Ok, say I have 6 inputs/switches. Either on or off.

A

B

C

D

E

F

And I want to turn on a light. To get it to turn on all the way, I have to turn on all 6 inputs/switches.

A+B+C+D+E+F= 1

But, if i want the light, half on, I can turn on F.

F = 1/2

A+B+C+D+E=1/2

what ratios/fractions/whatever can A,B,C,D, and E equal, so that the sum of them equals 1/2 and A<B<C<D<E

I know this is somehow a simple binary problem, but I just can't figure the math out.

I think it's like if in binary, you had 100, you have 2... but if you had 000001, what is that?

Bah, it should be simple.

EDIT: I'm going to paraprhase what I want to do.

A+B=C

A+B+C=D

A+B+C+D=E

A+B+C+D+E=F

A+B+C+D+E+F=1

F=1/2

A

B

C

D

E

F

And I want to turn on a light. To get it to turn on all the way, I have to turn on all 6 inputs/switches.

A+B+C+D+E+F= 1

But, if i want the light, half on, I can turn on F.

F = 1/2

A+B+C+D+E=1/2

what ratios/fractions/whatever can A,B,C,D, and E equal, so that the sum of them equals 1/2 and A<B<C<D<E

I know this is somehow a simple binary problem, but I just can't figure the math out.

I think it's like if in binary, you had 100, you have 2... but if you had 000001, what is that?

Bah, it should be simple.

EDIT: I'm going to paraprhase what I want to do.

A+B=C

A+B+C=D

A+B+C+D=E

A+B+C+D+E=F

A+B+C+D+E+F=1

F=1/2