Comparison of Formula Evaluators: TI-60X, TI-68, Sharp EL-5150, fx-4200P, fx-5000f

Comparison of Formula Evaluators

Happy New Year! Let’s start the new year by comparing formula evaluator calculators. The calculators featured are:

TI-60X (early 1990s)

TI-68 (late 1980s/1990s)

Sharp EL-5150 (late 1970s/early 1980s)

fx-4200P (late 1980s/early 1990s)

fx-5000f (late 1980s/early 1990s)

Formula evaluator: A calculator which strictly evaluates simple formulas. There are no loops, no solvers, no sums. The formula evaluates to one answer but can have more than one inputs.

Example:

Allowed: f(x) = x² + 3 – 1 / x

Allowed: f(a,b) = (a * b) / (a + b)

Not Allowed: f(x) = Σ(x² / 3, x = 0, 10)

Not Allowed: f(x) = [1 if x ≥ 0, else 0]

	TI-60X	TI-68	Sharp EL-5150	fx-4200P	fx-5000F
Battery	1 x CR2032	1 X CR2032	3 x SR44/LR44	1 x CR2032	2 x CR2032
Memory (bytes)	12 registers (84 bytes)	55 registers (440 bytes)	80 steps	279 steps	675 steps
Variables: Number and Type	12, Single letter: A through I, X, Y, Z	Up to three character variables (3 character variables take up 2 registers)	11: A – J, M	26 single letters for formulas only: A – Z; 6 separate numerical constants (K1-K6)	Letters and Greek characters for formulas only; separate numerical constants (K0-K9)
Does store values to variables take space?	Yes, each variable takes up a register	Yes, 1 register for 1 or 2 character variables, 2 for 3 character variables	No	No	No
How Formulas are accessed	[ 2nd ] [ EE ] (FMLA)	[ 2nd ] [ EE ] (FMLA)	AER Mode; up to 5 lines	[ IN ]/[ OUT ]	[ MODE ] 2: WRT Prog 0-9,A,B: 12 slots
Integration? ∫ f(x) dx	Yes	Yes	No	No	No
Base conversions?	Yes, with Boolean logic	Yes, with Boolean logic	No	Yes, 32 bit binary block	No
Complex numbers?	No	Yes, with trig and log complex calculations	No	No	No
Engineering symbols?	No	No	Display toggle switch	Display toggle switch	Display toggle switch
Conversions?	Yes. 4 pairs (in/cm, gal/L, lb/kg, °F/°C)	Yes. 4 pairs (in/cm, gal/L, lb/kg, °F/°C)	No	No	No
Scientific Constants?	No	No	No	No	Yes ([ALPHA] [ ln ] (CONST)), 13
Other		Special 13 digit precision mode	Landscape form		128 built in formulas

The four pairs of conversions included in the TI-60X and TI-68 are:

in/cm: inches/centimeters

gal/L: gallons/liters

lb/kg: pounds/kilograms

°F/°C: degrees Fahrenheit/degrees Celsius

The scientific constants included on the fx-5000F are:

c: Speed of Light

h: Planck’s Constant

G: Universal Gravitational Constant

e: Elementary Charge

me: Electron Mass

u: Atomic Mass Unit

k: Boltzmann Constant

Vm: Molar Volume of Ideal Gas at Standard, Temperature, and Pressure

g: Earth’s Gravity Constant

R: Molar Gas Constant

ε0: Permittivity of Vacuum

µ0: Permeability of Vacuum

All the constants are in SI units.

Out of the calculators listed, my favorites are the TI-68 and fx-5000F.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

fx-3650P and TI-68: Quadratic Equation and Arc Length between Roots of a Quadratic Curve

fx-3650P and TI-68: Quadratic Equation and Arc Length between Roots of a Quadratic Curve

Two approaches using two well-liked, classic calculators. The fx-3650P uses Basic like language while the TI-68 handles formulas.

Quadratic Equation

Solve for A x^2 + B x + C = 0, with the discriminant D = B^2 – 4 * A * C.

We know the solutions: X = (-B ± √(B² – 4 * A * C)) / (2 * A)

fx-3650P Program

? → A : ? → B : ? → C :

B² – 4 A C → D ◢

-B ÷ ( 2 A ) → M :

√ ( √ ( D² ) ) ÷ ( 2 A ) → Y :

D ≥ 0 ⇒ Goto 1 : M ◢ Y ◢ Goto 2 :

Lbl 1 : M + Y → X ◢ M – Y → Y ◢ Lbl 2

D: discriminant

If D<0; roots are in the form of M ± Yi

Else, the roots are real and are stored in X, Y

TI-68 Formula

X = 0 × A + (-B + √(B² – 4 × C × A) × J) ÷ (2 × A)

The 0 × A is added to force A to be prompted for first.

J = -1 for one root, J = 1 for the other

TI-68 takes care of both real and complex roots, no worries.

The coefficients can be complex!

Examples

A	B	C	D	Roots
2	-3	-9	81	3, -1.5
1	0	25	-100	5i, -5i
-48	64	28	9472	-0.347127088, 1.680464022

Arc Length of a Quadratic Equation between its Real Roots

Give roots X, Y: (t – X) * (t – Y) = t^2 – (X + Y )* t + X * Y

f(t) = t^2 – (X + Y) * t + X * Y

f’(t) = 2 * t – (X + Y)

arc = ∫( √(1 + f’(t)^2) dt

TI-68 will set up for the outside integral function, while the fx-3650P can use the integral function inside of the program.

We are going to assume that X < Y.

fx-3650P Program

? → A : ? → B : ∫ ( √ (1 + (2 X – A – B) ² ), A, B)

This is the direct approach.

TI-68 Formula

ARC = √(1 + (2 × X – A – B)²)

for X use the integral function (dx)

[ 3^rd ] [ Σ+ ] (dx) [ = ]

Enter low, high, and the number of intervals.

The more intervals, generally, the more accurate the integral is.

Examples

I compared results against the fx-991CW.

A	B	TI-68, intv = 16	fx-3650P	fx-991 CW
2	9	26.070832160	26.070800000	26.070797720
0	5	13.903768900	13.904000000	13.903767950
-2	2	9.293567375	9.293568000	9.293567525

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

Retro Review: Sharp EL-5100

Retro Review:  Sharp EL-5100

Company:  Sharp

Year Introduced:  1979

Type:  Scientific, Formula Programming

Memory:  80

Operating System: Algebraic

Memory Registers: 11, A through J, M

Background

I have to give a shout out to the Pasadena Antique Mall in Pasadena, California.   The EL-5100 was a lucky find for me, and the ladies at the counter were kind enough to let me walk quickly to nearby Target to get batteries so the EL-5100 can be tested.  The calculator tested perfectly!  If you are in the greater Los Angeles area, the Pasadena Antique Mall is great place to visit for all things retro.  

Landscape and Thin Calculator

The EL-5100 is a light weight calculator in a silver, thin design.  The calculator is well built and the keys are solid.   The keys are arranged in three sections, from left to right:

*  Scientific functions

*  Number keypad and arithmetic functions

*  Storage and alpha keys:  A-J, M

A staple of calculators from the 1970s is the physical mode switch.   The EL-5100 has one mode switch:

* AER:  Program and store formulas

* COMP:  Computational mode

* STAT:  Statistics mode, including linear regression  (y = a + bx)

Formula Storage

The EL-5100 can store up to five formula areas, with 80 steps allocated between them.   The formulas can be separate or stored as a chain of formulas.  An example of the chain formula:

c = √(a^2 + b^2)

d = c / (b + c)

would be stored as:

(switch to AER mode, CA)

1; f(A,B)=√(A^2+B^2) STO C ◣

2; C ÷ (B + C) STO D

(switch back to COMP)

Press [ COMP ] 

(an example)

A =?   (pressing COMP again takes the last value of A)

Example:  Let A = 19, B = 79

[COMP]

A = ?   19 [COMP]

B = ?   79 [COMP]

1; ANS 1 = 81.25269226  (C)

[2nd F]  2;  

2;  ANS 1 = 0.507028563  (D)

An alternative way to chain formulas (multistep):

1; f(A,B)=√(A^2+B^2) STO C,  C ÷ (B + C) STO D

Example:  Let A = 19, B = 79

[COMP]

A = ?   19 [COMP]

B = ?   79 [COMP]

1; ANS 1 = 81.25269226  (C)  [COMP]

2; ANS 2 = 0.507028563  (D)

You can store immediate results, however, they will end the execution.  However, this is still handy when you are using the M register and the M+ feature.

* Note:  In AER mode, the [ COMP ] key is the comma.  

Statistics Mode

In STAT mode, it was common for Sharp calculators to assign data entry keys to the M register keys.

[ RM ] becomes CD  (clear data)

[ →M ] becomes the comma for bivariate data (x,y)

[ M+ ] becomes DATA for storing data

The multiplication key can be used to store data with frequency greater than.  However, you can do mathematical operations as long as they are enclosed in parenthesis.

Even though the variable keys A-J are not available during STAT mode, the stat values are stored in the following variables and can be used later in COMP mode.

E = n

F = ∑x

G = ∑x^2

H = ∑xy

I = ∑y

J = ∑y^2

Sharp EL-5100 vs TI-68

The EL-5100 ushered in a category of formula storage calculators.  Here is a comparison table between 1979's EL-5100 and 1989's TI-68.

EL-5100		TI-68
1979	Year of Introduction	1989
3 x SR44/LR44/357	Batteries	1 x CR2032
landscape	Form	portrait
5, sequential	Number of Storage Areas	1 at a time, as memory allows
80	Number of Steps	440 (55 registers)
y = a + bx, r	Linear Regression	y = SLP x + ITC, COR
A through J, M	Variable Names	variable names up to 3 characters
chain formulas, physical mode switch	Unique Features	complex numbers, base conversions, integrals, solver, conversions

Verdict

The EL-5100 is a simple calculator which is a joy to use.  

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Retro Review: Texas Instruments TI-68

Retro Review:  Texas Instruments TI-68

Company:  Texas Instruments

Years:  1989 - 2002

Type:  Scientific, Formula Programming

Memory:  440 bytes, in 55 8-bit registers

Operating System: Algebraic

Memory Registers: Up to three characters

Batteries:  1 CR2032

Hard to Find:  One with a good screen is hard to find.  It took me two tries to do so. 

Features

The TI-68 is a popular scientific calculator and back in the day, it had pretty much most of the bells and whistles (with the obvious exception of graphing):

*  Base Conversions and Boolean Logic (9 bits, signed integer, max binary value: 511, minimum binary value: -511)

*  Linear Regression

*  Polynomial Solver: Quadratic, Cubic, Quartic

*  Simultaneous Equation Solver:  Up to 5 x 5 systems

*  Expanded Storage Arithmetic:  +, -, *, /, ^, Δ%, and, or, xor

* Number Parts: signum, integer, fraction, real, imaginary, absolute value (but strangely enough, no argument/angle function, did TI run out of space?)

Complex Numbers

What I love about the TI-68 is how complex numbers are integrated in the operating system.  There is no need to switch to a separate mode.  Best of all, the TI-68 handles exponential, logarithmic, power, and trigonometric functions with complex numbers. 

The simultaneous solver also allows for complex numbers.  This is indeed rare, as not even most graphing calculators’ simultaneous solving apps allow for complex numbers as coefficients.  (Note:  The HP Prime’s simult command allows for complex numbers)

Complex numbers on the TI-68 are notated as such:

Rectangular:  (x, y)

Polar:  (r ∠ θ)

Part extraction of complex numbers works slightly different:  real and imag extract the real and imaginary portions of the complex number, regardless of setting.  

Choosing the Precision?

The TI-68 allows for two precision settings:  10 digits or 13 digits.   The display uses 10 digits.  I think this is a rarity, if not a completely unique feature, since calculators in general uses an accuracy of 13 to 15 digits automatically.

I tested a couple of integrals and the precision setting does not affect the length of time either way.  Both integrals were calculated in about 3 seconds. 

Test Integral 1:  ∫ (T^3 * e^(-T) dT, 0, 100, intervals = 6)

Test Integral 2:  ∫ (X^2/(X^2 + X – 1) dX, 25, 75, intervals = 12)

Integration

The TI-68 uses the Simpson’s Rule during integration.  To integrate, during evaluation, designate the variable to be integrated by pressing [CLEAR], [ 3rd ], [ Σ+ ] (dx). 

Formula Programming

The TI-68 has formula programming.  There are no loops or comparison tests, but all variables are local, meaning their stored values can be transferred between formulas.

Something I learned about the TI-68: you can have variables up to 3 characters. 

Each formula can be evaluated (right hand side of the equation) by pressing [SOLVE].  Each variable can accept a real or complex number.

Keyboard

Let’s talk about the keyboard.  The keys are nice and responsive.  But get a look of all those shift keys!  There are two shift keys, [ 2nd ], [ 3rd ], along with an inverse key [ INV ].  This is reminiscent of the 1974 Hewlett Packard HP 65 calculator, where its shift keys were [ f ], [ f^-1 ], and [ g ].

Here is what the inverse [INV] key (it’s like a “4th” key) operates on:

Key	[ INV ] Key	Key	[ INV ] Key
[2nd] (DRG>) D: D to R R: R to G G: G to D Angle conversion*	D:  D to G R:  R to D G:  G to R	[2nd] (>DD) Convert: DMS>DD	Convert: DD>DMS
[HYP] Hyperbolic	Inverse hyperbolic	[2nd] (P>R) Polar to Rectangular	Rectangular to Polar
[SIN] Sine	Arcsine (sin^-1)	[2nd] (in-cm) Inches to centimeters	Centimeters to inches
[COS] Cosine	Arccosine (cos^-1)	[2nd] (gal-l) Gallons to liters	Liters to gallons
[TAN] Tangent	Arctangent (tan^-1)	[2nd] (lb-kg) Pounds to kilograms	Kilograms to pounds
[ Σ+ ] add a data point	Erases the last data point (Σ-)	[3rd] (°F-°C)  Fahrenheit to Celsius	Celsius to Fahrenheit

‘*  D = Degrees, R = Radians, G = Grads.  Angle mode is unaffected.  To change angle mode, press [ 3rd ] (DRG) (it cycles Degrees, Radians, Grads).

The Basic Cousin, TI-60X

TI-60X (left), TI-68 (right).  Their memory capacities are shown.

In 1991, Texas Instruments released a more basic version of the TI-68, the TI-60X.  For more details, check out this link:  http://edspi31415.blogspot.com/2017/01/retro-review-ti-60x.html.

Final Verdict

I regret not getting the TI-68 when it first came out (which would have consisted in asking my family for one).  It’s finally nice to have one and it’s worth the hype and praise it got. 

Eddie

This blog is property of Edward Shore, 2017