Sunday, July 23, 2017

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

1 comment:

  1. Hello,

    That's why I also like the programmable TI-86, which handles complex numbers like any other number, and even allows sophisticated operations on matrices, like EXP(Matrix) (applying Taylor series, without doing EXP(each element)). In the No Graph-No CAS category, the TI-68 is impressive, but sadly you cannot write programs for it (except formulas). Thanks

    ReplyDelete

Adventures in Python: String Manipulation and Function/Derivative Table (Subroutines)

Adventures in Python:  String Manipulation and Function/Derivative Table (Subroutines) String Manipulation This script demonstrate...