Retro Review: HP 22S

Retro Review:  HP 22S

HP 22S

Pioneers:  10B, 10bII+ (updated), 14B, 17bII+ (updated), 20S, 21S, 22S, 27S, 32SII, 42S

Essentials

Company:  Hewlett Packard

Years:  1988 - 1991

Type:  Scientific, Formula Programming

Memory:  371

Operating System: Algebraic

Memory Registers: 26 (A-Z)

Number of Built In Equations: 16

Batteries:  3 LR44, 3 A76, 3 357

Features

The HP 22S is an algebraic calculator that shares the similar style with the HP 20S, 21S, 32S, and 42S.  The top row of keys ([ √x ], [ e^x ], [ LN ], [ y^x ], [ 1/x ], [ Σ+ ]) act not only as function keys but soft menu keys. 

The standard variety of functions are present:

* Trigonometric, hyperbolic, exponential, and logarithmic functions

* Conversions:  kg/lb, °C/°F, cm/in, ltr/gal, H/HMS, DEG/RAD

* Probability:  nCr, nPr, n!  (the factorial function only accepts integer)

* Integer part, fractional part, absolute value, round to fix setting

* Statistics:  1 Variable and Linear Regression (y = mx + b)

* Storage arithmetic

* Base conversions: Binary, Decimal, Octal, Hexadecimal.  Decimal mode is floating decimal mode.

* This is really cool:  the rectangular (x-COORD, y-COORD) and polar (RADIUS, ANGLE) conversions get their own keys (well, shifted functions of [ 1 ], [ 2 ], [ 3 ], and [ - ], respectively)

* Percent Change:  old [INPUT] new [(shift)] [1/x] (%CHG)  (nPr and nCr work the same way)

Overall the keys are really easy to work with and the calculator is a pleasure to use.  I like the crisp display.  Plus, if blue is your favorite color like me, the light blue font against the dark background is a plus. 

There are two manuals with the HP 22S:  the User Manual, and the excellent Science Student Applications for the HP 22S. 

Equations

You can either use one of the 14 built-in equations (listed below) or create your own.  While you are creating your own, you can use either the [STO] or [RCL] keys to call up a letter.  All variables are one letter and global. Equations that are longer than the 12 character display can be scrolled by the [ √x ] and [ Σ+ ] keys.

Equations can be evaluated (evaluate the right side of the equation) or solved (a menu will show the variables to be solved for).  Equations are solved in a reasonably amount of time.

The 16 built in equations, which are displayed by the equations themselves (no titles):

(Source: HP 22S manual)

Title	Equation
Length of a Line/Vector	R=SQRT(X^2+Y^2+Z^2)
Roots of a Quadratic Equation	X=(-B+J*SQRT(B^2-4*A*C))÷2÷A Real roots only, J = -1 or 1
Equation of Motion (Position)	X=S+V*T+.5*A*T^2 X = position, V = velocity, A = acceleration
Equation of Motion (Final Velocity)	F=V+A*T
Kinetic Energy	E=.5*M*V^2
Force Between Two Objects (Physics or Electric Force)	F=K*A*B÷R^2 K = 6.67408E-11 m^3 kg^-1 s^-2 (gravitational force) K = 1.602176621E-19 J (electron charge)
Joule’s Law	P=I^2*R
Ideal Gas Law	P*V=N*R*T
Gibb’s Free Energy	G=H-T*S
Pressure of a Fluid	P=I+D*G*H G = 9.80665 m/s^2
Radioactive Decay	-K*T=LN(N÷I)
Thin Lens Equation	O*F+I*F=O*I
Diffraction	A=ASIN(M*L÷D)
Exponential Growth and Decay	Y=F+(I-F)*EXP(K*T)
Root Mean Square	R=SQRT(Σx^2÷n) Σx^2 and n come from statistical data
Time Value of Money (End of Period payments/periods assumed)	(P*100÷I-F)*(1+I÷100)^-N-P*100÷I=B N = number of payments/periods B = present value I = periodic interest rate P = payment F = future value

Final Verdict

The HP 22S is a great calculator to own.  I love the rectangular/polar conversion set up.  The display is great.

My only criticism is that I wish the 22S had more memory.  371 bytes can store a handful equations, but data points that are used in the statistical calculations and storing values in the variables A-Z eat up the memory as well.    

4 out of 5 stars.

Eddie

This blog is property of Edward Shore, 2017

Coming soon (tentative):  a review of a favorite Texas Instruments calculator, TI-68.

Casio fx-CG50, TI-84 Plus CE, HP Prime: Square Root-Linear Regression

Casio fx-CG50, TI-84 Plus CE, HP Prime:  Square Root-Linear Regression

The program SQLINREG attempts to fit data to the curve:

Y = √(A + B*X)

We can use the linear transformation:

y^2 = a + b*x

This allows us to enter each data point as (x, y^2) and execute the linear regression function.  The HP Prime version uses the LSQ function.  Both the Casio fx-CG50 and TI-84 Plus CE versions give the correlation, r. 

Casio fx-CG50 Program: SQLINREG

“EWS 2017-07-16”

“SQUARE ROOT FIT”

“Y=√(A+BX)”

“X: “? → List 1

“Y: “? → List 2

List 2^2 → L2

LinearReg(a+bx) List 1, List 2

“A=” ◢

a ◢

“B=” ◢

b ◢

“CORR=” ◢

R

How to access: 

*  LinearReg(a+bx):  EXIT the main program menu, F4 (MENU), F1 (STAT), F6 (CALC), F6 ( > ), F1 ( X ), F2 (a+bx)

*  a, b, r:  VARS, F3 (STAT), F3 (GRAPH), a/b/r

TI-84 Plus CE Program: SQLINREG

"EWS 2017-07-16"

Disp "SQUARE ROOT FIT"

Disp "√(A+BX)"

Input "X: ",L1

Input "Y: ",L2

L2^2→L2

LinReg(a+bx) L1,L2

Disp "A=",a

Disp "B=",b

Disp "r=",r

HP Prime Program:  SQLINREG

EXPORT SQLINREG(L1,L2)

BEGIN

// EWS 2017-07-16

// Square Root-Linear Regression

// Y=√(A+BX)

LOCAL S:=SIZE(L1);

LOCAL L0:=MAKELIST(1,X,1,S);

L2:=L2^2;

LOCAL M1,M2,M3;

M1:=list2mat(CONCAT(L0,L1),S);

M1:=TRN(M1);

M2:=list2mat(L2,S);

M2:=TRN(M2);

M3:=CAS.LSQ(M1,M2);

RETURN

{"Y=√(A+BX)",M3};

END;

Example

x	y	y^2
0.9	2.40	5.76
1.3	2.68	7.1824
1.8	3.03	9.1809
2.4	3.39	11.4921
3.6	4.05	16.4025
5.2	4.77	22.7529
6.1	5.14	26.4196

Results:

A = 2.03165434

B = 3.989146461

CORR = 0.999950438

Equation:  y = √(2.03165434 + 3.98914641*x)

Predicted Values:

y(2) = 3.163850053

y(4) = 4.241254529

Eddie

This blog is property of Edward Shore, 2017

Review: Sharp EL-W516T

Review:  Sharp EL-W516T

Essentials

Company:  Sharp

Year:  2017

Type:  Scientific, 4 line display

Power:  Solar

Statistics: 1 and 2 Variables

Other:  Distributions, Conversions, Constants, Matrices, Vectors, Solver

Operating System:  Algebraic

Number of Memory Registers: 9

Cost:  approximately $18.00

I purchased the calculator at my university bookstore. 

Introduction

The EL-W516T is a spiritual update of Sharp’s EL-W516 model.  The arrow keys are trapezoidal and slightly enlarged, the keys are no longer glossy, and the placements on the keyboard for some features are different (examples are the calculus functions d/dx, ∫ dx, Σ). 

What I like about the EL-W516T is that you can set the WriteView mode to either show exact values or show all answers in approximate decimals.  In approximate mode, only decimal answers and fractions will be shown.  If you want answers in terms of square roots (radicals) or π, you will need to be in exact mode. In earlier models, exact was the default.   

The display is still four lines and very crisp.  The processing speed of the EL-W516T is about the same as its predecessor, which is still decent and fast.  It took about 27 seconds to calculate Σ(1/(x^2), x, 0, 500). 

The EL-W516T carries over the statistics mode, along with the regressions, drill mode, complex number mode, and the solve mode.  You can solve general equations (in the form of f(x) = 0), quadratic equations, cubic equations, 2 x 2 linear systems, or 3 x 3 linear systems. 

There are several added functions to the EL-W516T.  In normal mode, we get LCD, GCD, integer division, and the product of f(x) calculus functions.  In matrix mode, we get the row echelon forms (ref and rref).  The EL-W516T bumps the number of available distributions to 3, adding Binomial and Poisson, and creates a separate mode for it.  We also gain the valuable inverse normal distribution function. 

However, not everything from the EL-W516X made it to the EL-W516T.  For instance, instead of lists, the EL-W516T has vectors.  Regretfully, the formula memory registers that the EL-W516X had are not present on the EL-W516T. 

  

The ALPHA/”3rd F” Key

The [ALPHA] key acts more as a hybrid ALPHA/third shift key.  Case in point:

[ALPHA], [ ( ]:  Integral (∫)

[ALPHA], [ ) ]:  Derivative (dx)

[ALPHA], [ * ]:  Sum (Σ)

[ALPHA], [ ÷ ]: Product (Π)

[ALPHA], [ 4 ]: Constants

[ALPHA], [ 5 ]: Conversions

[ALPHA], [ 1 ] and [ 2 ]:  Engineering notation shifts

[ALPHA], [ 9 ]:  Display A-F, X, Y, and M on one screen

Comparison Sharp EL-W516 vs. EL-W516T

Sharp EL-W516X on the left (older), EL-W516T on the right (newer)

Here is a side by side comparison with the new EL-W516T against the previous EL-W516.  You can see my review for the EL-W516 here:    http://edspi31415.blogspot.com/2011/09/sharp-el-w516x-review.html

That was six years ago. Time flies!   In the EL-W516T column, I marked additional functions in green and things that didn’t make it to the EL-W516T in red. 

The EL-W516T (the one with the T) is the new version. 

	EL-W516 (2011)	EL-W516T (2017)
Number of Functions, according to Sharp	556	640
Calculus	Derivative (d/dx) Integral ( ∫ dx) Sum (Σ)	Derivative (d/dx) Integral ( ∫ dx) Sum (Σ f(x)) Product (Π f(x))
Catalog	Yes	Not available
Variables	9:  A, B, C, D, E, F, X, Y, M (independent)	9:  A, B, C, D, E, F, X, Y, M (independent)
Formula Memory	4:  F1, F2, F3, F4	Not available
Stored Function Memory	3:  D1, D2, D3, D4	3:  D1, D2, D3, no forth slot
Complex Numbers	Arithmetic, rectangular/polar conversion, square, cube, conjugate, absolute value	Arithmetic, rectangular/polar conversion, square, cube, conjugate, absolute value, argument, real part, imaginary part
Bases	5:  Decimal (default), Hexadecimal, Binary, Octal, Pental (base 5).  Logic operations AND, OR, XOR, NOT, XNOR included in non-decimal modes.	5:  Decimal (default), Hexadecimal, Binary, Octal, Pental (base 5). Logic operations AND, OR, XOR, NOT, XNOR included in non-decimal modes.
Number of Regressions	7:  Linear (a+bx), Quadratic (a+b+cx^2), Exponential (a*e^(bx)), Logarithmic (a+b*ln x), Power (a*x^b), Inverse (a + b/x), Geometric (a*b^x)	7:  Linear (a+bx), Quadratic (a+b+cx^2), Exponential (a*e^(bx)), Logarithmic (a+b*ln x), Power (a*x^b), Inverse (a + b/x), Geometric (a*b^x)
Numeric Functions	% (divided by 100), log_a	% (divided by 100), log_a, GCD, LCM, iPart, fPart, int÷
Price Factorization	No	Yes
Number of Conversions	44	44
Number of Constants	52	52
Table Function	No	Up to 2 functions in the form of f(x), table can be scrolled
Polynomial Solver	Quadratic, Cubic	Quadratic, Cubic
Simultaneous Equations	2 x 2 system, 3 x 3 system	2 x 2 system, 3 x 3 system
Matrix Size Limit	4 x 4, 4 matrices	4 x 4, 4 matrices
Matrix functions	Inverse, determinant, transpose, identity, fill, random matrix, cumulative matrix, augment 2 matrices	Inverse, determinant, transpose, identity, fill, random matrix, ref, rref (cumulative matrix, augment are not available)
Approx/Exact	Exact by default, press [CHANGE] for approximate	Can be set up
Random functions	Random number, dice roll, coin toss, random integer	Random number, dice roll, coin toss, random integer
Distributions	Normal (area only) – in Statistics Mode	Distributions gets their own mode:  Normal and inverse, Binomial, Poisson
Lists	List functions	Not available (gets replaced with Vector Mode, see below)
Vectors	Not available	Vectors: 4 vectors up to 3 elements each: dot product, cross product, angle between vectors, unit vector
Home Button: automatically switch to Normal Mode	No	Yes

Final Verdict

Sharp has revamped the EL-W516 line with the EL-W516T.  I like the additional functions and the new vector and table modes.  The only thing that I wish Sharp didn’t drop was the definable function registers.  Sharp instead kept the quick functional slots (D1 – D3) instead. 

For me, the non-glossy keys are a plus, but this is a personal preference.

Overall, the EL-W516T is a good calculator to consider purchasing. 

Eddie

This blog is property of Edward Shore, 2017

TI-84 Plus CE and Sharp EL-9600c: Composite Area

TI-84 Plus CE and Sharp EL-9600c: Composite Area

The program COMPAREA will compile a composite area made of the following geometric shapes:

* Right Triangle:  base and height known

* General Triangle:  side lengths known

* Rectangle: side lengths known

* Square:  length of side known

* Ellipse:  lengths of the semi-axis known

* Circle: radius known

Holes can accounted for entering one of the measurements as negative:

* For circular holes, choose Ellipse with A = -radius, B = radius.  (A < 0) 

* For square holes, choose Rectangle with A = -side length, B = side length. (A < 0)

TI-84 Plus CE Program COMPAREA

"EWS 2017-07-12"

0→T

Lbl 0

Menu("COMPOSITE AREA","RIGHT TRIANGLE",1,"TRIANGLE",2,"RECTANGLE",3,"SQUARE",4,"ELLIPSE",5,"CIRCLE",6,"FINAL",7)

Lbl 1

Disp "RIGHT TRIANGLE"

Prompt B,H

T+B*H/2→T

Goto 0

Lbl 2

Disp "TRIANGLE"

Prompt A,B,C

(A+B+C)/2→S

√(S*(S-A)*(S-B)*(S-C))+T→T

Goto 0

Lbl 3

Disp "RECTANGLE"

Prompt A,B

T+A*B→T

Goto 0

Lbl 4

Disp "SQUARE"

Prompt A

T+A²→T

Goto 0

Lbl 5

Disp "ELLIPSE"

Prompt A,B

T+π*A*B→T

Goto 0

Lbl 6

Disp "CIRCLE"

Input "RADIUS: ",A

T+π*A²→T

Goto 0

Lbl 7

Disp "TOTAL AREA=",T

Sharp EL-9600c Program COMPAREA

0⇒T

Label MENU

Print “1. RIGHT TRIANGLE

Print “2. TRIANGLE

Print “3. RECTANGLE

Print “4. SQUARE

Print “5. ELLIPSE/CIRCLE

Print “6. FINAL

Input I

If I=1 Goto RTRI

If I=2 Goto GTRI

If I=3 Goto RECT

If I=4 Goto SQUA

If I=5 Goto CIRC

If I=6 Goto CALC

Goto MENU

Label RTRI

Print “RIGHT TRIANGLE

Input B

Input H

T + B*H/2 ⇒ T

Goto MENU

Label GTRI

Print “TRIANGLE

Input A

Input B

Input C

(A + B + C)/2 ⇒ S

√(S * (S – A) * (S – B) * (S – C)) + T ⇒ T

Goto MENU

Label RECT

Print “RECTANGLE

Input A

Input B

T + A*B ⇒ T

Goto MENU

Label SQUA

Print “SQUARE

Input A

T + A^2 ⇒ T

Goto MENU

Label CIRC

Print “ELLIPSE/CIRCLE

Print “CIRCLE: A=B

Input A

Input B

T + π*A*B ⇒ T

Goto MENU

Label CALC

Print “TOTAL AREA=

Print T

Examples

Example 1:

Composite area of:

(I):  Right triangle:  base of 3, height of 8

(II): Rectangle:  side lengths of 8 and 15

(III): General triangle: side lengths of 8, 6, and 6

Result:  149.8885438

Example 2:

(I):  Rectangle: lengths of 10 and 20

(II):  Circular hole with radius of 2.5.  (Enter as ellipse:  A = -2.5, B = 2.5)

(III): Square hole with side of 5 (Enter as rectangle, A = -5, B = 5)

Result:  155.3650459

Eddie

This blog is property of Edward Shore, 2017.