"I_C

We begin far apart with simple ideas and with little knowledge of the path before us,

But we shall meet at the middle and handshake our grand triumph." --David Cole (aka primework123)

Stage 0:

Keywords: Decomposition of n = p * q, primes are the atoms of the integers, base-10 and the finite field, [tex]Z_{2 }[/tex], are sub-atomic levels of the integers,...

Relevant Keywords: Carry-bit/number input, Residue bit/number, Carry-bit/number output, Optimization and Synchronization (or Handshaking), ...

If we let s, t[tex]\in[/tex] [tex]Z_{10 }[/tex] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, the product, s* t, can be easily computed as follows:

Carry-bit input or [tex]c_{i0 }[/tex] = 0 (always);

Residue bit or [tex]r_{0 }[/tex] = s * t (mod 10);

Carry-bit output or [tex]c_{o0 }[/tex] = (s * t - [tex]r_{0 }[/tex])/10 ;

Simple Example: Let s = 4 and s = t, then we have the following results:

[tex]c_{i0 }[/tex] = 0 (always);

[tex]r_{0 }[/tex] = s * t (mod 10) = 12 (mod 10) = 2;

[tex]c_{o0 }[/tex] = (s * t - [tex]r_{0 }[/tex])/10 = ( 12 - 2 ) /10 = 10/10 =1;

So, s * t = 12.

... End of Stage 0.

David Cole

(aka primework123)

Please support my research work at: https://www.gofundme.com/david_cole

Thank you! Thank Lord GOD!