Casio fx-3650P vs. Casio fx-3650P II: Programs

Here are four programs that are done with both the fx-3650P and fx-3650P II to illustrate some programming similarities and differences.

When we start a new program with the fx-3650P II, we are prompted to the choose the appropriate mode at the beginning:

COMP (main calculation with real numbers)

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

Left:  Casio fx-3650P (2002), Right:  fx-3650P II (2013)

Program 1: Exponential Distribution

This program calculates:

PDF: e^(-X ÷ A)

CDF (lower tail): 1 - e^(-X ÷ A)

where:

A = 1/λ parameter (i.e. average waiting time, time for an event to occur/fail/succeed)

X = time parameter

fx-3650P, 25 bytes:

? → A : ? → X :

e(-X ÷ A) ÷ A ◢

1 – e(-X ÷ A)

fx-3650P II, 25 bytes:

? → A : ? → X :

e^(-X ÷ A) ÷ A ◢

1 – e^(-X ÷ A)

Example 1:

Inputs: A = 100, X = 50

Outputs: 6.065306597E-3 (*10^-3), 0.39346934

Example 2:

Inputs: A = 50, X = 3

Outputs: 0.01883529, 0.058235466

Program 2: Using Newton’s Method to get the real root of the cubic equation that is closest to zero:

x^3 + A * x^2 + B * x + C = 0

Using Newton’s Method:

x1 = x0 – f(x0) / f’(x0) [ let y = f(x0) / f’(x0) ]

x1 = x0 - (x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B)

fx-3650P, 72 bytes:

? → A : ? → B : ? → C : 0 → X :

Lbl 0 :

(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :

√(Y²) → D :

X – Y → X :

D ≥ 1E-8 ⇒ Goto 0 : X

√(Y²) returns Abs(Y) in Comp mode.

D is set up to be the control variable, where

D = abs((x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B))

fx-3650PII, 67 bytes:

? → A : ? → B : ? → C : 0 → X : 1 → Y :

While Abs(Y) ≥ 1E-8 :

(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :

X – Y → X :

WhileEnd: X

We could have used the derivative function (d/dx) but typing out the derivative took less room.

Example 1: X³ + 2X² – 5X + 4 = 0

Inputs: A = 2, B = -5, C = 4

Output: -3.663076827

Example 2: X³ – 3X² + 9X + 6 = 0

Inputs: A = -3, B = 9, C = 6

Output: -0.5481911635

Program 3: Sum of the polynomial: Σ((AX + B)^C, X = 1 to Y)

fx-3650P, 57 bytes:

0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :

Lbl 0 :

(AX + B)^C M+ : X + 1 → X : X > Y ⇒ Goto 1 : Goto 0 :

Lbl 1 : M

fx-3650PII, 41 bytes:

0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :

For 1 → X To Y : (AX + B)^(C) M+ : Next : M

Example 1: Σ((5X – 3)^2, X = 1 to 8)

Inputs: A = 5, B = -3, C = 2, Y = 8

Output: 4092

Example 2: Σ((2X + 1)^3, X = 1 to 10)

Inputs: A = 2, B = 1, C = 3, Y = 10

Output: 29160

Program 4: Complex Roots of Unity

x^n = 1

where:

x = cos(2 * m * π / n) + i * sin(2 * m * π / n) = r * e^(2 * m * i / n)

m = 0 to n – 1, i = j = √-1

fx-3650P, 47 bytes:

Switch to complex mode. The CMPLX indicator will be displayed but not shown as a step.

Rad : ? → A : 0 → B :

Lbl 0 :

cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢

1 + B → B : A > B ⇒ Goto 0 : 1

We must have an else condition when the jump command is used, that is why the second one is there. Also, that one “indicates” the end.

fx-3650PII, 34 bytes:

Rad : ? → A :

For 0 → B To A :

cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢

Next : 1

The second one “indicates” the end and can be omitted.

In complex mode, the real and imaginary parts are displayed on part at a time. A settle R←→I indicator displays at the right hand side of the screen. Switch between seeing the parts by pressing [ SHIFT ] [ EXE ].

Example 1: x^3 = 1

Input: A = 3

Outputs:

1 + 0 i

-0.5 + 0.866025403 i

-0.5 - 0.866025403 i

Example 2: x^5 = 1

Input: A = 5

Outputs:

1 + 0 i

0.309016994 + 0.951056516 i

-0.809016994 + 0.587785252 i

-0.809016994 - 0.587785252 i

0.309016994 - 0.951056516 i

Eddie

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.

Spotlight: Casio fx-3650PII and Comparison with the fx-3650P and fx-50FH (II)

 Spotlight: Casio fx-3650PII and Comparison with the fx-3650P and fx-50FH (II)

Quick Facts: fx-3650P II

Model: fx-3650P II

Company: Casio

Type: Solar Scientific Algebraic, Programmable with battery backup: 1 x LR44/AP76

Memory: 7 memory registers: A, B, C, D, X, Y, M (M has memory addition and subtraction)

Programming Memory: 390 bytes, 4 program slots

Years in Production: 2013 (per fx-3650PII manual) to Present

Primary Market: Asia

Display: 10 digits

Casio’s fx-3650PII web page: https://www.casio.com/intl/scientific-calculators/product.FX-3650PII/

The fx-3650P II is the successor to the fx-3650P. The interface, menu structure, and the display of the fx-3650PII match that of Casio’s other current dual-powered programmable, the fx-50FH series (current as this blog entry fx-50FHII).

The modes available for the fx-3650 PII are:

COMP: This is our main calculator mode, with all the scientific functions available.

CMPLX: Complex Number mode: features complex arithmetic, conjugate, modulus (Abs), argument, rectangular/polar conversions.

BASE: Base conversions of integers between the four well known bases: binary, decimal, octal, and hexadecimal. The mode contains the standard Boolean operations.

SD: Single variable statistics (formerly named standard deviation mode)

REG: Regressions/two-variable statistics. A is usually the y-intercept and B is the slope.

The regressions available are:

Linear: y = a + b * x

Logarithmic: y = a + b * ln x

e-Exponential: y = a * e^(b* x)

Power: y = a * x^b

Inverse: y = a + b / x

Quadratic: y = a + b * x + c * x^2

ab-Exponential: y = a * b^x

Casio fx-3650P vs Casio fx-3650P II

Both of these calculators are (or were) sold primarily in Asia.  They are dual-powered: solar with a backup battery.  

Casio fx-3650P

*  Years Released: 2002 – about 2013

*  Pressing [ e^x ] types e. e(n) takes e^n not e × n.

*  Program space: 4 programs, total of 360 bytes

*  Absolute value function (Abs) is available in complex number mode (CMPLX) mode only.

The [ MODE ] key:  

Page 1: 1: COMP, 2: CMPLX

Page 2: 1: SD, 2: REG, 3: BASE

Page 3: 1: PRGM, 2: RUN, 3: PCL

Page 4: 1: Deg, 2: Rad, 3: Grad

Page 5: 1: Fix, 2: Sci, 3: Norm

Page 6: 1: Disp (display setup, fractions, rectangular/polar in complex mode)

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

Program Functions (P-CMD), which is a limited set:

Page 1: ? (prompt), → (store), : (separator), ◢ (output/pause)

Page 2: ⇒ (jump/if-then-else), =, ≠, >, ≥

Page 3: Goto, Lbl

To exit program editing mode, press [ MODE ], [ MODE ], select 2 for RUN

fx-3650 PII

*  Production: 2013 – current? (not in United States, but in Asia)

*  Pressing [ e^x ] types e^(. This is gives a clear indication that we are using a function (exponential).

*  Program space: 4 programs, total of 390 bytes

*  Absolute value function (Abs) is available in all modes.

The [ MODE ] key: 

Page 1: 1: COMP, 2: CMPLX, 3: BASE

Page 2: 4: SD, 5: REG, 6: PRGM

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

The SET UP menu, use arrows to navigate:

Page 1, Angles: 1: Deg; 2: Rad; 3: Gra

Page 2, Fraction: 1: a b/c; 2: d/c

Page 3, Complex Number: 1: a+bi; 2: r∠Θ

Page 4, Statistical Frequency: 1: FreqOn; 2: FreqOff

Page 5, Contrast Setting

Operating structure has adopted the structure of the fx-50FH (a past model, it’s since been updated to the fx-50FHII).

Program Commands (P-CMD), available on both the fx-3650PII and fx-50FH series:

Page 1: ? (prompt), → (store), : (separator), ◢ (output/pause)

Page 2: ⇒ (jump/if-then-else), =, ≠

Page 3: >, <, ≥, ≤

Page 4: Goto, Lbl

Page 5: While, WhileEnd

Page 6: Next, Break

Page 7: For, To, Step

Page 8: Else, IfEnd

Page 9: If, Then

To exit program editing mode, press [ MODE ], [ MODE ], select 2 for RUN

When entering a new program, you are prompted to select the type of program at the start: COMP, CMPLX, SD, REG, or BASE.

Casio fx-3650 PII vs. Casio fx-50FH (II)

The main difference is that the fx-3650 PII has the numerical calculus functions integration and derivative, while the fx-50 FH has a library of scientific constants and 23 built in formulas. The fx-50FH has 680 bytes of programming memory.

The next post will have four programs that are done with both the fx-3650P and fx-3650P II to illustrate the programming differences.

Eddie

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.

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.

Casio fx-3650P: Circular Segment

Casio fx-3650P: Circular Segment

Introduction

Variables:
X:  radius
Y:  angle (in degree)
C:  chord length
D:  altitude
A:  area
B:  arc length

Program 1:  Given Chord Length and Altitude

Calculate:  Radius, Angle, Area, Arc Length

? → C : ? → D : Deg :
( ( C ÷ 2 )^2 + D^2 ) ÷ ( 2D ) → X ◢
2 cos^-1 ( ( X - D ) ÷ X ) → Y ◢
X^2 ÷ 2 * ( π Y ÷ 180 - sin Y ) → A ◢
X Y π ÷ 180 → B

Example:
Input C = 8,  D = 11.75

X:  6.555851064 (radius)
Y:  284.8004594 (angle)
A:  127.5950317 (area)
B:  32.58720643 (arc length)

Program 2:  Given Radius and Angle

Calculate:  Chord Length, Altitude, Area, Arc Length

? → X : ? → Y : Deg :
2 * sin(Y ÷ 2) → C ◢
2 X ( sin(Y ÷ 4))^2 → D ◢
X^2 ÷ 2 * ( π Y ÷ 180 - sin Y ) → A ◢
X Y π ÷ 180 → B

Example:
Input X = 17.25, Y = 204

C:  33.74609223 (chord length)
D:  20.83647667 (altitude)
A:  590.2462124 (area)
B:  61.41813638 (arc length)

Source:

John W Harris and Horst Stocker.  Handbook of Mathematics and Computational Science Spring:  New York.  2006 ISBN 978-0-387-94746-4

Announcement

I am going to have surgery this week and my family is having medical issues.  I will be taking some time off in the next few weeks.  Tomorrow I have a special post reviewing the classic TI-30 from 1976. Take care everyone and thank you so much for your support.  I love doing this blog. 

Eddie

All original content copyright, © 2011-2020.  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.

Fun With the Casio fx-3650P: Program Collection 5/29/2018

Fun With the Casio fx-3650P

Previous Entries

5/11/2014:

http://edspi31415.blogspot.com/2014/05/casio-fx-3650p-programming.html

1. Circular Sectors
2. Stopping Sight Distance
3. Resistors in Parallel
4. Net Present Value
5. Rod Pendulum
6. Vectors: Dot and Cross Products

10/27/2015:

http://edspi31415.blogspot.com/2015/10/casio-fx-3650p-programming-sequel.html

1.  Combination with Replacement

2.  Great Circle (Distance in km) 

3.  Orbital Speed and Period 

4.  Eccentricity and Area of an Ellipse

5.  Super Factorial

6.  Escape Velocity 

7.  Finance: Payment of a Monthly Mortgage

8.  Wind Chill Factor

9.  Speed of Sound in Dry Air 

7/2/2017:

https://edspi31415.blogspot.com/2017/07/fun-with-casio-fx-3650p.html

1.  Modulus Function

2.  Normal CDF

3.  Sum:  Σ (AX + B)^C,  from X = 0 to X = Y

4.  Sun Altitude and Azimuth Based on the Vernal Equinox

5.  Trapezoid: Midsegment, Height, and Area

6.  Solar Irradiance

7.  General a list of X Random Integers from 0 to Y

Contents for this Blog Entry:

1. kth Derivative of f(x) = y^n

2. Sight Reduction Table

3. Distance Off at Second Bearing by Two Bearings and Run

4. Hydraulic Cylinder:  Force and Flow

5. Mass Held by Two Strings

6. Atwood Machine: Tension and Acceleration

kth Derivative of f(x) = x^n

This program calculates the kth derivative of x^n. Using the variables of the Casio fx-3650p, this program calculates:

‘d^A/dx^A X^B.  A is an integer, where B and X are real numbers.

Program (47 steps):

? → A : ? → B : → X : 1 → C : Lbl 1 : CB → C : B – 1 → B : A – 1 → A : A ≠ 0 ⇒ Goto 1 : CX ^ B

Input order:  A = order, B = power, X = x

Examples:

A = 3, B = 2.5, X = 3.  Result:  1.08253175473

A = 4, B = 6, X = 1.  Result:  360

Sight Reduction Table

The program calculates altitude and azimuth of a given celestial body.

Inputs:

A: Local Hour Angle (LHA)

B: The observer’s latitude on Earth, north is positive, south is negative (L)

D: Declination of the celestial’s body, north is positive, south is negative (δ)

The latitude is often entered in degrees/minutes/seconds format. 

Do this using the [ ° ‘ “ ] key.   The calculator is set in Degrees program.

Formulas:

Altitude: 

H = asin (sin δ sin L + cos δ cos L cos LHA)

Zenith:

Z = acos ((sin δ – sin L sin H) ÷ (cos H cos L))

If sin LHA < 0 then Z = 360° - Z

Output variables:

C = altitude

X = zenith

Program (67 steps):

Deg : ? → A : ? → B : ? → D : sin^-1 ( sin D sin B + cos D cos B cos A ) → C ◢ cos^-1 ( ( sin D – sin B sin C ) ÷ ( cos C cos B ) ) → X: sin A > 0 ⇒ 360 – X → X : X

Source:  “NAV 1-19A Sight Reduction Table”    HP 65 Navigation Pac.  Hewlett Packard, 1974.

Distance Off at Second Bearing by Two Bearings and Run

This program calculates the distance off between to bearings. 

Input variables:

A:  first bearing

B:  second bearing

C:  run (typically in miles, distance will be in the same length unit)

Distance formula:

D = C * sin A° / sin |A° - B°|

Since the Casio fx-3650P does not have an absolute value function, the workaround    √(x^2) is used instead. 

Program (31 steps):

Deg : ? → A : ? → B : ? → C : C sin A ÷ sin ( √ (A – B) ^ 2 ) → D

Example:

A = 15°, B = 8 °, C = 1.5 miles

Result:  3.185613024 miles

(updated 7/1/2018; the result is now correct)

Source:  Henry H. Shufeldt and Kenneth E. Newcomer.  The Calculator Afloat: A Mariner’s Guide to the Electronic Calculator Naval Institute Press:  Annapolis, MD.  1980

Hydraulic Cylinders: Force and Flow

The program calculates the force and flow.

Input variables:

D:  large radius

C:  small radius, radius of the cut

X:  pressure

Y:  speed of the cylinder

Formulas:

Area: A = π (D^2 – C^2) / 4

Force: F = pressure * area = X * A

Flow:  q = velocity * area = Y * A

Program (36 steps):

? → D : ? → C : π ( D^2 – C^2 ) ÷ 4 → A : ? → X : AX ◢ ? → Y : AY

Example:

Input:

D = 8 in, C = 4 in  (8 in cylinder with a 4 in cutout), X = 68 psi, Y = 3.6 in/sec

Results:

Force:  2563.539605 lb,  Flow:  3.6 in^3/sec

Mass Held by Two Strings

The program calculates the tension of the two strings shown in the diagram above.  The tension of both strings are found by solving the following system of two equations:

cos A° * X – sin B° Y = 0

sin A° * X – cos B° * Y = M * g

Where g is Earth’s gravitation constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2

SI units are used in this program.

Program (45 steps):

Deg : ? → A : ? → B : ? → M : 9.80665 M ÷ ( tan A sin B – cos B ) → Y : Y sin B ÷ cos A → X ◢ Y

Example:

Input:

A = 43°, B = 89°, M = 16 kg

Results:

X = 234.4572201 N, Y = 171.4972763 N

Atwood Machine:  Tension and Acceleration

The program calculates the tension in the string of the Atwood Machine and the acceleration of the system.  If the acceleration is negative, the pulley is turning clockwise, otherwise it is turning counterclockwise.  The following system of equations is solved, where X is the tension of the strings and Y is the acceleration of the system.

X + A * Y = g * A

-X + B * Y = -g * B

Where g is Earth’s gravitation constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2

SI units are used in this program.

Program (45 steps):

? → A : ? → B : 9.80665 (A – B) ÷ ( A + B ) → Y : A (9.80665 – Y) → X ◢ Y

Examples:

Input:

A = 11.2 kg, B = 10.3 kg

Results:

X = 105.2367576 N, Y = 0.41051093 m/s^2

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.