HP 75C Program Collection

HP 75C Program Collection

Merry Christmas everyone!   I hope everyone is safe, happy, and blessed.

LAWCOS:  Law of Cosines

335 bytes

100 DISP "Law of Cosines" @ WAIT .25

105 OPTION ANGLE DEGREES

180 DISP "Θ is opp. side a" @ WAIT .25

110 INPUT "1) Side, 2) Angle? "; H

115 ON H GOTO 1000, 2000

1000 INPUT "b?, c?, Θ? "; B,C,T

1010 A=SQR(B^2+C^2-2*B*C*COS(T))

1020 DISP "a: "; STR$(A) @ END

2000 INPUT "a?, b?, c? "; A,B,C

2010 T=ACOS((B^2+C^2-A^2)/(2*B*C))

2020 DISP "Θ:"; STR$(T); "°" @ END

Example:

1) Side:  1

B = 11.78, C = 32.12, T = 60

Result:  a = 28.1440793063

2)  Angle: 2

A = 14.55, B = 12.65, C = 17.00

Result:  Θ = 56.5108780171°

SPECPOLY:  Special Polynomials

526 bytes  (10/27/2022)

1.Cheb:  Chebyshev Polynomial of the 1st order

2.Herm:  Hermite Polynomial 

3.Lagur:  Laguerre Polynomial (with α=0)

4.Legen:  Legendre Polynomial of the 1st Order

100 DISP "Polynomials:  Type?" @ WAIT .5

105 INPUT "1.Cheb 2.Herm 3.Lagur 4.Legen:"; H

110 INPUT "x? "; X

115 INPUT "order? ";N

120 A=1 @ B=X*(H=1 OR H=4)+2*X*(H=2)+(1-X)*(H=3)

300 IF N=0 THEN DISP A @ END

302 IF N=1 THEN DISP B @ END

305 FOR I=2 TO N

310 ON H GOSUB 500,505,510,515

315 A=B

320 B=C

325 NEXT I

330 DISP C

335 END

500 C=2*X*B-A @ RETURN

505 C=2*X*B-2*(I-1)*A @ RETURN

510 C=((2*(I-1)+1-X)*B-(I-1)*A)/I @ RETURN

515 C=((2*I-1)*X*B-(I-1)*A)/I @ RETURN

Source:

Davidson, James J.  "Chebyshev Polynomials, First & Second Kind, Tn(x) & Un(x)", "Hermite Polynomials, H(n); n≥n", "Laguerre Polynomials, Generalized, Ln^(α)(x)", "Legendre Functions, First & Second Kinds, Pn(x) & Qn(x)"  ENTER 65 NOTES  Vol. 3 No. 8 September 1976  pp. 11-12

Examples:

x = 11, order = 6

1.  Cheb:  55989361

2.  Herm: 106439224

3.  Lagur: -35.5902777778

4.  Legen: 25289461

ENGINE:  Automotive Engine Mathematics

630 bytes (10/27/2022)

100 DISP "Engine Math" @ WAIT .5

110 INPUT "# cylinders? "; N

120 DISP "Solve for?" @ WAIT .25

125 INPUT "1)DSP, 2)STROKE, 3)BORE "; H

130 IF H#1 THEN INPUT "DSP? "; D

135 IF H#2 THEN INPUT "STROKE? "; S

140 IF H#3 THEN INPUT "BORE? "; B

145 IF H=1 THEN LET D=PI/4*B^2*S*N

150 IF H=2 THEN LET S=D/(PI/4*B^2*N)

155 IF H=3 THEN LET B=SQR(D/(PI/4*S*N))

160 DISP "DPS= "; D @ STOP

165 DISP "STORKE= "; S @ STOP

170 DISP "BORE= "; B @ STOP

205 INPUT "RPM? (y/n) "; I$

210 IF UPRC(I$)="N" THEN 400

300 INPUT "RPM? "; R

310 P=S*R/6

320 E=R*D*.85/3456

350 DISP "Piston Speed="; P @ STOP

360 DISP "St. Carb CFM= "; E @ STOP

370 INPUT "Again? (y/n) "; I$ 

375 IF UPRC(I$)="Y" THEN 300

400 DISP "Done."

Source:

Lawlor, John.  Auto Math Handbook.  Calculations, Formulas, Equations, and Theory for Automotive Enthusiasts.  HP Books:  Berkeley Publishing Group:  New York, NY.  1991.  ISBN 1-55788-020-4

LINREG:  Linear Regression

568 bytes (10/31/2022)

100 DISP "y=mx+b" @ WAIT .5

110 S0=0 @ S1=0 @ S2=0 @ S3=0 @ S4=0 @ S5=0

120 DISP 'Σ+ Σ- Calc'

130 K$=KEY$ @ IF K$='' THEN 130

140 IF K$="+" THEN H=1 @ GOTO 200

150 IF K$="-" THEN H=-1 @ GOTO 200

160 IF UPRC$(K$)='C' THEN 400

170 GOTO 130

200 INPUT 'x,y? '; X,Y

210 S0=S0+H @ S1=S1+H*X @ S2=S2+H*Y

220 S3=S3+H*X^2 @ S4=S4+H*Y^2 @ S5=S5+H*X*Y

230 DISP S0 @ WAIT .5 @ GOTO 120

400 B=(S5-S1*S2/S0)/(S3-S1^2/S0)

440 A=(S2-B*S1)/S0

450 R=B*SQR((S0*S3-S1^2)/(S0*S4-S2^2))

470 DISP 'type cont...' @ WAIT .5

500 DISP 'SLP=';B @ STOP

510 DISP 'ITC=';A @ STOP

520 DISP 'CORR=';R

Instructions:

Press + to add data.  Separate  x and y with a comma.

Press - to delete data.  Separate x and y with a comma.

Press C to determine the slope, intercept, and correlation.

Example:

Data:

5, 4.066

8, 4.125

11, 4.202

18, 4.293

21, 4.349

ITC ≈ 3.99046

SLP ≈ 0.01719

CORR ≈ 0.99376

Source:

Hewlett Packard.  HP 12C User Guide  Edition 4.  San Diego, CA  2004.

SIMPSON:  Integral Using Simpson’s Rule Approximation

size varies - around 300 bytes

∫ FNF(X) dX from X = a to X = b

Line 100 is where you have to define your function (of X). 

100 DEF FNF(X) = [define f(x) here]

115 OPTION ANGLE RADIANS

120 INPUT "a? ";A

125 INPUT "b? ";B

130 INPUT "# parts (even)? ";N

135 T=FNF(A)+FNF(B)

140 H=(B-A)/N

145 FOR I TO N-1

150 IF FP(I/2)=0 THEN 155 ELSE 160

155 T=T+2*FNF(A+I*H) @ GOTO 165

160 T=T+4*FNF(A+I*H)

165 NEXT I

170 T=T*H/3

175 DISP "Integral = ";T

Examples:

For both examples, n = 24

FNF(X)= 2*X^2+3,  a = 1, b = 6, result:  158.333333333

FNF(X)=2*COS(X), a = 0, b = .785398163398, result:  1.41421357139  (exact √2)

Happy Holidays everyone!

Next post will be on New Years' Eve:  December 31, 2022.

Eddie 

All original content copyright, © 2011-2022.  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. 

Proving Chebyshev Polynomial Closed Formulas for n = 0, n = 1, and n = 2

Proving Chebyshev Polynomial Closed Formulas for n = 0, n = 1, and n = 2

Chebyshev Polynomials of the First Kind

Recurrence Definition:

T_0(x) = 1

T_1(x) = x

T_n+1(x) = 2 * x * T_n(x) - T_n-1(x)

Closed Definition:

T_n(x) = 1/2 * [ (x - √(x^2 - 1))^n + (x + √(x^2 - 1))^n ]

Let: w = √(x^2 - 1)

T_n(x) = 1/2 * [ (x - w)^n + (x + w)^n ]

n = 0

T_0(x) 

= 1/2 * [ (x - w)^0 + (x + w)^0 ]

= 1/2 * [ 1 + 1 ] 

= 1

n = 1

T_1(x)

= 1/2 * [ (x - w)^1 + (x + w)^1 ]

= 1/2 * [ x - w + x + w ]

= 1/2 * [ 2 * x]

= x

n = 2

T_2(x)

= 1/2 * [ (x - w)^2 + (x + w)^2 ]

= 1/2 * [ x^2 - 2*w + w^2 + x^2 + 2*w^2 + w^2 ]

= 1/2 * [ 2 * x^2 + 2 * w^2 ]

= x^2 + x^2 - 1

= 2 * x^2 - 1

Chebyshev Polynomials of the Second Kind

Recurrence Definition:

U_0(x) = 1

U_1(x) = 2 * x

U_n+1(x) = 2 * x * U_n(x) - U_n-1(x)

Closed Definition:

U_n(x) = [ (x + √(x^2 - 1))^(n + 1) - (x - √(x^2 - 1))^(n + 1) ] ÷ [ 2 * √(x^2 - 1) ]

Let: w = √(x^2 - 1)

U_n(x) = [ (x + w)^(n + 1) - (x - w)^(n + 1) ] ÷ [ 2 * w ]

n = 0

U_0(x)

= [ (x + w)^(1) - (x - w)^(1) ] ÷ [ 2 * w ]

= [ x + w - x + w ] ÷ (2 * w)

= (2 * w) ÷ (2 * w)

= 1

n = 1

U_1(x)

= [ (x + w)^(2) - (x - w)^(2) ] ÷ [ 2 * w ]

= [ (x^2 + 2 * x * w + w^2) - (x^2 - 2 * x * w + w^2) ] ÷ (2 * w)

= [ 4 * x * w ] ÷ (2 * w)

= 2 * x

n = 2

U_2(x)

= [ (x + w)^(3) - (x - w)^(3) ] ÷ [ 2 * w ]

= [ x^3 + 3*x^2*w + 3*x*w^2 + w^3 - (x^3 - 3*x^2*w + 3*x*w^2 - w^3)] ÷ [ 2*w ]

= [ x^3 + 3*x^2*w + 3*x*w^2 + w^3 - x^3 + 3*x^2*w - 3*x*w^2 + w^3] ÷ [ 2*w ]

= [ 6*x^2*w + 2*w^3 ] ÷ [ 2*w ]

= [ 6*x*√(x^2 - 1) + 2*(x^2 - 1)^(3/2) ] ÷ [ 2*√(x^2 - 1)  ]

= [ 6*x*√(x^2 - 1) + 2*(x^2 - 1)*√(x^2- 1) ] ÷ [ 2*√(x^2 - 1)  ]

= [ 6*x*√(x^2 - 1) + 2*(x^2 - 1)*√(x^2- 1) ] ÷ [ 2*√(x^2 - 1)  ]

= [ 6*x*√(x^2 - 1) + (2*x^2 - 2)*√(x^2- 1) ] ÷ [ 2*√(x^2 - 1)  ]

= [ (8*x - 2)*√(x^2 - 1) ] ÷ [ 2*√(x^2 - 1)  ]

= 4*x^2 - 1

Good that the closed formulas hold up, at least for n = 0, 1, 2.   The closed formulas would be good if you don't want to use recurrence relations.  

Sources:

"Chebyshev polynomials"  Wikipedia.   https://en.wikipedia.org/wiki/Chebyshev_polynomials  Last Updated July 20, 2022.  Last Accessed June 21, 2022

Oldman, Keith, Jan Myland, & Jerome Spainer  An Atlas of Functions: with Equator, the Atlas Function Calculator  2nd Edition   Springer:  New York, NY.  2009  ISBN 978-0-387-48806-6

Eddie

All original content copyright, © 2011-2022.  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 HP 42S

Fun With the HP 42S

Previous Links:

HP 42S Programming Part I:  Matrix Column Sum, GCD, Error Function:  http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-i-matrix-column.html

HP 42S Programming Part II:  Dew Point, Ellipse Area and Eccentricity, Easy Transverse:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-ii-dew-point.html

HP 42S Programming Part III: Numerical Derivative, Recurring Sequences, Fractions:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-iii-numerical.html

HP 42S Julian Date

Given month, day, year, and university time (Greenwich), the Julian date is calculated.  For January 1, 2000 at 12:00 AM, the date is 2,451,545.5.

00 {141-Byte Prgm}

01 LBL “JULDATE”

02 “MONTH”

03 PROMPT

04 STO 01

05 “DAY”

06 PROMPT

07 STO 02

08 “4 DIGIT YEAR”

09 PROMPT

10 STO 03

11 “UT TIME”

12 PROMPT

13 STO 04

14 367

15 RCL* 03

16 STO 00

17 9

18 RCL+ 01

19 12

20 ÷

21 IP

22 RCL+ 03

23 4

24 ÷

25 7

26 *

27 IP

28 STO -00

29 RCL 01

30 9

31 –

32 7

33 ÷

34 RCL+ 03

35 100

36 ÷

37 IP

38 3

39 *

40 4

41 ÷

42 IP

43 STO- 00

44 275

45 RCL* 01

46 9

47 ÷

48 IP

49 STO+ 00

50 RCL 02

51 STO+ 00

52 1721028.5

53 STO+ 00

54 RCL 04

55 24

56 ÷

57 STO+ 00

58 RCL 00

59 END

Example:

Input:  May 8, 2017, 03:00 UT.  Result:  2457881.6250

HP 42S Sun Approximate Declination, Altitude, and Azimuth

Original Post:  http://edspi31415.blogspot.com/2013/06/hp-35s-sun-altitude-azimuth-solar-pond.html

Input:  Days after the vernal equinox (typically March 21), Earth’s latitude (north/south), number of hours after local noon (example:  for 7 AM, enter -5.  For 7 PM, enter 7).

00 { 147-Byte Prgm }

01 LBL “SUNAA”

02 DEG

03 “DAYS AFTER EQ.”

04 PROMPT

05 STO 00

06 “LATTITUDE”

07 PROMPT

08 STO 01

09 “HRS AFTER NOON”

10 PROMPT

11 STO 02

12 0.9856

13 RCL* 00

14 SIN

15 23.45

16 *

17 STO 04

18 COS

19 RCL 01

20 COS

21 *

22 15

23 RCL* 02

24 COS

25 *

26 RCL 01

27 SIN

28 RCL 04

29 SIN

30 *

31 +

32 ASIN

33 STO 05

34 SIN

35 RCL 01

36 SIN

37 *

38 RCL 04

39 SIN

40 –

41 RCL 05

42 COS

43 RCL 01

44 COS

45 *

46 ÷

47 ACOS

48 STO 06

49 RCL 04

50 “DECLINATION”

51 AVIEW

52 STOP

53 RCL 05

54 “ALTITUDE”

55 AVIEW

56 STOP

57 RCL 06

58 “AZIMUTH”

59 AVIEW

60 END

Example:

Input:  100 days after the vernal equinox, 43.72° N, about 12 noon (T = 0)

Results:  Declination ≈ 23.1888°, Altitude:  69.4688°, Azimuth: 0.0002°

 HP 42S Chebyshev Polynomial

The trigonometric definition is used to calculate T_n(x):

For |x| > 1, cosh (n * acosh x)

For |x| ≤ 1, cos (n * acos x)

00 {42-Byte Prgm}

01 LBL “CHEBY”

02 “N”

03 PROMPT

04 STO 00

05 “X”

06 PROMPT

07 STO 01

08 ABS

09 1

10 X≥Y?

11 GTO 00

12 RCL 01

13 ACOSH

14 RCL* 00

15 COSH

16 GTO 01

17 LBL 00

18 RCL 01

19 ACOS

20 RCL* 00

21 COS

22 LBL 01

23 END

Examples:

T_4(2) (n = 4, x = 2).  Result:  97

T_4(0.5)  (n = 4, x = 0.5)  Result:  -0.5

HP 42S Pulley

There are two weights in a pulley system, held by a rope has a negligible contribution.  The program uses SI units (kg, m, s, with g = 9.80665 m/s^2).  The simultaneous equations solve for acceleration (m/s^2) and tensions:

T – m1 * a = m1 * g

T + m2 * a = m2 * g

Source:  HP 22S Science Student Applications.  Edition 1.  Corvallis, Oregon.  May 1988

00 {161-Byte Prgm}

01 LBL “PULLEY”

02 “MASS 1 (KG)”

03 PROMPT

04 STO 01

05 “MASS 2 (KG)”

06 PROMPT

07 STO 02

08 9.80665

09 STO 00

10 2

11 ENTER

12 2

13 DIM “MAT1”

14 INDEX “MAT1”

15 1

16 STOEL

17 J+

18 RCL 01

19 +/-

20 STOEL

21 2

22 ENTER

23 1

24 STOIJ

25 1

26 STOEL

27 J+

28 RCL 02

29 STOEL

30 2

31 ENTER

32 1

33 DIM “MAT2”

34 INDEX “MAT2”

35 RCL 00

36 RCL* 01

37 STOEL

38 I+

39 RCL 00

40 RCL* 02

41 STOEL

42 RCL “MAT1”

43 INVRT

44 RCL “MAT2”

45 *

46 STO “MAT3”

47 INDEX “MAT3”

48 RCLEL

49 “T”

50 AVIEW

51 STOP

52 I+

53 RCLEL

54 “a”

55 AVIEW

56 END

Example:  m1 = 32 kg, m2 = 56 kg

Result:  tension = 399.3981, a = 2.6745 m/s^2

 HP 42S Rotation Matrix

R = [[ cos θ, -sin θ ],[ sin θ, cos θ ]]

00 {138-Byte Prgm}

01 LBL “ROTATE2”

02 DEG

03 “ANGLE °”

04 PROMPT

05 STO 00

06 1

07 ENTER

08 2

09 DIM “MAT1”

10 INDEX “MAT1”

11 “X0”

12 PROMPT

13 STOEL

14 J+

15 “Y0”

16 PROMPT

17 STOEL

18 2

19 ENTER

20 2

21 DIM “MAT2”

22 INDEX “MAT2”

23 RCL 00

24 COS

25 STOEL

26 J+

27 RCL 00

28 SIN

29 +/-

30 STOEL

31 2

32 ENTER

33 1

34 STOIJ

35 RCL 00

36 SIN

37 STOEL

38 J+

39 RCL 00

40 COS

41 STOEL

42 RCL “MAT1”

43 RCL “MAT2”

44 *

45 STO “MAT3”

46 INDEX “MAT3”

47 RCLEL

48 “X1”

49 AVIEW

50 STOP

51 J+

52 RCLEL

53 “Y1”

54 AVIEW

55 END

Example:

Input:  [3, -2], at an angle θ = 40°

Result:  [ 1.0126, -3.4605 ]

 Always fun working with the classic HP 42S!

Eddie

This blog is property of Edward Shore

Programming with the Radio Shack EC-4004

Programming with the Radio Shack EC-4004

(Another milestone: this is blog #600! I can't thank you all enough!) 

To see my retro review of this calculator I did two years ago, click here:

http://edspi31415.blogspot.com/2014/09/retro-radio-shack-ec-4004.html

The Radio Shack EC-4004 calculator’s programming mode is AOS (algebraic operating system).  Rarely you see a calculator with AOS any more (think the Casio fx-260 and Texas Instruments TI-30A), but it used to be prominent operating system with RPN.   In AOS, the uniary functions (trigonometric, logarithmic, factorial, for example) are entered after you enter the number.  Hence:  14 [ln] calculates ln(14) ≈ 2.639057329.

The storage of the EC-4004 is a mere 38 steps which can be distributed into two program slots.  That is not a lot.  Furthermore, if you enter numeric constants, each digit counts a step.  Remember, the display does NOT display the key, so be careful when entering programs.  There are a few program commands:

RTN ([INV] [ 9 ]):  Returns program control the first step (beginning). 

X ≤ M ([INV] [ 8 ]):  If the display is less than or equal to M, return to the first step.  Otherwise, go to the next step.

X > 0 ([INV] [ 7 ]): If the display is greater than 0, return to the first step.  Otherwise, go to the next step.

ENT ([RUN] in learn mode):  Prompt for a number.  The next step is to put a “placeholder” number as long as it will be valid in calculations.  Since each digit counts as a step, try to use placeholder numbers like 0, 1, or 2.  I’m not sure if the placeholder number is merged with ENT.  You can instead, use Kin or Min to store the entry in memory.

HLT ([INV] [RUN]): Halts the program to display immediate results.  Think of it as the PAUSE command.

X<>K ([INV] [Kout]): Exchange with a memory register.  The EC-4004 has six memory registers, plus one additional independent memory register (M).

[Kin] and [Kout] is your store and recall, respectively.

On to the list of sample programs!  Anything after double slashes (\\) is a comment. The hashtag (#) stands for placeholder number.

Area of a Regular Polygon

Formula:  (n*s^2)/(4*tan(180°/n)), n = number of sides, s = side length

MODE,  4 \\ sets Degree mode

ENT \\ prompt for n

#  \\ enter a placeholder number

Min \\ store in M

*

ENT \\ prompt for s

#  \\ placeholder number

X^2

÷

(

4

*

(

180

÷

MR \\ recall n

)

TAN

)

=

Test 1:  n = 6, s = 2.6,  result 17.56299519

Test 2:  n = 10, s = 3.87, result 115.2353964

 Sum of f(x)

In particular, Σ x^2 + 1 from x = 1 to M.  M is the upper limit.  You can adapt this to include any f(x), but remember you’ll only have 26 steps to work with for f(x).  Your variable for f(x) is register 1 (use [Kout], 1)

Before running, store the upper limit minus 1 in M, 0 in both registers 1 and 2.  (0, [ Kin ], 1; [ Kin ], 2).  Register 1 is your counter, register 2 is your sum.   In Summary:

M = upper limit – 1, Register 1 = 0, Register 2 = 0

Kout 1  \\ recall register 1 and add one

+

1

=

Kin 1

X^2 \\ f(x) starts here

+

1

=   \\ end f(x) with equals

+   \\ add result to register 2

Kout 2

=

Kin 2

Kout 1 \\ put register 1 in the display

X≤M   \\ is X≤M? If so, go to the beginning

Kout 2 \\ display sum

Test 1:  If the upper limit is 5, store 4 in M.  Result:  60

Test 2:  If the upper limit is 8, store 7 in M.  Result:  212

Payment of a Loan (with no balloon)

Formula:  PMT = PV / ((1 – (1 + r)^-n)/r)

Store the following amounts before running:

K1 = PV, present value or loan amount

K2 = n, number of payments.  Example: For 30 years for monthly payments, store 360 in K2.

K3 = r, periodic interest rate as a decimal.  Example: For 6% compounded monthly, enter 0.06/12 in K3.

Kout 1 \\ recall PV

÷

(

(   

1

-

(

1

+

Kout 3  \\ recall r

)

X^Y

Kout 2 \\ recall n

+/-

)

÷

Kout 3

)

=

Test 1:  K1 = 200,000, K2 = 360, K3 = 0.055/12.  Result:  1,135.58

Test 2:  K1 = 234,000, K2 = 360, K3 = 0.038/12.  Result:  1,090.34

Easy Traverse Calculation

Calculates the new point knowing the original coordinates, direction, and angle of travel.  The angle 0° comes from due east and rotates counterclockwise (see diagram below). 

Store before hand:

K1 = original coordinate easting (E, x)

K2 = original coordinate northing (N, y)

Distance is stored in K3 and angle is stored K4.  At the completion of the program, the new coordinates are stored in K1 and K2, respectively, to allow chain calculations.

MODE 4 \\ degrees mode

Kout 1

+

ENT \\ prompt for distance

# \\ placeholder number

Kin 3

*

ENT \\ prompt for angle

# \\ placeholder number

Kin 4

COS

=

Kin 1

HLT \\ display new easting coordinate

Kout 2

+

Kout 3

*

Kout 4

SIN

=

Kin 2 \\ display new northing coordinate

Test:  E0 = 10,000,  N0 = 10,000

Given distance = 110, angle = 126°,  E1 ≈ 9,935.343, N1 ≈ 10,088.992

Continuing,

Given distance = 150, angle = 30°, E2 ≈ 10,065.247, N2 ≈ 10,163.992

Measuring Dew Point (in degrees Celsuis)

Formula (source:  http://ag.arizona.edu/azmet/dewpoint.html ): 

W = 237.3 * V/(1 – V)

V = (ln H + (17.27*C)/(237.3+C))/17.27

Where:

H = relative humidity, store as a decimal (Example:  for 55.8% store 0.558 in K1)

C = temperature in degrees Celsius

Store before hand:  H in register 1 (K1), C in register 2 (K2). 

This program illustrates a perfect example of the effect of the limited programming space.  During the calculation, 17.27 and 237.3 are stored in K3 and K4, respectively to save program space.  And believe me, we’ll need every bit of it.

Kout 1 \\ H

LN

+

17.27

Kin 3

*

Kout 2 \\ C

÷

(

237.3

Kin 4

+

Kout 2

)

=

÷

Kout 3

Min // store V in M

*

Kout 4

÷

(

1

-

MR

)

=

Remember K1 = H, K2 = C

Test 1:  H = 51% (0.51), C = 27°C, Result ≈ 16.0003°C

Test 2:  H = 46% (0.46), C = 85°F = 29.44444444°C, Result ≈ 16.6110°C

Chebyshev Polynomial of the First Kind, for -1<x<1

Formula for -1<x<1:  T_n(x) = cos(n * acos x)   (source: Wolfram, http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html, see line 44)

ENT \\ prompt for x

#  \\ placeholder number

COSˉ¹

*

ENT \\ prompt for n

#  \\ placeholder number

=

COS

Test 1:  T_2(0.25) = -0.875  (x = 0.25, n = 2)

Test 2:  T_3(-0.68) = 0.782272  (x = -0.68, n = 3)

That is a small collection of programs for the EC-4004.  If you want me to do more, let me know.  Until then, have a great day everyone and stay safe!

Eddie

This blog is property of Edward Shore, 2016