1. Edward Shore, HHC 2017 September 2017
Expanding the HP 12C
Edward Shore, HHC 2017
September 2017

2. Objectives
To expand the HP 12C beyond the basic and financial capabilities
Mathematical Tips and Tricks for the HP 12C
Applications

3. Assumptions
The regular/classic version of the HP 12C is used instead of the Platinum Edition
99 programming steps vs. 400 programming steps
Always RPN vs. RPN/ALG setting
Two digit vs. Three digit step markers
LST X Code (43, 36 vs. 43, 40)
No trigonometric functions are used
Fix 2 Mode (round everything to 2 decimal places) is set

4. Other Sources Polynomial Solver Polynomials: Valentin Abillo
Trig Functions
Trigonometric Functions: Valentin Abillo

5. Quick Mathematical Tips

6. Arithmetic
Multiplying by 100: [ENTER], 1, [x<>y], [%T] One key stroke less than [ENTER], 1, 0, 0, [ * ] Dividing by 100: [ENTER], 1, [ % ] Two key strokes less than [ENTER], 1, 0, 0, [ ÷ ]

7. Mathematical Functions
Absolute Value: 2, [y^x], [ g ] ( √ ) Sign Function: [ENTER], [ENTER], 2, [y^x], [ g ] ( √ ), [ ÷ ] Modulus of two positive numbers (a mod b): a, [ENTER], b, [ ÷ ], [ g ] (LSTx), [ x<>y ], [ g ] (FRAC), [ * ]

8. Mathematical Functions
Number of Digits of an integer: [ g ] (LN), [EEX], 1, [ g ] (LN), [ ÷ ], [ g ] (INTG), 1, [ + ]

9. Keying in π
The HP 12C does not have a π button, we’ll have to enter π manually or use an approximation.
Using the 10 digit approximation
This will take 11 steps, one for each digit and the decimal point.
We can use the approximation π ≈ 355/113.
355/113 = (to 5 decimal places)
This takes 8 steps: 3, 5, 5, ENTER, 1, 1, 3, ÷
Richard Nelson suggests this memory aid: take the first three odd digits twice (113355), divide last three by first three (355/113).

10. Example: Surface Area & Volume of Sphere
Step
Code
Key
Notes 01
44, 0
STO 0
Store radius in R0 02 2
Calculate surface volume 03 21
Y^X 04 4 05 20 * 06 3
Enter π 07 5 08 09 36
ENTER 10 1 11 12 13 ÷ 14 15 31
R/S
Display surface volume 16
Calculate volume 17 18
45, 0
RCL 0 19
43, 33, 00
GTO 00
Display volume, stop program execution

11. Number of Inputs Three ways to generate inputs:
Loading the stack before executing the program. This is useful when you have only one input.
Prompt for the inputs using the [R/S].
Store all the required inputs in the registers before execution. This is my preferred method when I have 3 or more inputs.

12. Using x=0 to determine choices
You can designate a memory register, such as R0, as a choice variable. For example:
Choice 0 executes function f(x)
Choice 1 executes function g(x)
And so on
Depending on program size, 2 to 4 choices could fit within program memory.
General algorithm:
RCL R#, test value, -, x=0, GTO appropriate line number

13. Example – Choices: US to SI Unit Conversion
Step
Code
Key
Notes 01
44, 0
STO 0
Store choice variable in R0 02 34
X<>Y 03
44, 1
STO 1
Store value to be converted in R1 04 05
43, 35
X=0
Conversion: lb to kg? 06
43, 33, 18
GTO 18 07
45, 0
RCL 0
Conversion: in to cm? 08 1 09 30 - 10
X=0? 11
43, 33, 27
GTO 27 12
Conversion: gal to L? 13 2 14 15 16
43, 33, 34
GTO 34 17
43, 33, 43
GTO 43
Conversion: mi to km? 18
45, 1
RCL 1
Conversion: lb to kg, flag = 0 19 20 48 .

14. Example – Choices: US to SI Unit Conversion
Step
Code
Key
Notes 21 2 22 23 4 24 6 25 10 ÷ 26
43, 33, 00
GTO 00 27
45, 1
RCL 1
Conversion: in to cm, flag = 1 28 29 48 . 30 5 31 32 20 * 33 34
Conversion: gal to L, flag = 2 35 3 36 37 7 38 8 39 40

15. Example – Choices: US to SI Unit Conversion
Step
Code
Key
Notes 41 20 * 42
43, 33, 00
GTO 00 43
45, 1
RCL 1
Conversion: mi to km, flag = 3 44 1 45 48 . 46 6 47 9 49 3 50 51

16. Use of Statistics Variables
We can use stat variables for additional analysis
The cost is that six variables will be used (R1 to R6). This leaves only four variables for inputs and outputs (R0, R7, R8, R9)
Statistics Variables
R1: n
R4: Σy
R2: Σx
R5: Σy^2
R3: Σx^2
R6: Σxy

17. Example – Simple Logistic Curve Fitting
This program uses the statistics variables, particularly Σx for R2
Curve: y = 1 / (A + B*e^(-x))
Transformation: X’ = e^(-X), Y’ = 1/Y

18. Example – Simple Logistic Curve Fitting
Step
Code
Key
Notes 01 16
CHS
Enter data 02
43, 22
e^x
Adjust X: e^-x 03 34
x<>y 04 22
1/x
Adjust Y: 1/y 05 06 49 Σ+
Enter data point, n is displayed 07
43, 33, 00
GTO 00
Stop program execution 08
Calculate b 09
43, 2 y^ 10
44, 7
STO 7 11 31
R/S
Display b 12 1
Calculate m 13 14 15 33 R↓ 17 30 - 18
44, 8
STO 8 19
Display m

19. Simulating Subroutines
The HP 12C does not have subroutine commands, but you can simulate subroutines. Here is one way to do it, if you know the subroutine will be used twice:
It is very important you plan your program in advance, with line numbers. Marking the line numbers will facilitate where the subroutine and return markings will be located.

20. Simulating Subroutines
Designate a register as a flag variable. Store 1 in the flag variable.
Enter the main portion of the program. Determine where the subroutine will be called.
Follow the subroutine call with the roll down command (R↓).
At the end of the subroutine, recall the flag variable.
Determine which round it is by recalling the flag variable. First round: flag = 1. Second round: flag = 0. Use the test x=0. If it passes, send the pointer to the second R↓. If it fails, subtract 1 from the flag variable and send the pointer to the first R↓.

21. Subroutine Example: Derivative Approximation
Step
Key
Code
Notes 01
44, 0
STO 0
Store x in R0 02 1 03
44, 3
STO 3
Set up flag variable, 2 subroutine rounds 04 05 26
EEX 06 5 07 16
CHS 08
44, 1
STO 1
Store h in R1 09
45, 0
RCL 0 10
45, 1
RCL 1 11 40 +
x+ h 12
43, 33, 23
GTO 23
Subroutine: 1st round 13 33 R↓
Return: 1st round 14
44, 2
STO 2
Store temp result, f(x + h) 15 x
Subroutine: 2nd round 17 18
44, 30, 2
STO- 2
f(x+h) – f(x) 19
45, 2
RCL 2 20

22. Subroutine Example: Derivative Approximation
Step
Key
Code
Notes 21 10 ÷
(f(x+h) – f(x))/h 22
43, 33, 00
GTO 00
Stop execution 23 36
ENTER
Subroutine begins here, f(x) 24 25 2 26
Y^X 27 34
X<>Y 28
43, 22
e^x 29 20 *
End of f(x) 30
45, 3
RCL 3
Need the next 7 steps to the end of f(x) – Check flag variable 31
43, 35
X=0 32
43, 33, 17
GTO 17
Are we in round 2? 33 1
If yes, go to 2nd return point
44, 30, 3
STO- 3
Otherwise, decrease flag variable 35 R↓
Set up display
43, 33, 13
GTO 13
Go to 1st return point

23. Additional Examples

24. Quadratic Equation Step Code Key Notes 01 45, 2 RCL 2
Start with values stored in R1, R2, R3. Calculate discriminant. 02 36
ENTER 03 20 * 04
45, 1
RCL 1 05
45, 3
RCL 3 06 07 4 08 09 30 - 10
44, 0
STO 0 11 31
R/S
Display discriminant which is stored in R0. 12 13
43, 34
X≤Y
Is 0 ≤ R0? 14
43, 33, 32
GTO 32
If so, go to step 32. 15
Complex Roots: real part 16 17 40 + 18 19
CHS

25. Quadratic Equation Step Code Key Notes 20 34 X<>Y 21 10 ÷ 2221 10 ÷ 22
44, 4
STO 4 23 31
R/S 24
43, 36
LSTx
Complex Roots: imaginary part 25
45, 0
RCL 0 26 16
CHS 27
43, 21 √ 28 29 30
44, 5
STO 5
43, 33, 00
GTO 00
Stop execution 32
45, 2
RCL 2
Real root calculations 33 35 36 40 + 37
45, 1
RCL 1 38
ENTER 39

26. Quadratic Equation Step Code Key Notes 40 10 ÷ 41 44, 4 STO 4 42 3141
44, 4
STO 4 42 31
R/S
Real root 1 43
43, 36
LSTx 44
45, 2
RCL 2 45
45, 0
RCL 0 46
43, 21 √ 47 + 48 16
CHS 49 34
X<>Y 50 51
44, 5
STO 5 52
43, 33, 00
GTO 00
Real root 2

27. Greatest Common Divisor
Step
Code
Key
Notes 01
43, 34
X≤Y
Determine which integer is greater 02 34
X<>Y 03
44, 1
STO 1
R1 = max(X,Y) 04 05
44, 0
STO 0
R0 = min(X,Y) 06
45, 1
RCL 1
Begin Euclidian division routine 07
Recall R1 twice 08
45, 0
RCL 0 09 10 ÷
Divide R1 by R0
43, 25
INTG
int(R1/R0) 11 12 20 * 13 30 -
Calculate remainder:
remainder = int(R1/R0) * R0 – R1 14
43, 35
X=0
Is remainder = 0? 15
43, 33, 21
GTO 21
If yes, go to the end 16
If not, set up for the next loop 17
Old min becomes new max, R0 → R1

28. Greatest Common Divisor
Step
Code
Key
Notes 18 34
X<>Y 19
44, 0
STO 0
Store new min 20
43, 33, 06
GTO 06
Start Euclidian division routine again 21
45, 0
RCL 0
End Result: display GCD 22
43, 33, 00
GTO 00
Stop execution

29. Binary to Decimal Conversion
Step
Code
Key
Notes 01
44, 0
STO 0
Store the binary integer, assume no sign bit 02
43, 23 LN
Determine the number of digits 03 26
EEX 04 1 05 06 10 ÷ 07
43, 25
INT 08 09 40 +
44, 2
STO 2
Store number of digits in R2 11
Initialize decimal conversion, store 0 in R1 12
44, 1
STO 1 13
44, 3
STO 3 14
45, 0
RCL 0
Conversion process 15
45, 3
RCL 3 16 17 18 19

30. Binary to Decimal Conversion
Step
Code
Key
Notes 20 34
X<>Y 21
Y^X 22 10 ÷ 23
43, 24
FRAC 24 26
EEX 25 1 * 27
43, 25
INTG 28 2 29 36
ENTER 30
45, 3
RCL 3 31 32 33
44, 40, 1
STO+ 1 35
44, 40, 3
STO+ 3
Determine the number of digits left to work with

31. Binary to Decimal Conversion
Step
Code
Key
Notes 37
45, 2
RCL 2 38 30 - 39
43, 35
X=0 40
43, 33, 42
GTO 42 41
43, 33, 14
GTO 14 42
45, 1
RCL 1
Display decimal integer 43
43, 33, 00
GTO 00

32. Thank you! Any questions?