(11C) Digit Sum
01-16-2018, 08:52 AM (This post was last modified: 01-16-2018 08:53 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 518 Joined: Dec 2016
(11C) Digit Sum
In mathematics, the digit sum of a given integer is the sum of all its digits
The digit sum of 84001 is calculated as 8+4+0+0+1 = 13

Code:
 LBL A 0 STO 1 R↓ LBL 1 1 0 ÷ FRAC STO+1 LSTx INT X≠0 GTO 1 10^x 10^x RCL 1 x RTN

Gamo
01-16-2018, 07:16 PM
Post: #2
 Dieter Senior Member Posts: 2,398 Joined: Dec 2013
RE: (11C) Digit Sum
Gamo, this is one of your best-coded programs. And it uses a clever algorithm: it sums 1/10 of the digits and finally multiplies the result by 10. Which is obtained by two consecutive 10x commands (0 → 1 → 10).

I like such little tricks (altough a plain 10 is faster and doesn't require more steps). Let me add one more: If you want to zero data register 1 without affecting the stack, a simple STO 1 STO–1 does it. Saves one step here.

By the way...

(01-16-2018 08:52 AM)Gamo Wrote:  In mathematics, the digit sum of a given integer is the sum of all its digits
The digit sum of 84001 is calculated as 8+4+0+0+1 = 13

And the digit sum of this (the digital root) is 4 (simply run the program once more).
But you can calculate this directly, it's simply n mod 9. Or 9 if this yields zero (and n≠0).

Dieter
01-20-2018, 08:14 AM
Post: #3
 wawa Junior Member Posts: 29 Joined: Dec 2013
RE: (11C) Digit Sum
I like this program very much too.

I've made a little modification to operate only in the stack, avoiding the use of the register 1.
Code:
 LBL A 0 X<>Y LBL 0 1 0 ÷ FRAC LST X R↓ + R^ INT X̣!=0? GTO 0 R↓ 1 0 x RTN

and here is a HP42s version of this program with a little modification in the way I use the stack
Code:
 00 { 38-Byte Prgm } 01▸LBL "SumDg" 02 0 03 10 04▸LBL 00 05 STO÷ ST Z 06 RCL ST Z 07 IP 08 X=0? 09 GTO 01 10 X<> ST T 11 FP 12 STO+ ST Z 13 R↓ 14 GTO 00 15▸LBL 01 16 R↓ 17 X<> ST Z 18 + 19 × 20 RTN 21 END
01-20-2018, 09:23 AM
Post: #4
 Dieter Senior Member Posts: 2,398 Joined: Dec 2013
RE: (11C) Digit Sum
(01-20-2018 08:14 AM)wawa Wrote:  and here is a HP42s version of this program with a little modification in the way I use the stack
...

This one is shorter and requires less stack acrobatics. Works on the 41 and the 42s and also preserves Y.

Code:
01 LBL"DSUM" 02 0 03 X<>Y 04 LBL 01 05 10 06 / 07 FRC 08 ST+ Y 09 X<> L 10 INT 11 X≠0? 12 GTO 01 13 + 14 10 15 * 16 END

Note for 42s users: Y and L are stack registers (ST Y and ST L).

Dieter
01-20-2018, 10:10 AM (This post was last modified: 01-20-2018 11:57 AM by Gamo.)
Post: #5
 Gamo Senior Member Posts: 518 Joined: Dec 2016
RE: (11C) Digit Sum
Here is a "4 Digits Random Number to the Digit Sum" for Practice adding digits.

To Run:
Press A and calculator briefly show 4 digits number then return 0.
Try to add the digits in your head and check to see the number and answer.

Press R/S shown number and X<>Y show answer. Press X<>Y again will cycle to number and answer.

Program:
Code:
 LBL A FIX 0 RAN# EEX 4 x INT STO 0 PSE CLx RCL 0 0 STO 1 Roll Down LBL 1 10 / FRAC STO+1 LSTx INT X≠0 (TEST 0) GTO 1 10^x 10^x RCL 1 x STO 2 CLx R/S RCL 2 RCL 0 R/S

Gamo
01-20-2018, 05:21 PM (This post was last modified: 01-20-2018 06:49 PM by Dieter.)
Post: #6
 Dieter Senior Member Posts: 2,398 Joined: Dec 2013
RE: (11C) Digit Sum
(01-20-2018 10:10 AM)Gamo Wrote:  Press A and calculator briefly show 4 digits number ...

The program generates a number between 0 and 9999, so this number may have one, two, three or four digits. A four-digit number, i.e. between 1000 and 9999, is generated this way:

Code:
RAN# 9 EEX 3 x INT EEX 3 +

Also, why do you waste another register (R2) for the digit sum? It is already stored in R1 (OK, 1/10 of it).

Code:
... GTO 1 1 0 ST0x1 CLx R/S RCL 1 RCL 0 RTN

Every byte counts. ;-)

Dieter
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