Casio fx-CG 100 in Pictures and First Impressions

Casio fx-CG 100 in Pictures and First Impressions

Quick Facts:

Model: fx-CG 100

Company: Casio

Battery: 4 x AAA (included with the calculator)

Memory: 61,440 bytes for regular memory. However, Python scripts are stored in Storage Memory, which is 4,793,072 bytes (almost 4.8 MB).

Price (US): $119.99

Site: https://www.casio.com/us/scientific-calculators/product.FX-CG100/

Display: 216 x 384 pixels

Programming Language: Python

Connection: USB Port, USB-C (a cord was not provided in the box, but this cord is easily obtainable because the USB-C fits works with most smart phones, tablets, and current Numworks N120)

Languages: English, Spanish, French, Italian, Portuguese

Country Settings: International, Portugal, United Kingdom, United States (this seems to arrange the order the apps, but I'm not sure what else is effected)

Python Modules available at the beginning: Math, Random, PyPlot, Turtle, CasioPlot including getkey()

The fx-CG 100 is a graphing calculator that is modeled after the ClassWiz series, like it’s non-graphing flagship fx-991 CW. Instead of function keys (F1 – F6), navigation is done using tab keys ( [ |< ] and [ >| ]), and the [CATALOG] and [ TOOLS ] keys. The options available in the CATALOG and TOOLS change depending on the current app operated.

At default the [ FORMAT ] key toggles between exact answers and approximates. We can set the format key to act like the fx-991 CW, which it brings up menu which gives formatting options exact, approximate, sexagesimal, and engineering. For me personally, I will leave it as toggle. We can always bring up the format menu by pressing [ SHIFT ] [ FORMAT ].

The menus include short cut option numbers. We can disable them, but I don’t think there is a reason to.

The Calculate app is now only in Math Input/Output (textbook). No more linear (one-line) entry, despite the current manual mentioning Linear Input. I have not found that setting (yet).

The list brackets are no longer on the keyboard, but instead only in the CATALOG-Statistics menu.

Pressing the [ HOME ] key will bring up the following apps:

Calculate (includes Unit Conversions)

Graph & Table (used to be two separate apps – function, parametric, polar, x=, inequality)

Statistics

Equation (solve linear systems, polynomials, general solver)

Recursion (sequences)

Dynamic Graph

Distribution (Binomial, Normal, Poisson, Geometric, Hypergeometric, Student-t, Chi Square, F)

Numeric Inequality Solver

Base-N (base conversions and logic returns to its own app instead of being integrated in Calculate)

Conic Graphs

Spreadsheet (better access to the cell functions)

Geometry

Financial

3D Graph (including z(x,y), parametric (x(s,t), y(s,t), z(s,t), conic sections)

Probability Simulations

Python

Database – Periodic Table, Scientific Constants (which can be stored in variables A-Z). Scientific constants are in SI units (meters, kilograms, seconds, Joules, Kelvins, etc.)

Memory Management

Exam Mode (which personally I’ll never use)

Given a quick glance, except for the loss of Casio basic, all of the functionality of the fx-CG 50 make it over to the fx-CG 100. Python scrips are stored in Storage Memory (about 4.8 MB).

The keyboard feels nice. And the contrast of the green, orange, and white against the black background makes the keyboard easy to read.

[SHIFT] [ 0 ]: Select. Press [ OK ] or [EXE] to cut or past

[SHIFT] [ 1 ]: Paste

[SHIFT] [ 2 ]: Screen Capture

Pictures:

Overall, the fx-CG 100 is impressive and I will have to get used to the catalog/tools keys.

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.

Casio fx-991CW: The Inequalities Mode

Casio fx-991CW: The Inequalities Mode

Solving Inequalities

The Casio fx-991CW, along with other high-end scientific calculators from Casio has an Inequalities mode.

The inequalities mode solves quadratic, cubic, and quartic polynomials. The mode works similar to Equation-Polynomial module. Below is an example (all screenshots were created in Casio’s classpad.net website):

The Inequalities mode can assist in calculus and geometry problems.

Circle Problem

Task: Find valid points (x, y) that fit in the circle:

x^2 / 3 + y^2 / 6 = 1

Step 1: We can use the Inequalities mode to find the allowed x values.

Start by solving for y:

x^2 / 3 + y^2 / 6 = 1

6 × (x^2 / 3 + y^2 / 6) = 1 × 6

2 × x^2 + y^2 = 6

y^2 = 6 – 2 × x^2

y = √(6 – 2 × x^2)

For the equation to be “valid”, or to not return complex numbers, find all x where 6 – 2 × x^2 is not negative.

6 – 2 × x^2 ≥ 0

We find that the allow range is -√3 ≤ x ≤ √3.

Step 2: Store the Equations

We can do define f(x) in any mode. To do this, press [ f(x) ], select Define f(x). Press [ OK ] to store the function. The fx-991CW allows for two functions, f(x) and g(x).

In this example, we defined f(x) and g(x) as follows:

f(x) = √(6 – 2 × x^2)

g(x) = -f(x)

Step 3: Use the Table mode to find values in the appropriate range.

Set the Table Type as f(x)/g(x). Set the Table Range as Start: -√(3), End: √(3), Step: 2×√(3)÷5

Table:

	x ≈	f(x) ≈	g(x) ≈
1	-1.732	0	0
2	-1.0392	1.9595	-1.9595
3	-0.3464	2.4	-2.4
4	0.3464	2.4	-2.4
5	1.0392	1.9595	-1.9595
6	1.732	0	0

The Area Between f(x) and x ≥ 0

Find the area between the curves:

f(x) = -x^4 + 2 × x^3 + 25 × x^2 – 26 × x – 120 and x ≥ 0.

Step 1: Find the boundaries.

With the Inequalities mode, we can find the boundaries and intersection points where f(x) ≥ 0. We find that: -4 ≤ x ≤ -2 and 3 ≤ x ≤ 5. Write down these results. The area will be in the intervals [-4, -2] and [3, 5].

Confession: I ultimately chose this function because of its integer roots. Unfortunately we are not able to store coefficients or roots in variables directly on the fx-991CW to variables.

Step 2: Store the Equations

Store -x^4 + 2 × x^3 + 25 × x^2 – 26 × x – 120 to f(x). This will allow us to save keystrokes while calculating the area.

Step 3: Calculate the Area in the Calculate Mode

Use the integral function from the Catalog - Func Analysis menu.

∫( f(x), -4, -2) + ∫( f(x), 3, 5)

The area is: 1928/15 ≈ 128.5333333

Hint: To always get a decimal approximation (skipping the exact result), press [SHIFT] [ = ] ( ≈ ).

Another example:

Find the area between the curves:

f(x) = x^3 + 8 × x^2 – 3 and x ≥ 0.

The boundaries are: -7.952564217 ≤ x ≤ -0.63837179, 0.5909359176 ≤ x

Which means the intervals are: [ -7.952564217, -0.63837179] and [ 0.5909359176, ∞). We can see that the area given these boundaries, the area will approach infinity.  

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.

Sharp EL-512: Lorentz Factor, Table, Geometric Mean, 3D Vectors

Sharp EL-512: Lorentz Factor, Table, Geometric Mean, 3D Vectors

Blog entries now made in Windows 11. 

Two Sharp calculators. Left: EL-510RN (current) and EL-512 from 1984

Today’s blog will feature the classic Sharp EL-512 from the 1980s. The Sharp EL-512 is a keystroke programming calculator. The EL-512 has four program slots with a memory of 128 programming steps. All programs on the EL-512 are “entered in the blind” and must be entered in full each time.

Program commands:

[ x ]: prompt for a number. When editing a program, we will need to enter a valid number to continue the program.

LOOK: Stops the program and shows the immediate results.

Memory and recall:

STO: Stores the number in the display to memory register 1-9

x → M: Store the number in the display to memory M

M+: add to memory M

RM: recall memory M

Kn:

After a clear or an arithmetic key, just recalls the contents of memory register 1-9.

After entering a number, multiplies the number in the display by the contents of the memory register 1-9 (like RCL× K#)

To recall a register without alteration, it is always safe to multiply the register by 1:

1 Kn #

My review from 2020:

https://edspi31415.blogspot.com/2020/09/retro-review-sharp-el-512-scientific.html

Lorenz Factor

LF = (√(1-v²/c²))⁻¹

c = Speed of light in a vacuum = 299,792,452 m/s

Program:

x²

÷

299792458

x²

+/-

1

=

√

1/x

Examples:

v = 2.1E8 (2.1 * 10^8) m/s; Result: 1.401212716

v = 2,456,000 m/s; Result: 1.000033559

v = 1,000,000 m/s; Result: 1.060752

Table: Quadratic Polynomial

Generate a table using the function:

f(x) = K3 × x² + K2 × x + K1

where x increases by 1.

Before running the program, store the following:

x² coefficient: K3

x coefficient: K2

constant coefficient: K1

beginning value: Subtract 1, then store the starting value in M. For example, if we want to start with x = 1, store 0 in M.

Program:

1

M+

RM

x²

Kn 3

+

RM

Kn 2

+

1

Kn 1

=

Example:

f(x) = 0.3 × x² + 4 × x – 2.01

Start with x = 1

0.3 STO 3

4 STO 2

-2.01 STO 1

1-1 = 0 x→M

Run the program:

f(1) = 2.29

f(2) = 7.19

f(3) = 12.69

f(4) = 18.79

f(5) = 25.49

Geometric Mean

This program calculates the geometric mean (Π(x_i)^(1/n)) by the formula:

GM = 1/n × Σ(ln x_i) (x≠0)

This will require two program slots, so I’m using program slots 1: and 2:.

Memory registers used:

K1 = Σ(ln x_i)

M = n

Steps:

1. Store 0 to memory M (x→M) and memory 1 (STO 1)

2. Enter x_i and press 1:. Continue until you enter all the data. The number of data points is shown.

3. Press 2: to get the geometric mean.

Program 1:

ENT (enter a valid number)

LN

+

Kn 1

=

STO 1

1

M+

RM

Program 2:

RM

1/x

Kn 1

e^x

Example:

Find the geometric mean of 4, 9, 3, 7, 2, 8, 8, 5, and 6. 9 data points.

0 x→M, 0 STO 1

4 [1:], 9 [1:], 3 [1:], 7 [1:], 2 [1:], 8 [1:], 8 [1:], 5 [1:], 6 [1:]

[2:]

Result (geometric mean): 5.2254102087

3D Vectors: Norm of Two Vectors, Dot Product, Angle between Vectors

For this, I presume that the calculator is set to the desired angle setting (DRG). For the example, I have the EL-512 set to degree mode.

Store the vectors as follows:

First vector: [ register 1, register 2, register 3 ]

Second vector: [ register 4, register 5, register 6 ]

The program returns four values:

Norm of the first vector, stored in register 7

Norm of the second vector, stored in register 8

Dot product, stored in registered in M

Angle between two vectors, stored in register 9

Program:

1

Kn 1

↕

1

Kn 2

→rθ

↕

1

Kn 3

→rθ

STO 7

LOOK

1

Kn 4

↕

1

Kn 5

→rθ

↕

1

Kn 6

→rθ

STO 8

LOOK

1

Kn 1

Kn 4

x→M

1

Kn 2

Kn 5

M+

1

Kn 3

Kn 6

M+

RM

LOOK

÷

(

1

Kn 7

Kn 8

)

=

cos⁻¹

STO 9

Example:

First vector: [ 70, 64, 36 ]

Second vector: [ 55, 18, 94 ]

Results:

Norm of first vector: 101.4494948

Norm of second vector: 110.3856875

Dot product: 8386

Angle: 41.50953299°

Hope you enjoyed this trip down memory lane. Did you have or do you have a Sharp EL-512 or any similar calculator?

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.

Spotlight: Commodore P50

Spotlight: Commodore P50

Quick Facts

Model: P50

Company: Commodore

Timeline: 1978

Type: Scientific, Programming

Memory: 24 Steps

Order of Operations? No

Battery: 1 x 9-volt battery

Memory Registers: 1

Screen: 8 digits, red LED lights

Manual: www.wass.net/manuals/Commodore%20P50.pdf

From Kate Wasserman, Ph. D.’s website: https://www.wass.net/

This is my first Commodore calculator. The purchase included the calculator a manual, which is available from Kate Wasserman’s website above.

Calculating With the P50

Even though the P50 is a larger sized calculator, the calculator feels light weight. The keys are a pleasure to press.

The set of the P50’s functions is a set of basic of scientific calculators:

* Arithmetic functions

* 1/x, x^2, √x. The power function is missing.

* Logarithmic and exponential functions: log, 10^x, ln, e^x

* Trigonometric Functions: sin, cos, tan, arcsin, arccos, arctan, π key.

* Factorial of positive integer: [ n! ]

* Integer part: [ INT ]

* Memory keys: store, recall, product, sum, exchange. We only get one memory register on the P50.

Every function is a primary key except the inverse the inverse trigonometric functions, which are accessed by the [ arc ] key first.

The P50 operates in Chain mode. That is, operations happen in the order of the keys pressed, without regard to the order of operations.

Example:

9 [ × ] 7 [ + ] 8 [ = ] returns 71.

8 [ + ] 9 [ × ] 7 [ = ] returns 119.

There are no parenthesis keys, hence for more complex calculations, the use of the memory key is needed.

Powers and Roots

The P50 is missing the power function. The manual suggests that powers are calculated by the following keystroke sequence:

y^x: y [ ln ] [ × ] x [ = ] [ e^x ]

y^(1/x): y [ ln ] [ × ] x [ 1/x ] [ = ] [ e^x ]

Alternatively:

y^x: y [ log ] [ × ] x [ = ] [ 10^x ]

y^(1/x): y [ log ] [ × ] x [ 1/x ] [ = ] [ 10^x ]

Example:

5^8: 5 [ ln ] [ × ] 8 [ = ] [ e^x ]; returns 390,625

5^(1/8): 5 [ ln ] [ × ] 8 [ 1/x ] [ = ] [ e^x ] returns 1.2228445.

Other function sequences:

Absolute Value, abs(x): [ x^2 ] [ √x ]

4^th Power, x^4: [ x^2 ] [ x^2 ]

Cube, x^3: [ STO ] [ x^2 ] [ x^2 ] [ ÷ ] [ RCL ] [ = ] (memory is used)

Sign Function, x ≠ 0, sgn(x): [ STO ] [ x^2 ] [ √x ] [ ÷ ] [ RCL [ = ] (memory is used)

Fraction Part, frac(x): [ STO ] [ - ] [ RCL ] [ INT ] [ = ] (memory is used)

Programming

The P50 has a 24-step capacity. There are no merged keystrokes with exceptions:

* The arcsin, arccos, and arctan key sequences ( [ arc ] [ sin ], [ arc ] [ cos ], [ arc ] [ tan ]) are merged.

* The [ GOTO ] key is followed by a two digit address. In this case any steps 0 through 9 are preceded by a zero (00 -09).

The low amount of programming steps and the one memory register to work with, the P50 programming module is good for short, quick repeated calculations. The programming keys available are:

[ lrn ]: Learn/(Run) Mode Toggle. In run mode you are only shown the step number and nothing else.

[ R/S ]: Run/Stop

[ SSTP ]: Single Step key. However, it only works in run mode, executing program steps one step at a time. This is the most annoying quirk of the P50, almost making it programming in the blind calculator. There are no key codes with each step, and they really should be.

[ GOTO ] ##: Directs the P50 to go to step 00-23. The two digit number after a GOTO counts as one step.

There are three skip functions. If the test is true, the program either:

* Skips the next step or

* Skips the next two steps if the step that follows the test is a GOTO.

[ SKZ ]: Skip if the number in the display is zero. (skip if x = 0)

[ SKN ]: Skip if the number in the display is negative. (skip if x < 0)

[ SKP ]: Skip if the number in the display is positive or zero. (skip if x ≥ 0)

In order for the program to stop and display results and reset for the next calculation, we need the following sequence of steps:

R/S

GTO 00

Otherwise, the program could run unintentionally forever.

There is no clear program button, but programs are not kept when the P50 is turned off.  

P50: Sample Programs

Round to the nearest hundredths (2 decimal places)

× 1 0 0 + . 5 INT ÷

1 0 0 = R/S GTO 00

Examples:

36.728 → 36.73

54.616 → 54.62

40.303 → 40.30 (display shows 40.3)

Permutation

nPr = n! / (n – r)!

STO - R/S n! 1/x

× RCL n! = R/S

GTO 00

To Run: (GTO 00): n R/S r R/S nPr

Examples:

n = 20, p = 8: 5.0791104 E09 (5,079,110,400)

n = 12, p = 6: 665,280

n = 13, p = 7: 8,648,640

Volume of a Sphere

V = 4 * π * r^3 / 3

STO x^2 x^2 ÷ RCL

× π × 4 ÷

3 = R/S GTO 00

Examples:

r = 11.1: 5,728.7193

r = 6: 904.77868

r = 10: 4,188.7902

Pseudo Random Number Generator

#_i = frac( (π + #_i) ^ 5) = M – int (M) (where M = e^( 5 * ln (#_i + π))

+ π = ln ×

5 = e^x - INT

= R/S GTO 00

To run: seed R/S, R/S, R/S, ….

Examples:

0.552 → 0.4561281 → 0.7501096 → 0.6846062

0.838 → 0.1437699 → 0.7511575 → 0.8871519

Modulus of Positive Numbers

a > 0, b > 0, a mod b = a – int(a / b) * b

÷ R/S STO = -

INT × RCL = R/S

GTO 00

To run: a R/S b R/S result

Examples:

19 mod 7 = 5

288 mod 17 = 16

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.