My International Casio Collection (So Far)

 Pictured:

Pic 1:  Casio fx-991CN X (China) 

Pic 2:  Casio fx-570SPX II Iberia (Spain)

Pic 3:  Casio fx-92 Collège (France)

All original content copyright, © 2011-2026. 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.

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.

AOS Calculators: Duplicating a Value Without Retyping It

AOS Calculators: Duplicating a Value Without Retyping It

Note: The following applies to scientific classic calculators who operate under the algebraic operating system (AOS) (that is what Texas Instrument’s calls it). I tested this procedure with the following calculators: TI-30X ECO, HP 10bII+ (Algebraic mode), and Casio fx-260 Solar.

Introduction: Going Back to 1976

Imagine it is 1976 and you have have an SR-56 from Texas Instruments. Here is what an SR-56 looks like: http://www.datamath.org/Sci/WEDGE/ZOOM_SR-56.htm

You are tasked to calculate 1.401103287^1.401103287 and do not want to write the number twice. According to page 53 of the SR-56 manual, one approach is to key in:

1.401103287 [ y^x ] [ CE ] [ = ]

Result: 1.604057054

For that particular calculator, SR-56, pressing [ CE ] once stores the number in the display as the second operand allowing the value to duplicated without having to retype the number.

If we tried that on a modern TI-30Xa/TI-30 ECO RS, the display would clear to zero instead of showed the previous number.

However, there are a few tricks we can employ to achieve the similar result.

Trick 1: Pressing the Reciprocal Key Twice

As long as the number in the display is nonzero, pressing [ 1/x ] [ 1/x ] registers the number in the display for as a second operand. In calculators operating in AOS, executing one-argument functions only operate and effect the number in the display only.

Pressing [ 1/x ] takes the reciprocal of the number and registers the number in the display. Pressing [ 1/x ] again returns the number.

**The keystrokes omits any [ 2^nd ] or [ SHIFT ] keys.

Example 1:

Expression: x * log x

Keystrokes: x [ × ] [ 1/x ] [ 1/x ] [ LOG ] [ = ]

5.8 * log 5.8

Keystrokes: 5.8 [ × ] [ 1/x ] [ 1/x ] [ LOG ] [ = ]

Result: 4.427882363

Example 2:

Expression: x^x

Keystrokes: x [ y^x ] [ 1/x ] [ 1/x ] [ = ]

3.088 ^ 3.088

Keystrokes: 3.088 [ y^x ] [ 1/x ] [ 1/x ] [ = ]

Result: 32.51797379

Example 3:

Expression: x * sin x

Keystrokes: x [ × ] [ 1/x ] [ 1/x ] [ SIN ] [ = ]

50° * sin 50°

Keystrokes: ([DRG] to DEG/[ MODE ] (DEG))

50 [ × ] [ 1/x ] [ 1/x ] [ SIN ] [ = ]

Result: 38.30222216

4^4 + 1 / (3^3)

Keystrokes:

4 [ y^x ] [ 1/x ] [ 1/x ] [ + ]

[ ( ] 3 [ y^x ] [ 1/x ] [ 1/x ] [ ) ] [ 1/x ] [ = ]

Result: 256.037037

If the calculator has a cube function (x^3), we can execute this keystroke:

4 [ y^x ] [ 1/x ] [ 1/x ] [ + ]

[ ( ] 3 [ x^3 ] [ ) ] [ 1/x ] [ = ]

Trick 2: Inverse Function Trick

This trick extends the reciprocal trick to include a function that acts on two (and theoretically more) “reversible” functions. This trick applies to the expressions with the following format:

f(x) OP g(x)

f(x)	f^-1(x)	f(x)	f^-1(x)	f(x)	f^-1(x)
SIN	SIN^-1	e^x	LN	X^3	∛
COS	COS^-1	LN	e^x	∛	X^3
TAN	TAN^-1	10^x	LOG	Hyperbolic	Inverse Hyperbolic
SIN^-1	SIN	LOG	10^x	Inverse Hyperbolic	Hyperbolic
COS^-1	COS	X^2	√
TAN^-1	TAN	√	X^2

OP covers the arithmetic operations: [ + ], [ - ], [ × ], [ ÷ ], [ y^x ], and [ y^(1/x) ]

The general keystroke sequence is: x [ f(x) ] [ OP ] [ f^-1(x) ] [ g(x) ] [ = ]

Let’s illustrate this with a few examples. Assume the calculator is in degrees mode.

Example 1:

sin 40° * cos 40°

f(x) = sin x, f^-1(x) = sin^-1 x, g(x) = cos x

Keystrokes: 40 [ SIN ] [ × ] [ SIN^-1 ] [ COS ] [ = ]

Result: 0.492403877

Example 2:

tan 32° * sin 32°

f(x) = tan x, f^-1(x) = tan^-1 x, g(x) = sin x

Keystrokes: 32 [ TAN ] [ × ] [ TAN^-1 ] [ SIN ] [ = ]

Result: 0.331130307

Example 3:

log 881 * ln 881

f(x) = log x, f^-1(x) = 10^x, g(x) = ln x

Keystrokes: 881 [ LOG ] [ × ] [ 10^x ] [ LN ] [ = ]

Result: 19.97005314

Example 4:

e^3.5 / √3.5

f(x) = e^x, f^-1(x) = ln x, g(x) = √x

Keystrokes: 3.5 [ e^x ] [ ÷ ] [ LN ] [ √ ] [ = ]

Result: 17.70095363

Example 5:

√4.555 + e^4.555

f(x) = √x, f^-1(x) = x^2, g(x) = e^x

Keystrokes: 4.555 [ √ ] [ + ] [ x^2 ] [ e^x ] [ = ]

Result: 97.24099983

The inverse function “recovers and registers” the original x. It’s kind of simulating the LAST x feature on RPN calculators.

Sources

Datamath. “Texas Instruments SR-56“ December 5, 2001. http://www.datamath.org/Sci/WEDGE/SR-56.htm

Texas Instruments. Programmable Slid-Rule Calculator SR-56: Owner’s Manual. Dallas, TX. 1976

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.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.

Battle of the “Cheap” Calculators: Sharp EL-501W vs. Bazic 3003

Battle of the “Cheap” Calculators: Sharp EL-501W vs. Bazic 3003

“Let’s Get Ready to Rumble!”

Today is an accuracy battle between the:

Sharp EL-501W

This is brand name calculator. In the 2010s, Sharp manufactured one with blue casing. However, their current EL-501W type (really named the EL-501XBWH) has black casing. Both the EL-501W and EL-501XBWH have the same keyboard and the same amount of functions. The average price runs from $9 to $16 (US).

This is the Bazic 3003, a clone of the Sharp EL-501W/EL-501XBWH. This model sells in discount stores for anywhere from $3 to $6 (US).

There is another clone, the Jot Scientific Calculator which is physically smaller than both models I mentioned, and is even cheaper, close it $1 to $3. (US) I won’t be using this model in today’s tests.

The features on all these models include:

* trigonometric, hyperbolic, logarithm, and power functions

* binary, decimal, octal, and hexadecimal base conversions

* two buttons, [ a ] and [ b ] which assists with complex number arithmetic and polar/rectangular conversions

* random numbers

* one-variable statistics with basic analysis

The Exchange Function: { ↕ }

The exchange key switches the operands in arithmetic calculation. The key sequence is the same: [ 2^ndF ] [ ( ] { ↕ }. If we complete an arithmetic calculation by pressing the equals button [ = ], the exchange function recalls the second operand for each operation. Well, almost.

Operation	Keystrokes	Result
Addition	A [ + ] B [ = ] [ 2ndF ] [ ( ] { ↕ }	B
Subtraction	A [ - ] B [ = ] [ 2ndF ] [ ( ] { ↕ }	B
Multiplication	A [ × ] B [ = ] [ 2ndF ] [ ( ] { ↕ }	A
Division	A [ ÷ ] B [ = ] [ 2ndF ] [ ( ] { ↕ }	B
Power	A [ y^x ] B [ = ] [ 2ndF ] [ ( ] { ↕ }	B

(A, B are two arbitrary numbers)

The Sharp EL-501W has plastic keys, a slide case, and takes two LR44 batteries, while the Bazic 3033 has rubber keys, a flip case, and takes two LR1130 batteries. As a personal preference, I prefer plastic keys to rubber keys.

Let’s compare.

A Comparison of Accuracy

The Trigonometric Forensics Evaluation

This test calculates:

arcsin( arccos( arctan( tan( cos( sin( 9° )))))) (six set of parenthesis)

However, we do not need parenthesis:

[ DRG ] (press until degrees mode is set)

9 [ SIN ] [ COS ] [ TAN ]

[ 2ndF ] [ TAN ] {TAN^-1} [ 2ndF ] [ COS ] {COS^-1} [ 2ndF ] [ SIN ] {SIN^-1}

Ideally, the answer returned should be exactly 9.

This test is presented on datamath.org web site (see source below), and this test was used to determine what chips were used in various Texas Instruments calculators.

Results:

Sharp EL-501W	8.9999 98637
Bazic 3003	8.9999 9986

Bazic gets the slight edge on this test.

The Cube of a Complex Number

The next test calculates (4.5 + 2.2i)^3.

The complex number mode only works for arithmetic functions (+, -, ×, ÷).

First, lets’ calculate the cube in complex mode.

Keystrokes:

[ 2ndF ] [ → ] {CPLX} (until CPLX indicator appears)

4.5 [ a ] 2.2 [ b ] [ × ] 4.5 [ a ] 2.2 [ b ] [ × ] 4.5 [ a ] 2.2 [ b ] [ = ]

Results:

Sharp EL-501W	25.785 + 123.002i (press [ b ] for the imaginary part)
Bazic 3003	25.785 + 123.002i (press [ b ] for the imaginary part)

Now in Real Mode using the polar/rectangular conversion functions.

Keystrokes:

[ 2ndF ] [ → ] {CPLX} (until CPLX indicator disappears)

4.5 [ a ] 2.2 [ b ] [ 2ndF ] [ a ] { →rθ }

[ b ] [ x→M/STO ] [ a ] [ y^x ] 3 [ = ] (manually record 125.6756071)

[ RM/RCL ] [ × ] 3 [ = ] [ b ] 125.6756071 [ a ] [ 2ndF ] [ b ] { →xy }

Results:

Sharp EL-501W	25.78499999 + 123.002i (press [ b ] for the yi part)
Bazic 3003	25.78499999 + 123.002i (press [ b ] for the yi part)

Test of the Logarithm Bug

This test to check to the accuracy of the approximation of e^x, where

e^x = lim n → ∞ (1 + x / n) ^n

If x = 1, then e = e^x = lim n → ∞ (1 + 1 / n) ^n

This test came about because there were several TI-30X and TI-36X calculators that were manufactured in the 1990s. See the Logarithm Bug in the Sources section for more details.

At various values of n:

(1 + 1 / N)^N	Sharp EL-501W	Bazic 3003
N = 10	2.59374246	2.59374246
N = 1,000	2.716923932	2.716923932
N = 100,000	2.718268237	2.718268237
N = 10,000,000 = 1E7	2.718281693	2.718281693

Both calculators give the same results. More importantly, there is no “logarithm bug” present from these results. Yay!

Statistics of Large Numbers

Sometimes when doing statistics of large numbers, which the numbers themselves differ by little, accuracy can suffer.

The data points for this sample:

100 008	100 014
100 007	100 016
100 009	100 006
100 010	100 015
100 012	100 018

Both calculators give these results:

Mean: 100011.5

Sum: 1000115

Sum^2: 1.0002E+11 (1.000230015E+11)

σx = 3.905124838

sx = 4.116363012

n = 10

Overall, the two calculators return the same result. Based off these results, it’s down to how much money you want to spend and what type of keys do you prefer.

Sources

Woerner, Joerg. “Calculator Integrated Circuits Forensics” Datamath.org. Last updated December 12, 2001

http://www.datamath.org/Forensics.htm. Retrieved March 16, 2024.

Senzer, Bob, Mike Sebastian, and Joerg Woerner. “Logarithm Bug” Datamath.org. Last updated October 11, 2005. http://www.datamath.org/Story/LogarithmBug.htm Retrieved March 16, 2024.

For the Star Wars fans, may the Fourth and Force be with you,

Eddie

All original content copyright, © 2011-2024. 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.