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Don Shepherd · 06-18-2014, 06:53 PM

OK, you've got your old 17b or 17bii you use for all your financial needs, but now you need something to do number base conversions. There is no need to go to a scientific model, the solver is your friend.

B1 = old base (2-10)
B2 = new base (2-10)
N = number to convert
ANS = solve for this

Either B1 or B2 must be 10.

BC:ANS=\(\Sigma\)(I:0:LOG(N)\(\div\)LOG(B2):1:MOD(N:B2)\(\times\)B1^I+0\(\times\)L(N:IDIV(N:B2)))

Thomas Klemm · (This post was last modified: 06-19-2014 08:55 AM by Thomas Klemm.)

(06-18-2014 06:53 PM)Don Shepherd Wrote: BC:ANS=\(\Sigma\)(I:0:LOG(N)\(\div\)LOG(B2):1:MOD(N:B2)\(\times\)B1^I+0\(\times\)L(N:IDIV(N:B2)))

Very cool! Thanks for consistently bringing up this calculator.
You don't need MOD if you combine the calculations from successive lines.

Example: DEC → OCT

Code:

         2014

+   2 *   251

+  20 *    31

+ 200 *     3

         ----

         3736

BC:ANS=
0\(\times\)L(K:FROM-TO)
+N
+\(\Sigma\)(I:1:LOG(N)\(\div\)LOG(TO):1:
G(K)\(\times\)L(N:IDIV(N:TO))
+0\(\times\)L(K:FROM\(\times\)G(K))
)

Kind regards
Thomas

Thomas Klemm · 06-19-2014, 09:06 AM

A little shorter:

BC:ANS=
N+
(FROM-TO)\(\times\)
\(\Sigma\)(I:0:LOG(N)\(\div\)LOG(TO):1:
L(N:IDIV(N:TO))\(\times\)FROM^I
)

Don Shepherd · 06-19-2014, 01:45 PM

(06-19-2014 09:06 AM)Thomas Klemm Wrote: A little shorter:

BC:ANS=
N+
(FROM-TO)\(\times\)
\(\Sigma\)(I:0:LOG(N)\(\div\)LOG(TO):1:
L(N:IDIV(N:TO))\(\times\)FROM^I
)

Thomas, that is way cool! Thanks.

The method I chose was based on how I learned to manually convert numbers from one base to another back in computer programming school in 1968. That method is described at the bottom of this page. I just converted those manual steps to an equivalent solver equation.

I like your method also, it is simple and elegant.

Don

Thomas Klemm · 06-19-2014, 02:06 PM

(06-18-2014 06:53 PM)Don Shepherd Wrote: Either B1 or B2 must be 10.

You could set either B1 or B2 to 100. This allows conversions between HEX and DEC.

Example: CAFE_HEX
B1: 16
B2: 100
N: 12101514
ANS: 51,966

Don Shepherd · 06-19-2014, 02:36 PM

(06-19-2014 02:06 PM)Thomas Klemm Wrote:
(06-18-2014 06:53 PM)Don Shepherd Wrote: Either B1 or B2 must be 10.

You could set either B1 or B2 to 100. This allows conversions between HEX and DEC.

Example: CAFE_HEX
B1: 16
B2: 100
N: 12101514
ANS: 51,966

I am stunned! I never thought that was possible. You are a true missle-man.

Thomas Klemm · 06-19-2014, 10:15 PM

(06-19-2014 02:36 PM)Don Shepherd Wrote: I am stunned! I never thought that was possible.

It's been there for a while: Base Conversion for HP-11C

Thomas Klemm · 06-21-2014, 10:18 PM

Here's a program for the HP-12C:

Code:

01 -       36  ENTER

02 -       36  ENTER

03 -    45 15  RCL FV

04 -       10  ÷

05 -    43 25  INTG

06 -    43 13  CFo

07 -    45 15  RCL FV

08 -       10  ÷

09 -    43 25  INTG

10 -    43 35  x=0

11 - 43,33 14  GTO 14

12 -    43 14  CFj

13 - 43,33 07  GTO 07

14 -       33  R↓

15 -        1  1

16 -    45 14  RCL PMT

17 -       22  1/x

18 -       24  Δ%

19 -    44 12  STO i

20 -       33  R↓

21 -       33  R↓

22 -    42 13  NPV

23 -    45 14  RCL PMT

24 -    45 15  RCL FV

25 -       30  −

26 -       20  ×

27 -       40  +

Example: 2014₁₀ → 3736₈
10 STO PMT
8 STO FV
2014 R/S

Don Shepherd · 06-21-2014, 11:27 PM

(06-21-2014 10:18 PM)Thomas Klemm Wrote: Here's a program for the HP-12C:

Code:

01 - 36 ENTER 02 - 36 ENTER 03 - 45 15 RCL FV 04 - 10 ÷ 05 - 43 25 INTG 06 - 43 13 CFo 07 - 45 15 RCL FV 08 - 10 ÷ 09 - 43 25 INTG 10 - 43 35 x=0 11 - 43,33 14 GTO 14 12 - 43 14 CFj 13 - 43,33 07 GTO 07 14 - 33 R↓ 15 - 1 1 16 - 45 14 RCL PMT 17 - 22 1/x 18 - 24 Δ% 19 - 44 12 STO i 20 - 33 R↓ 21 - 33 R↓ 22 - 42 13 NPV 23 - 45 14 RCL PMT 24 - 45 15 RCL FV 25 - 30 − 26 - 20 × 27 - 40 +

Example: 2014₁₀ → 3736₈
10 STO PMT
8 STO FV
2014 R/S

That is just amazing, Thomas. I'm sure the creators of NPV and delta-percent on the 12c never envisioned those functions being used for number base conversions.

I tip my hat to you, you are "da man".

Thomas Klemm · (This post was last modified: 06-22-2014 12:26 AM by Thomas Klemm.)

But then I realized that the 1:1 translation of my HP-11C program was shorter. And it uses only 3 registers. However it was fun to figure it out.

Addendum:
As long as the from-base PMT doesn't change the following lines could be removed:

Code:

15 -        1  1

16 -    45 14  RCL PMT

17 -       22  1/x

18 -       24  Δ%

19 -    44 12  STO i

20 -       33  R↓

21 -       33  R↓

With this we are at the same number of lines.
Of course you still have to calculate i once and store it.

(06-21-2014 11:27 PM)Don Shepherd Wrote: That is just amazing, Thomas. I'm sure the creators of NPV and delta-percent on the 12c never envisioned those functions being used for number base conversions.

I've seen this trick in Valentin's paper: HP-12C’s Serendipitous Solver