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how to use RPN calculator to calculate manually without using program.

For example:

To find modulo: X mod Y for X > Y

Key in as follow:

Y [ENTER] [ENTER] X [X<>Y] [÷] (key in only integer part) [-] [x]

Example: 128 mod 17

17 [ENTER] [ENTER] 128 [X<>Y] [÷] display 7.5294 key in 7 [-] [x] display 9

Could be a good thread to use RPN manually sometime manual calculation is faster than using the program.

Gamo
Another example: To find GCD and LCM

To find GCD ( X, Y ) where X < Y

Setup: X [ENTER] [ENTER] [ENTER] Y [X<>Y]

Iterations: [÷] (input only integer part) [-] [x] display <1 ?

NO: [ENTER] [ENTER] [Rv] [Rv] continue Iterations

YES: [Rv] Finish (Round to an integer if necessary)

—————————————————————————

To find LCM ( X, Y)

X [ENTER] Y [x] (GCD answer) [÷]

————————————————————————-
Example: GCD and LCM of ( 555, 666 )

To find GCD

555 [ENTER] [ENTER] [ENTER] 666 [X<>Y]

[÷] Display 1.2 input 1 [-] [x] display 111 ( not <1 )

[ENTER] [ENTER] [Rv] [Rv]

[÷] Display 5.0 input 5 [-] [x] display 0 (now <1)

[Rv] display 111

——————————————————

To find LCM

555 [ENTER] 666 [x] display 369630

111 [÷] display 3330

—————————————————————
Gamo
Check out some of the application manuals for the pre-65 models on the museum doc set. This is exactly the sort of thing they do, with the human operator standing in for a program-controlled algorithm.
Dave Britten Thank You

I read the HP-45 Applications Book which provide step-by-step solutions to

More than 200 problems all with manually keys in steps that also use the

Store and Recall store registers.

According to this book my GCD and LCM solutions use much fewer steps to

Solve the same problem and this book don’t have the modulo calculation.

Next post I will show the financial problem to calculate manually by

input steps to solve for the interest [i] with known [n] [PV] and [PMT]

This will take some iterations process to the solution.

Gamo
An excerpt from REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS, 23 [12.00] - HP ADVANCED PRODUCTS DIVISION, HP-45 Applications Book, pg. 380

"For two reasons this book will have a cursory interest to readers outside its intended audience of users of HP-series calculators.
First, keystroke sequences and examples are listed alphabetically for more than two-hundred purposes, including applications from algebra, geometry, statistics and numerical methods, among other areas. With a minimal understanding of the Polish logic of HP-series calculators, most of these sequences can easily be converted to use on other scientific calculators.
Secondly and primarily, these sequences are of interest more for their nature than for their specific solution. For they illustrate particularly graphically the recent innovations and inherent limitations of nonprogrammable calculators. To illustrate the advances in calculator capacities, they include directions for such calculations as Bessel and Gamma functions, multiple linear regression,and Gauss-Legendre quadrature, and readily suggest other potential extensions of hand-calculator usage.
At the same time, even in their most efficient form the most interesting of these routines require so many keystrokes as to be impractical in real use and to discourage efforts to create counterparts for unlisted topics. The longest sequence in the book, for three-variable linear regression, requires 155 + 32n keystrokes to process n 3-tuples of data, a number so large as practically to insure key misstroking.
C. MCMANUS"

BEST!
SlideRule
Nice citation, is there a web link
Pedro
(10-30-2019 01:32 PM)PedroLeiva Wrote: [ -> ]Nice citation, is there a web link

The thread contains the text of the review in its' entirety. I scanned the article from my 'print' library then 'lifted' the text for a copy-&-paste to the forum.

BEST!
SlideRule
Manually calculate the Interest Rate for an Annuity.

Formula use to solve for [ i ] the interest rate when these three variables are known.

n - Period
PV - Present Value
PMT - Payment

f(i) = (PMT ÷ PV) + [ i ÷ 1 - (1+i)^n ]

———————————————————-

Steps: FIX 4

Setup: n [STO] 0 PMT [ENTER] PV [÷] [ENTER] [ENTER] [ENTER] [.] 1

Iterations: [ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-]

———————————————————-
Example: n = 25, PV = 2000, PMT = 203.61, i = ?

Using HP-12C result is 8.9998 or i = 9%

On the original HP-12C when calculate step to [Y^X] the screen will turn blank momentary.
and resume normal operation.

Calculate Manually:

25 [STO] 0 203.61 [ENTER] 2000 [÷] display 0.1018 [ENTER] [ENTER] [ENTER] . 1

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0916

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0903

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0900

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0900

Last two iterations got the same value based on 4 decimal places.

[EEX] 2 [x] display 9

———————————————————————————-
Note: The [.] 1 is a guess
Hint: For higher decimal place accuracy simply do more iterations.
———————————————————————————

Gamo
Calculations by hand are indeed helpful

The best collection for gcd, modulus and much more might easily be

Ball, Algorithms for RPN Calculators

If you are using an HP-41

Dearing, Calculator Tips & Routines

is very good too. That book is available as PDF on the net.

Felix
(10-31-2019 05:13 AM)Gamo Wrote: [ -> ]Manually calculate the Interest Rate for an Annuity.

Formula use to solve for [ i ] the interest rate when these three variables are known.

n - Period
PV - Present Value
PMT - Payment

f(i) = (PMT ÷ PV) + [ i ÷ 1 - (1+i)^n ]

———————————————————-

Steps: FIX 4

Setup: n [STO] 0 PMT [ENTER] PV [÷] [ENTER] [ENTER] [ENTER] [.] 1

Iterations: [ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-]

———————————————————-
Example: n = 25, PV = 2000, PMT = 203.61, i = ?

Using HP-12C result is 8.9998 or i = 9%

On the original HP-12C when calculate step to [Y^X] the screen will turn blank momentary.
and resume normal operation.

Calculate Manually:

25 [STO] 0 203.61 [ENTER] 2000 [÷] display 0.1018 [ENTER] [ENTER] [ENTER] . 1

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0916

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0903

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0900

[ENTER] [ENTER] 1 [+] [RCL] 0 [Y^X] 1 [-] [÷] [-] display 0.0900

Last two iterations got the same value based on 4 decimal places.

[EEX] 2 [x] display 9

———————————————————————————-
Note: The [.] 1 is a guess
Hint: For higher decimal place accuracy simply do more iterations.
———————————————————————————

Gamo

This works on the prime too, with some modification;
First set to fixed 4 and assuming home set to rpn mode:

1'HFormat' [SHIFT STO]
4 'HDigits' [SHIFT STO]

25'X' [SHIFT STO] 203.61 [SPACE or ENTER] 2000 [÷] display 0.1018 [ENTER] [ENTER] [ENTER] .1

[ENTER] [ENTER] 1 [+] X [X^Y] 1 [-] [÷] [-] display 0.0916

Etc..
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