Casio fx-3650p and fx-50FH: Integer Parts and Fractional Parts

Casio fx-3650p and fx-50FH: Integer Parts and Fractional Parts

Programming can be a pain if the popular functions INT (integer part) and FRAC (fractional part) are not present.  Here is a sample routine to extract the parts for the Casio fx-3650p and fx-50FH.  The key is to take advantage of:

* Switching to and from Fix 0 mode and

* Using the RND (round the number in the display) to the number of decimal places specified in the Fix mode

You can modify or incorporate the sample code to fit your needs.  This basic scheme should work on any programming calculator with at least 2 variable registers and the RND function.   Due to the syntax of RND, the programs for the fx-3650p and fx-50FH are slightly different.  

The following results will be stored in the following variables:

A = ABS(A)

B = INTG(A)

C = FRAC(A)

M = SGN(A) 

Casio fx-3650P:  Integer and Fractional Parts  (53 steps)

?→A:  \\ ask for a number 

A ÷ √( A ²) → M:  \\ sign of A

√( A ²) → A:  \\ absolute value

Fix 0:  \\ go into Fix 0 mode

RND:  \\ round answer in the display

Ans → B:

Norm 1:  \\ back into floating mode

B > A ⇒ B - 1 → B:  \\ adjust B if necessary

BM → B ◢  \\ integer portion

AM - B → C  \\ fractional portion

Casio fx-50FH: Integer and Fractional Parts  (51 steps)

?→A:  \\ ask for a number 

A ÷ Abs(A) → M:  \\ sign of A 

Abs(A) → A:  \\ absolute value

Fix 0:  \\ go into Fix 0 mode

Rnd(A) →  B :  \\ round A and store in B

Norm 1:  \\ back into floating mode

B > A ⇒ B - 1 → B:  \\ adjust B if necessary

BM → B ◢  \\ integer portion

AM - B → C  \\ fractional portion

Test 1:   13.913

Results:

B = 13 (integer portion)

C = 0.913 (fractional portion)

Test 2: -741.185

Results:

B = -741 (integer portion)

C = -0.185 (fractional portion)

If you find this helpful and can incorporate this routine into future programs.  To those calculators with fractional  and integer part commands: you're awesome.  

Eddie

This blog is property of Edward Shore, 2016 

Casio fx-50FH Programs: Ellipses

Casio fx-50FH Programs: Ellipses

Hello everyone!  It is good to be back.  What a crazy year this has been so far.  

Introduction

The programs assume that the center of the ellipse is (0,0).  They can be adopted on the current Casio graphing calculators and fx-5800p as well (some adjustments may be necessary).  

Casio fx-50FH Ellipse Program 1: Area, Eccentricity, Focal Points

(61 steps)

Text after double slash marks (\\) are comments.  

?→X:   \\ radius on X-axis

?→Y:   \\ radius on Y-axis

X≥Y ⇒ Goto 0:

X→B: Y→A: Goto 1:  \\ X ≥ Y 

Lbl 0: X→A: Y→B:   \\ X < Y

Lbl 1: πAB ◢  \\ calculate area

√(1 - B ² ÷ A ²) ◢   \\ calculate eccentricity 

√(A ² - B ²)  \\ focal distance 

Test 1: X = 6.63, Y = 1.86

Area:  38.74149229

Eccentricity: 0.959841462

Focal Distance: 6.36748895

Hence the focal points are (-6.36748895, 0) and (6.36748895, 0)

Test 2: X = 2.99, Y = 5.06

Area: 47.53041189

Eccentricity: 0.806738152

Focal Distance: 4.08209505

Hence the focal points are (0, -4.08209505) and (0, 4.08209505)

Casio fx-50FH Ellipse Program 2: Points on the Ellipse, and distance to center (0,0)

(54 steps)

You specify A, B, and D.  D represents the number of steps.  Degree mode is set. 

?→A: ?→B: ?→D:

Deg: For 0→M To 360 Step 360 ÷ D:  \\ set up loop

M ◢  \\ display angle 

A cos(M) → X ◢   \\ display X coordinate 

B sin(M) → Y ◢  \\ display Y coordinate

√( X ² + Y ² ) ◢  \\ distance to center

Next  \\ end loop

Test: A = 3.25, B = 2.75, D = 6

Results: (angle, X, Y, distance)

0.000, 3.250, 0.000, 3.250

60.000, 1.625, 2.382, 2.883

120.000, -1.625, 2.382, 2.883

180.000, -3.250, 0.000, 3.250

240.000, -1.625, -2.382, 2.883

300.000, 1.625, -2.382, 2.883

360.000, 3.250, 0.000, 3.250

Until next time, 

Eddie

This blog is property of Edward Shore, 2016

HP 12C Programming Part II: Weekday Number, Gross Up Calculation

HP 12C Programming Part II:  Weekday Number, Gross Up Calculation

Here is Part II of the HP 12C programming series.

HP 12C Weekday Number

This program determines (“extracts” in a sense) the workday number of a given date.  I have this program set to work properly after January 6, 1800, which was a Monday.  The results translate as follows:

1 = MON

2 = TUE

3 = WED

4 = THU

5 = FRI

6 = SAT

7 = SUN

The HP 12C is assumed to be use the United States date format (M.DY – [ g ] [ 5 ]).

Program:

STEP	CODE	KEY	COMMENT
01	1	1
02	48	.	Decimal point
03	0	0
04	6	6
05	1	1
06	8	8
07	34	X<>Y
08	43, 26	ΔDYS	Days between dates function
09	7	7
10	10	÷
11	43, 24	FRAC
12	7	7
13	20	*
14	1	1
15	40	+
16	43, 33, 00	GTO 00

Input:  Date in MM.DDYYYY format, [R/S]

Result: Date indicator

Test 1: May 22, 1999.

Input:  5.221999 [R/S]

Result:  6 (Saturday)

Test 2:  July 11, 2016

Result:  1 (Monday)

HP 12C Gross Up Calculation

We have to pay a person, and the person lives outside of your tax jurisdiction (outside of your state or the United States).  Tax withholding may be required.  However, you or someone else that is requesting the payment wants the face amount.  In order to give the face amount and fulfill the tax requirement at the same time, the payment is must be grossed up.

Link to the Investopedia article:  http://www.investopedia.com/terms/g/gross-up.asp

Formulas:

Gross up Amount = Face Amount/(1 – Tax Rate%)

Amount of Tax = Gross up Amount – Face Amount

Program:

STEP	CODE	KEY	COMMENT
01	44, 0	STO 0	Store Tax Rate
02	34	X<>Y
03	44, 1	STO 1	Store Face Value
04	45, 0	RCL 0
05	1	1
06	25	%
07	1	1
08	30	-
09	16	CHS
10	45, 1	RCL 1
11	34	X<>Y
12	10	÷
13	31	R/S	Display Gross up Amount
14	45, 1	RCL 1
15	30	-
16	43, 33, 00	GTO 00	Display Tax

Input:  face value, [R/S], tax rate, [R/S]

Result: gross amount, [R/S], tax

Part 1:  Face Value:  $1,000, Tax Rate:  30%.

Input:  1000 [R/S], 30 [R/S]

Result:  1428.57 [R/S], 428.57 [R/S]

The gross up amount is $1,428.57 (total amount to be paid), and corresponding tax is $428.57.

Part 2:  Face Value:  $2,500, Tax Rate:  7%.

Input:  2500 [R/S], 7 [R/S]

Result:  2688.17 [R/S], 188.17 [R/S]

The gross up amount is $2,688.17 (total amount to be paid), and corresponding tax is $188.17.

Another note, I will be taking some time off and plan to be back within two weeks.  I want to thank all of you readers and those who commentators, this blog would not be the success that it is without you.  Enjoy summer (or winter if you are in the Southern Hemisphere) and we'll talk again.  

Eddie

This blog is property of Edward Shore, 2016. 

HP 12C Programming Part I: Modulus, GCD, PITI

HP 12C Programming Part I:  Modulus, GCD, PITI 

The last stop (for now) on my 1980s tour is the Hewlett Packard HP 12C calculator, one of the most popular financial calculators of all time.  The HP 12C was first manufactured in 1982 and has been seen ever since.

Today, there are two versions of the HP 12C:  the original and the Platinum.  The original is RPN only and has 99 programming steps of memory.  The Platinum edition, first released in 2003, has room for 400 steps and includes Algebraic mode.

In this series, I'll concentrate on the 1982 classic.  Albeit, using one manufactured this decade, the processing speed in today's HP 12C's compared to those produced in the 1980s is tremendous.

HP 12C Modulus

This program takes the modulus of two numbers:

Y MOD X = X * FRAC(Y/X)

In this program, X > 0 and Y > 0.

STEP	CODE	KEY
01	10	÷
02	43, 36	LST x
03	34	X<>Y
04	43, 24	FRAC
05	20	*
06	43, 33, 00	GTO 00

Input:  Y [ENTER] X [R/S],  

Result:  Y MOD X

Test 1:  124 MOD 77  = 47

Test 2: 3862 MOD 108 = 82

HP 12C Greatest Common Divisor (GCD)

This program calculates the greatest common divisor of two integers.  You can enter the two integers in either order.

Program:

STEP	CODE	KEY	COMMENT
01	43, 34	X≤Y	Determine which integer is greater
02	34	X<>Y
03	44, 1	STO 1	R1 = max(X,Y)
04	34	X<>Y
05	44, 0	STO 0	R0 = min(X,Y)
06	45, 1	RCL 1	Begin Euclidian division routine
07	45, 1	RCL 1	Recall R1 twice
08	45, 0	RCL 0
09	10	÷
10	43, 25	INTG
11	45, 0	RCL 0
12	20	*
13	30	-
14	43, 35	X=0
15	43, 33, 21	GTO 21
16	34	X<>Y
17	44, 1	STO 1
18	34	X<>Y
19	44, 0	STO 0
20	43, 33, 06	GTO 06
21	45, 0	RCL 0
22	43, 33, 00	GTO 00

Input:  integer [ENTER] integer [R/S]

Result: GCD

Test 1:   GCD(142,25)

Input:  142 [ENTER] 25 [R/S]

Result: 1

Test 2:  GCD(2555, 1365).   Result: 35

HP 12 PITI (Principal, Interest, Taxes, Insurance)

Here is a simple program that calculates the payment (principal and interest) while taking property taxes and insurance in consideration.  Property taxes and insurance are assumed to be combined as an annual amount.  Payments are assumed to be on a monthly basis.

Program:

STEP	CODE	KEY	COMMENT
01	1	1
02	2	2
03	10	÷	(tax + ins)/12
04	44, 0	STO 0
05	14	PMT
06	14	PMT	Need to press PMT twice.  Second press calculates payment.
07	45, 0	RCL 0
08	16	CHS
09	40	+	PITI is assumed to be an outflow
10	43, 33, 00	GTO 00	Ends the program

Input:

Number of Years [ g ] [ n ] (12*)

Annual Interest Rate [ g ] [ i ] (12÷)

Loan Amount [PV]

Annual Property Insurance and Taxes [R/S]

Result:  PITI

Test:  Calculate PITI for a 30-year loan of $205,000.  The rate on the loan is 4.1%.  Annual insurance and property taxes are estimated to be $1,102.50.

Input:  30 [ g ] [ n ] (12*), 4.1 [ g ] [ i ] (12÷), 205000 [PV], 1102.50 [R/S]

Result:  -1,082.43  (PITI = $1,082.43)

This is blog is proerpty of Edward Shore, 2016.