.
Have two fresh buttoncell batteries at hand. Avoid touching the battery terminals handle batteries only by their edges.
2. Make sure the calculator is OFF. Do not press ON ( ) again until the entire batterychanging procedure is completed. If the calculator is ON when the batteries are removed, the contents of Continuous Memory will be erased. 3. Turn the calculator over and slide off the battery cover.
4. Never remove two old batteries at the same time, to prevent memory lose. Remove one of the two batteries. Press down the holder. Push the plate in the shown direction and lift it.


Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged EQN LIST TOP Cleared Null PRGM TOP Cleared Enabled Cleared to zero Cleared to zero


Degrees Decimal Medium " " 4095 FIX 4 Cleared Off Zero EQN LIST TOP Cleared Null PRGM TOP Cleared Enabled Cleared to zero Cleared to zero
Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted.

The Status of Stack Lift

The four stack registers are always present, and the stack always has a stacklift status. That is to say, the stack lift is always enabled or disabled regarding its behavior when the next number is placed in the Xregister. (Refer to chapter 2, "The Automatic Memory Stack.") All functions except those in the following two lists will enable stack lift.

Disabling Operations

The four operations ENTER, +, , and CLx disable stack lift. A number keyed in after one of these disabling operations writes over the number currently in the Xregister. The Y, Z and Tregisters remain unchanged. In addition, when
and ~ act like CLx, they also disable stack lift.
The INPUT function disables stack lift as it halts a program for prompting (so any number you then enter writes over the Xregister), but it enables stack lift when the program resumes.

Neutral Operations

The following operations do not affect the status of stack lift:




and STOP and * and ~* u { }** u { }** r r label nnnn EQN FDISP Errors and program
entry Switching binary windows Digit entry
Except when used like CLx. Including all operations performed while the catalog is displayed except { } and { } t, which enable stack lift.
The Status of the LAST X Register
The following operations save x in the LAST X register: +, , , LN, LOG yx,

x , x2, X y

x , x3
ex, 10x I/x, INT, Rmdr ASIN, ACOS, ATAN IP, FP, SGN, INTG, RND, ABS RCL+, , , DEG, RAD


y,x ,r

,r y, x

nCr nPr CMPLX +, , , kg, lb l, gal
Notice that /c does not affect the LAST X register. The recallarithmetic sequence x h variable stores a different value in the LAST X register than the sequence x h variable does. The former stores x in LAST X; the latter stores the recalled number in LAST X.

ALG: Summary

About ALG
This appendix summarizes some features unique to ALG mode, including, Twonumber arithmetic Chain calculation Reviewing the stack Coordinate conversions Operations with complex numbers Integrating an equation Arithmetic in bases 2, 8, and 16 Entering statistical twovariable data Press to set the calculator to ALG mode. When the calculator is in ALG mode, the ALG annunciator is on.

Chain Calculations

To do a chain calculation, you dont need to press but only at the very end. For instance, to calculate

after each operation,

you can enter either: 360

750 or 750

12 360
In the second case, the key acts like the key by displaying the result of 750 12. Heres a longer chain calculation:

68 18.5 1.9

This calculation can be written as: 18.1.9. Watch what happens in the display as you key it in:


The < or ; key produces a menu in the display X1, X2, X3, X4registers, to let you review the entire contents of the stack. The difference between the < and the ; key is the location of the underline in the display. Pressing the ; displays the underline on the X4 register; pressing the < displays the underline on the X2 register. Pressing
< displays the following menu:
; displays the following menu:
You can press or (or < and ;) to review the entire contents of the stack and recall them. However, in normal operation in ALG mode, the stack in ALG mode differs from the one in RPN mode. (Because when you press , the result is not placed into X1, X2 etc.) Only after evaluating equations, programs, or integrating equations, the values of the four registers will be the same as in RPN mode.
Enter the coordinates (in rectangular or polar form) that you want to convert. In ALG mode, the order is y w x or w r.
2. Execute the conversion you want: press (rectangulartopolar) or (polartorectangular). The converted coordinates occupy the X and Yregisters. 3. The resulting display (the Xregister) shows either r (polar result) or x (rectangular result). Press to see or y. Example:
If x = 5, y = 30, what are r, ?
Sets Degrees mode. Calculates hypotenuse (r). Displays.

{ } w5

If r = 25, = 56, what are x, y ?
Sets Degrees mode. Calculates x.

{ } w 25

Displays y.
If you want to perform a coordinate conversion as part of a chain calculation, you need to use parentheses to impose the required order of operations.

If r = 4.5, =

2 , what are x, y ? 3
Sets Radians mode. Use parentheses to impose the required order of operations.

{ } y23 j| w 4.5

Calculates x. Displays y.

Integrating an Equation

Key in an equation. (see "Entering Equations into the Equation List" in chapter 6) and leave Equation mode.
2. Enter the limits of integration: key in the lower limit and press in the upper limit.

w, then key

129 1218

Separates the two arguments

of a function.

1/x 10x % %CHG
, Reciprocal. ! Common exponential.
Returns 10 raised to the power.
m Percent. Returns (y x) 100. p Percent change. Returns (x y)(100 y). j Returns the
approximation 3.14159265359 (12 digits).

+ x x2

/ Accumulates (y, x) into

statistics registers.

- Removes (y, x) from
Returns the sum of xvalues.
Returns the sum of squares of xvalues.
Returns the sum of products of xand yvalues.
. { } Returns the sum of yvalues. . { }
Returns the sum of squares of yvalues.

1110 1110

+ { }
Returns population standard deviation of xvalues:

x )2 n

Returns population standard deviation of yvalues:

y )2 n

Polar to rectangular coordinates. Converts (r, ) to (x, y).

82 147

FN d variable

" { _} variable

Integrates the displayed equation or the program selected by FN=, using lower limit of the variable of integration in the Yregister and upper limit of the variable of integration in the Xregister.

y Open parenthesis.

Starts a quantity associated with a function in an equation.

| Close parenthesis.

Ends a quantity associated with a function in an equation.

h variable or e variable

Value of named variable.
^ Absolute value. Returns x. l Arc cosine.

Returns cos 1x.

Hyperbolic arc cosine. Returns cosh 1 x.
Activates Algebraic mode.

! Common exponential.

Returns 10 raised to the specified power (antilogarithm).
{ } Selects display of all significant digits. i Arc sine

Returns sin 1 x.

Hyperbolic arc sine. Returns sinh 1 x.


o Arc tangent.

Returns tan 1 x.

Hyperbolic arc tangent. Returns tanh 1 x.
% { } Returns the yintercept of the regression line: y m x.
Displays the baseconversion menu.

1217 55

Selects Binary (base 2) mode. Turns on calculator; clears x; clears messages and prompts; cancels menus; cancels catalogs; cancels equation entry; cancels program entry; halts execution of an equation; halts a running program.


Sets denominator limit for displayed fractions to x. If x = 1, displays current /c value. C

clearing stack, 25 copying viewed variable, 1214 duplicating numbers, 26 ending equations, 64, 68, 126 evaluating equations, 610 separating numbers, 116, 117, 25 stack operation, 25 } (exponent), 115 E in numbers, 114, 120, A1 ENG format, 120. See also display format

EQN annunciator

in equation list, 64, 66 in Program mode, 126 EQN LIST TOP, 67, F1


functions, 65, 615, G1 in programs, 124, 126, 1221, 1310 integrating, 82 lengths, 618, 126, B2 list of. See equation list long, 67 memory in, 1214 multiple roots, 78 no root, 76 no size limit, 64 numbers in, 65 numeric value of, 69, 610, 71, 75, 124 operation summary, 63 parentheses, 65, 66, 614 polynomial, 1520 precedence of operators, 613 prompt for values, 610, 612 prompting in programs, 1310, 141, 148 roots, 71 scrolling, 67, 126, 1214 simultaneous, 1512 solving, 71, D1 stack usage, 611 storing variable value, 611 syntax, 613, 618, 1214 TVM equation, 171 types of, 69 uses, 61 variables in, 63, 71 with (i), 1324 error messages, F1 errors clearing, 15 correcting, 27, F1 estimation (statistical), 117, 161
executing programs, 129 exponential curve fitting, 161 exponential functions, 115, 41, 93 exponents of ten, 114, 115 expression equations, 69, 610, 71
not programmable, 59 toggles display mode, 123, 51, A2 toggles flag, 139 factorial function, 414 financial calculations, 171 FIX format, 119. See also display format flags annunciators, 1311 clearing, 1311 default states, 138, B3 equation evaluation, 1310 equation prompting, 1310 fraction display, 56, 139 meanings, 138 operations, 1311 overflow, 139 setting, 1311 testing, 138, 1311 unassigned, 139 flow diagrams, 132 FN= in programs, 146, 149 integrating programs, 148 solving programs, 141


fractionalpart function, 416 Fractiondisplay mode affects rounding, 57 affects VIEW, 1213 setting, 123, 51, A2 fractions accuracy indicator, 52, 53 and equations, 58 and programs, 58, 1213, 139 base 10 only, 52 calculating with, 51 denominators, 122, 54, 55, 139, 1314 displaying, 123, 51, 52, 54, A2 flags, 56, 139 formats, 55 not statistics registers, 52 reducing, 52, 55 rounding, 57 roundoff, 57 setting format, 55, 139, 1314 showing integer digits, 54 typing, 121, 51 functions in equations, 65, 615 in programs, 126 list of, G1 names in display, 417, 127 nonprogrammable, 1222 onenumber, 117, 28, 92 realnumber, 41 twonumber, 117, 28, 93 future balance (finance), 171
finds PRGM TOP, 125, 1219, 136 finds program labels, 129, 1219, 135 finds program lines, 1218, 1219, 135 gamma function, 414 go to. See GTO grads (angle units), 44, A2 Grandma Hinkle, 117 Greatest integer, 416 grouped standard deviation, 1617 GTO, 134, 1317 guesses (for SOLVE), 72, 75, 77, 710, 146

Sign value, 416 simultaneous equations, 1512 sine (trig), 44, 93, A2 singlestep execution, 129 slope (curvefit), 117, 161 SOLVE asymptotes, D8 base mode, 1222, 1411 checking results, 76, D3 discontinuity, D5 evaluating equations, 71, 76 evaluating programs, 141 flat regions, D8 how it works, 75, D1 in programs, 146 initial guesses, 72, 75, 77, 710, 146 interrupting, B2 memory usage, B2 minimum or maximum, D8 multiple roots, 78 no restrictions, 1411 no root found, 76, 146, D8 pole, D5 purpose, 71 real numbers, 142 results on stack, 72, 76, D3 resuming, 141 roundoff, D13 stopping, 72, 77 underflow, D14 using, 71 square function, 117, 42 squareroot function, 117 stack. See stack lift affected by prompts, 613, 1212 complex numbers, 91
equation checksums, 618, B2 equation lengths, 618, B2 fraction digits, 54 number digits, 121, 126 program checksums, 1220, B2 program lengths, 1220, B2 prompt digits, 613 variable digits, 33, 1213 , 65 sample standard deviations, 116 SCI format. See display format in programs, 126 setting, 119 scrolling binary numbers, 106 equations, 67, 126, 1214 seed (random number), 414 selftest (calculator), A5 shift keys, 13 sign (of numbers), 114, 117, 93, 104 sign conventions (finance), 171


effect of , 25 equation usage, 611 exchanging with variables, 36 exchanging X and Y, 24 filling with constant, 26 long calculations, 211 operation, 21, 24, 91 program calculations, 1212 program input, 1211 program output, 1211 purpose, 21, 22 registers, 21 reviewing, 23, C6 rolling, 23, C6 separate from variables, 32 size limit, 24, 91 unaffected by VIEW, 1214 stack lift. See stack default state, B3 disabling, B4 enabling, B4 not affecting, B4 operation, 24 standard deviations calculating, 116, 117 grouped data, 1617 normal distribution, 1611 standarddeviation menu, 116 statistical data. See statistics registers clearing, 16, 112 correcting, 112 entering, 111 initializing, 112 onevariable, 112 precision, 119 sums of variables, 1110 twovariable, 112
statistics calculating, 114 curve fitting, 118, 161 distributions, 1611 grouped data, 1617 onevariable data, 112 operations, 111 twovariable data, 112 statistics menus, 111, 114 statistics registers. See statistical data accessing, 1111 clearing, 16, 112, 1111 contain summations, 111, 1110, 1111 correcting data, 112 initializing, 112 memory, 1111 no fractions, 52 viewing, 1111 STO, 32, 1211 STO arithmetic, 34 STOP, 1217 storage arithmetic, 34 subroutines. See routines sums of statistical variables, 1110 syntax (equations), 613, 618, 1214


Summing up the HP 33S

Jordi Hidalgo, #1046 Upon reading the last issue some of you, I think, must have got the impression the new HP 33S scientific calculator is good only for those who are a) Chinese and b) all thumbs. Let me, then, give you more information about this neat machine. Except to a few collectors, details of my beta 33S are pretty irrelevant so its better if I refer to my production unit, which is the latest version available to date (early May). Its serial number is CNA41101044. Ive been told that the A in the site code (not present in the first production units) is used for differentiating the multiple suppliers. Whats new? It is in the current context of resorting to redesigns of discontinued models that we must view this calculator, but the result is quite good all the same. In essence, the 33S is a 32SII with much more memory (31KB), more keys (though somewhat creased as described by Craig Finseth in his HPDATABase), a 2-line by 14 character dot-matrix LCD, a few new functions and the inevitable algebraic entry mode, which is not so useless as in the 12C Platinum, but equally unnecessary since the 32SII could already handle algebraic expressions as well. Some users will prefer the ALG mode, however, when operating with complex numbers as calculations are being displayed all the time, although the RPN sequence is shorter and is not required to view the imaginary part. Compare the following ways of evaluating (5 + 3i) (3 2i) and the resulting displays: In RPN mode: 2 z 3 c (all stack levels are used) In ALG mode: c y c () There is no provision for interchangeable overlays. Somehow they do not seem to be favoured in the slightest any more. (For instance, the five additional bezels for the 30S F1908A are only available in Australia). Despite the 11 new keys, there are still 14 menus, whose names are no longer printed on darker backgrounds (actually lighter on the black 32SII). The functions in the 32SII PARTS and PROB menus are now on keys, while there are two new menus: the CONST menu (), which displays an up-to-date list of 40 physics constants in metric units (nearly all the constants on the 48GX plus a few more, such as magnetic moments, muon mass, conductance quantum, etc.), and the menu displayed by < and ; in ALG
Summing up the HP 33S Page 1
mode to review the stack (four registers that keep the values returned by and "). Although the 33S is in general faster, it does not put the 32SII to shame. Simple loops with counters run about twice as fast on the 33S provided the ISG and DSE commands are not used: if 0.999 is stored in A, this program LBL A, ISG A, GTO A, RTN runs in 34 seconds on the 33S, whereas it takes only 16 seconds on the 32SII. With some exceptions such as the integral below, solving and integration calculations are 1.5-3 times faster on the 33S. These are the new functions and operations: In addition to the engineering display format, the programmable functions _ and ] cause the exponent of x (the contents of the X-register) to change in multiples of three. and move to the bottom/top of the equation or program list. and : programmable logic switches. The real-number functions @, \ and a (sign of x). g returns the greatest integer that is less than or equal to the argument. Same as FLOOR on the 48/49. b: same as INTG(y / x) (It returns IP(y / x) on early units!) `: same as the 48/49 MOD command, i.e. y x INTG(y / x) 0 stores a random value as the seed for The SCRL function has been replaced with cursor keys. The (for busy) and HYP annunciators replace the blinking PRGM and EQN, and the HYP prefix operator respectively. Flag 4 now has its own annunciator. And there is now a RESET hole on the back; the second edition of the manual (page A-4) states that stored data usually remain intact when pressed, but it always wipes out the memory in my units. Besides the changes derived from the two extra digits in the display, there are several differences between the 33S and the 32SII. The length of an equation is no longer limited only by the available memory, but to 255 characters! When entering equations, trailing parentheses ) of two-argument functions are now required; on the other hand z and can be used interchangeably when entering the second argument of such functions. Also in equations, expressions like EXP(X^2) now mean EXP((X^2)) fixing certain inconsistency of the 32SII, on which 255^2 evaluates to 0, while 5^2+25 evaluates to 50. A colon () and not a space is used for separating arguments of functions in equations; both the colon and the space can be used in messages. Calculations with TOO BIG numbers (out-ofrange numbers displayed in non-decimal modes) are now possible provided the result is not outside the range: e.g. (RPN) 4}(i.e. binary mode) (restores decimal base) returns 4E9, while the 32SII returns 3,435,973,836 (the largest 36-bit positive integer divided by 10). On the 33S, if a

Summing up the HP 33S Page 2
program is interrupted when calculating an integral, such calculation cannot be resumed. Lastly, certain calculations do not produce the same results on both machines (e.g. gamma of 9.29) which suggests that the CPU (a Sunplus SPLB31A, based on the 6502) is running native software rather than emulating the 32SII. In fact, MEM and SHOW readings have changed, as well as the checksum for equations and programs. The following table shows the allocation of user memory. The 32SII values have been taken from pages 12-22 and B-2 of the 32SII owners manual. The 33S users manual omits such details. On the 33S, SHOW readings for equations (length) do not match differences between two consecutive MEM readings (amount of memory used). Notice that nibbles no longer come into play. Data
Variables Statistics data
Amount of Memory Used 32SII 33S
8 bytes per non-zero value. (No bytes for zero values). 48 bytes maximum (8 bytes for each non-zero register). Integers 0 through 254: 1.5 bytes. All other numbers: 9.5 No bytes. Variables (including i and the statistics registers) take up no user memory. Always allocated. 15 bytes. No short form for frequently used values, but constants in program lines take 3 bytes, unless they are in an equation. 3 bytes

Numbers in program lines

Instructions in program 1.5 bytes lines 1.5 bytes + 1.5 for each function + 9.5 or 1.5 for each Equations in program number. Each ( and each lines ) uses 1.5 bytes, except the ( for prefix functions. Integers 0 through 254: 1.5 Numbers in equations bytes. All other numbers: 9.5 Operations in equations 1.5 bytes
3 bytes + 1 byte for each character (255 maximum). Each entry in the equation list takes 6 bytes + 1 byte for each character. (255 maximum).
Still more telling is the fact that the algorithms for and " have been rewritten. There is a detailed introduction to the new solver in the document Advanced Use of the Formula Solver, one of the numerous training guides for the 33S available at HPs website. SOLVE first tries to give a direct solution by rearranging the equation. The new message INVALID VAR is displayed when attempting to solve an equation for a variable not present. Incidentally, SOLVE now fails to find the pole in the example on page D-7 of the users manual (C-8 in the 32SII owners manual). VIEW and STOP instructions in programs that are being solved or integrated are executed only once, not each time the routine is
Summing up the HP 33S Page 3
called by SOLVE or Integrate; to monitor their execution, intermediate steps can be displayed by the sequence VIEW var PSE (refer to pages 14-2 and 14-10 of the manual). " returns exactly the same results as the 48GX integral function, including the uncertainty of the result (i.e. the 48GX IERR variable). The uncertainty (but no the actual error) tends to be a bit larger than the one returned by the 32SII. The following exception, taken from the August 1980 issue of the Hewlett-Packard Journal, shows that the integration algorithm is clearly different from the 32SII or the 15C, which return a wrong result in FIX 5:

x 1 0 x 1 ln x dx Result Uncertainty Actual error Running time
FIX 5 0.03662 0.00001 1.282E-sec FIX 7 0.0364900 0.0000001 1.131E-min 4 sec
FIX 5 0.03649 3.649E-7 5.373E-sec FIX 7 0.0364900 3.649E-9 5.198E-min 6 sec
The 33S is powered by two CR2032 batteries, which are held in place by the plates shown in Fig.1. Appendix A advises the user to remove the batteries and lightly press a coin against both battery contacts in case of malfunction. Ive never seen a Chinese coin, but I rather suspect its just a vestige of the manual for the 32SII As Leif Harcke wrote in V22N6 the manual is a one-to-one mapping from the 32SII manual. Fig. 1 The battery compartment 388 pages printed in black and blue but in a sans serif typeface this time. There are indeed a few errors in the adaptation that need fixing, but thats what revisions are for. Although the ALG mode is wisely confined to Appendix C, some sample programs have been transcribed to ALG. This is not so bad as it sounds because programming in ALG has its own tricks (e.g. how to use or w), which willing users can learn by studying the listings in the manual and in the learning modules theres no other way, Im afraid. In a posting to the comp.sys.hp48 Usenet newsgroup Bill Platt regrets that Horners method is now written in ALG. Too bad they did not keep the RPN version so that users could compare 5x4+2x3 in RPN (assuming x is on level one: 52) to the ALG routine supplied (5 hX)42hX)3, assumes x has been INPUT). Still, the ALG program for the general case Ax4+Bx3+Cx2+Dx+E on page 12-25 is one line shorter (but 25.5 bytes larger) than the 32SII version.
Summing up the HP 33S Page 4
Fig. 2 The HP 33S RPN/ALG Scientific Calculator. Actual size: 15.8 x 8.3 x 1.61 cm.
Summing up the HP 33S Page 5
Fig. 3 On the same scale, the HP32SII as last seen in 2002. Actual size: 14.7 x 8.1 x 1.5 cm.
Summing up the HP 33S Page 6
Fig. 4 Internal view of the HP 33S. Whats so wrong? The early production batches that Wodek Mier-Jdrzejowicz referred to in his previous Chairmans Bytes have provided HP with a good many first-hand impressions from contributors to the forum at, Paul Brogger and sharp-witted Ben Salinas being the most active. Leaving aside the chevron keyboard, the most often repeated criticisms are that it is too big to fit comfortably in a shirt pocket, that the decimal point is too small, that there are too few new features and that users cannot take advantage of that much RAM. As to the radix point size issue, theres only one thing for it to upgrade the LCD, which, according to HP, will be implemented this July. They should not pass up the chance to get rid of the annoying shadows too. By inspecting the new functions, it becomes apparent that the designers did not have the slightest intention to undertake massive changes to the 32SII firmware. Writing a complete simulation

Summing up the HP 33S Page 7
was challenging enough, I guess. Gene Wright says it all in this posting to the forum: My guess is HP said something like this: Were really moving the 32SII to a new package and arent going to be making many changes to it at all. We cant sell the old one because we cant make them any more. We face a choice guys.the cost of a 2K chip is the same (within pennies) as a 32K ram chipwhich do we put in? They went with the 32K ram. Will it be entirely useful? I dont knowI expect perhaps not. But, it is there to try to use. With all the room for improvement, however, it is quite a good remake. Whats wrong with more memory and an optional ALG mode? Nothing. Well, nothing much. Trouble is that there are up to ten thousand program lines at our disposal but only 26 program labels and 33 variables in total. Seen from the outside, giving the user more data registers even if only indirectly addressable does not appear to be too much of a hassle, but Kinpo must know best. A trick to create lists of constants with the ISG command and Pauls article on how to minimise label use (both posted to the forum) will help us get by with what we have. The algebraic mode is neither fish nor fowl. To quote Dave Johnson: a prefix/postfix mix characteristic of low end TI calculators. Nevertheless, users can now choose from three different modes since the equation list has its own entry system. Remaining bugs in my production 33S are the 0 SEED bug (described in V23N2, page 4); nCr returns bogus results for large arguments (e.g. 2000nCr1000); the bug reported by Ben: after exiting a self-test (-) or -,), the RAD/GRAD, 04 and HEX/OCT/BIN annunciators are always cleared (as well as the stack level one) but the corresponding modes and flags are not actually altered (i.e. if radians mode was active before starting the self-test, it will keep operating in radians mode after the self-test even though the RAD annunciator is not on). Speaking of -key combinations, & and not #, is now the still undocumented Oops! key, which cancels the -), -, and -#-/ operations so long as & is pressed before releasing , like ON-B on the 48/49. The forty-two learning modules and training guides for the 33S that Gene and Wodek have written are evidence less of the need for outsourcing than of HPs resolution to recover the good name they once had. The modules remind me of the instructional materials produced by the HP Educator Programme (see V20N2, pages 3 and 30). One of the activities for the 30S prepared by Colin Croft in Investigating Mathematics through Patterns (Volume 2) dealt with Dubois formula for estimating body surface area given a persons height and weight. The same problem is tackled in the 33S module Applications in Medicine. Its fascinating to compare the two approaches, as both authors carry out a careful presentation for different audiences. If I may digress for a moment By bringing expert users in, HP take advantage of the vast knowledge and experience of the user community. We know only too well that the dissolution of the Corvallis group meant a lack of continuity in too many things: mastery, innovation, responsiveness, etc. True continuity appears to be in

Summing up the HP 33S Page 8
the hands of users who know how older products were designed, where function keys were placed, or the best angle to view the display at wrote Bruce Horrocks in his first editorial (V19N6). Whether such users agree or not is another matter. While many enthusiasts swear by the 42S, others just dont understand why it is such a sought-after model on eBay. Quite telling is a posting to comp.sys.hp48 by Hydrix CEO Jean-Yves Avenard, software team leader as was, preserved at like a fly in amber: In my opinion youd have to be a nutcase to buy a 42S at that price [$320-$399]. I didnt want to buy it when it was still being sold, why would I pay so much for something that has so many problems and such a poor user interface? HP Lovecraft vs. Salvador Dali? Its about time we talked about the keyboard The following thought that Diana Byrne, R&D project manager for the 48GX and the 38G, wrote in her article for RCL 20 will put us in the picture: Its hard not to think about design while waiting for a flight at the Copenhagen airport. Posters of Scandinavian-designed chairs and lamps hang overhead as compact, quiet luggage carts glide across beautiful teak floors. These elegant, yet practical items are not only nice to use, they are also delightful. Many people feel this way about the traditional keys on HP calculators: they provide just the right feedback with a satisfying click. Despite a somewhat loud click, keys have a good if rigid tactile feel. Theres no sign of double-shot injection moulding yet (or is that now a red herring?) All keys on my units register flawlessly, even when hit on a side. Whether _, = and m deserve to be primary keys or not is certainly debatable, but the keyboard layout is a definite improvement on that of the first prototypes, where \, b and were all primary keys (see the cover picture on V22N5). If they were mistaken, it is well to remember that ACO enjoyed no better success: the ON key on the 10BII does nothing once the calculator has been turned on! Thinking back, the first time I saw the keyboard I was reminded of the paintings of Salvador Dali. Not that its a work of art, but its hard for a Catalan not to think about Dalis designs this year, when we are celebrating the centenary of his birth. Still, some functional design might well lie behind it all: some suggest that the chevron keyboard makes the 33S look less cluttered and helps the user find functions more quickly; others find it easier to use it with two hands but had the designers have that in mind, they should have placed the key in the middle or in the lower-right corner at least (as on the 30S or the 9S). Some believe the 33S will never fit in well in their workplace. I do find this calculator much slicker than the 32SII shown in Fig.3. Alas, theres no accounting for taste: The HP 33S is the most threatening-looking calculator I've ever seen, wrote Eric Smith, the awkward angles of the keys are very disconcerting, and somehow bring to mind the Cthulhu Mythos. A nightmare or surrealism? Oh well, Id better stop trying to understand it!

Summing up the HP 33S Page 9



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