What comes next?

[Thomas Klemm]

(10-15-2024 01:34 PM)Gil Wrote:  My next question is if I may ask: what is the code algorithm you used in your first post to get the binomial coefficient?

Let me again add some comments:

Code:

00 { 24-Byte Prgm }         ; a_n
01 1                        ; 1 a_n
02 RCL+ 00                  ; n+1 a_n
03 STO 00                   ; n=n+1 a_n
04 X<>Y                     ; a_n n
05 ENTER                    ; a_n Σa=a_n n
06 GTO 01                   ; jump to label 01
07▸LBL 00                   ; repeat
08 RCL- IND ST Z            ; Δa_k=a_{k+1}-a_k Σa k
09 STO+ ST Y                ; Δa_k Σa=Σa+Δa_k k
10▸LBL 01                   ; a_k Σa k
11 STO IND ST Z             ; R[k]=a_k
12 DSE ST Z                 ; a_k Σa k=k-1
13 GTO 00                   ; until k==0 
14 R↓                       ; Σa
15 END

We keep the increasing number of elements \(n\) in register 00.
Let's assume we're at the situation of post #4 and we want to add 35.

The difference is calculated in register X while the sum for the next value is calculated in register Y:

\(
\begin{array}{|l|l|l|}
\hline
X & Y & Z \\
\hline
35 & 35 & 6 \\
15=35-20 & 50=35+15 & 5 \\
5=15-10 & 55=50+5 & 4 \\
1=5-4 & 56=55+1 & 3 \\
0=1-1 & 56=56+0 & 2 \\
0=0-0 & 56=56+0 & 1 \\
\hline
\end{array}
\)

Meanwhile the counter in register Z is decremented until it is 0.

---

I suggest to give Free42 a try.
You can copy and paste the program when the simulator is in program mode: PRGM.
Switch back and clear the registers with CLEAR ▼ CLRG.
And then just follow the example.
Press ▼ to single step through the program.