23 February 2011

Eight-bit processor based on prime numbers


Accumulator:

Х Х Х ХХХХX —> 1 2 3 - low bits

| | | | | | | |

1713117 5 3 2 1

Register R0:

Х Х Х Х Х Х Х Х
43 41 37 31 29 23 19
__________ Primes to the processor ! (Complex for operations)

00000000 = 0 |

00000001 = 1 | “one“

00000010 = 2 | “two“

00000100 = 3 | “three“

00000110 = 4 | 3 two

00001000 = 5 | “four“

00001001 = 6 | 5 one

00010000 = 7 | “five“

00010001 = 8 | 7 one

00010010 = 9 | 7 two

00010100 = 10| 7 three

00100000 = 11| “six“

00100001 = 12| 11 one

01000000 = 13| “SEVEN“

01000001 = 14| 13 one

01000010 = 15| 13 two

01000100 = 16| 13 three

10000000 = 17| “EIGHT“

Every prime number, which is not low bit is able to be presented in more than one way.

It is always better to present one number with smaller bits.

Calculation rules

Sum:

Case А) ? no double bit:

01000100 = 16

+

00001001 = 6

=

01001101 = 22

Case B) ? the double bit is presented through lower bits:

01000100 = 16 = 13 three

+

00010100 = 10 = 7 three

=

01010100 =

+

00000100 = 00000011

=

01010111 = 26

01000000 = 13 = 13

+

01000001 = 14 = 13 one

=

01000001

+

01000000 = 00100010

=

01100011 = 27

01000001 = 14 = 13 one

+

01000010 = 15 = 13 two

=

01000011

+

01000000 = 00011000

=

00011011 = 29

We sum А and B, A>B

I. А+B=C+D , when C is a number including all significant bits no matter their repeating, and D consists only of double bits.
  1. D=E+F+… ; E, F ? numbers consisted only from one digit
E ? we begin from the highest bit making it to the lowest bits

Conclusion: Since the actual discharge means multiplication of the unit with a prime number, and because the numbers are hole, transformations II are actually bringing the numbers to end chain fractiones.

Substraction:

01000100 = 16 = 00100110 = 2+3+11

-

00001001 = 6 = 00000111 = 1 + 2 + 3

=

000010110 = 10

Substraction А from B, А>B

А and B are divided to significant bits with lower rates;

А-B = D-E ,E ?

The action is repeating until:

X=00000000 (0) или X=00000001 (1)

X=0 , the result is D

X=1, analogic -> try it yourself

Multiplication:

00001000 = 5 = 00000110 = 2+3

*

00001001 = 6 = 00000111 = 1 + 2 + 3

=

11000000 = 30 = 2*3*5 = 00000010

*

00000100

*

00001000

=

(2*3)*5

2*3

=

00000010

*

00000100

=

00000100

+

00000100

=

00000111=6

(2*3)*5

=

……….

Multiplication is alike sum !

…..

General conclusion: This kind of processor would be much faster and efficient.

Conclusion: One 9-bit processor should be much more precise at the point.

X Х Х Х ХХХХX —> 1 2 3

| | | | | | | | |

19171311 7 5 3 2 1

13 17 19 highest bits !

There is geometrical-physical matter !

1 is point, and 13+17+19=7*7 =circle*circle = Sphere