checkdigit calculation for HP-17b

[Thomas Klemm]

(07-28-2015 06:48 PM)Gerson W. Barbosa Wrote:  It intrigues me a bit why this more simple algorithm works

From Cadastro de Pessoas Físicas

Code:

v[1] := (1×cpf[1] + 2×cpf[2] + 3×cpf[3] + 4×cpf[4] + 5×cpf[5] + 6×cpf[6] + 7×cpf[7] + 8×cpf[8] + 9×cpf[9]) mod 11

Code:

v[2] := (9×(1×cpf[1] + 2×cpf[2] + 3×cpf[3] + 4×cpf[4] + 5×cpf[5] + 6×cpf[6] + 7×cpf[7] + 8×cpf[8] + 9×cpf[9]) +
                       1×cpf[2] + 2×cpf[3] + 3×cpf[4] + 4×cpf[5] + 5×cpf[6] + 6×cpf[7] + 7×cpf[8] + 8×cpf[9]) mod 11

We can do the multiplication by 9 mod 11:

Code:

v[2] := (9×cpf[1] + 7×cpf[2] + 5×cpf[3] + 3×cpf[4] + 1×cpf[5] - 1×cpf[6] - 3×cpf[7] - 5×cpf[8] - 7×cpf[9] +
                    1×cpf[2] + 2×cpf[3] + 3×cpf[4] + 4×cpf[5] + 5×cpf[6] + 6×cpf[7] + 7×cpf[8] + 8×cpf[9]) mod 11

This gives us:

Code:

v[2] := (9×cpf[1] + 8×cpf[2] + 7×cpf[3] + 6×cpf[4] + 5×cpf[5] + 4×cpf[6] + 3×cpf[7] + 2×cpf[8] + 1×cpf[9]) mod 11

But then you will say that v[1] wasn't calculated correctly:

Code:

v[1] := v[1] mod 11
v[1] := v[1] mod 10

Thus in case that v[1] = 10 we will get 0 instead of 10.
This is corrected with this step in your program:

Code:

  t:=t+9*((s Mod 11) div 10);

Kind regards
Thomas