Boolean Expression

A B C'D'E'F' v
A B'C'D'E'F  v
A'B C'D'E'F' v
: : : : : :
<absolute bucketload of boolean expressions>
: : : : : :
A'B'C'D'E F

bool nOf(int n, bool[] bs)
{
    foreach(bool b in bs)
    {
      if((n -= b ? 1 : 0) <= 0) break;
    }
    return n == 0;
}

expressions = [A, B, C, D, E, F, G ]
numTrue = len(filter(None, expressions)

$expressions = array(A, B, C, D, E, F, G);
$numTrue = count(array_filter($expressions));

(A  &  B &  C & ~D & ~E) |
(A  &  B & ~C &  D & ~E) |
(A  &  B & ~C & ~D &  E) | ...
(~A & ~B &  C &  D &  E)

2 : a&(b|c|d|e|f) | b&(c|d|e|f) | c&(d|e|f) | d&(e|f) | e*f
3 : a&(b&(c|d|e|f) | c&(d|e|f) | d&(e|f) | e*f) | b&(c&(d|e|f) | d&(e|f) | e*f) | c&(d&(e|f) | e*f) | d&e&f

bool AofB(int n, bool[] bs)
{
   if(bs.length == 0) return false;
   if(n == 0) return true;

   foreach(int i, bool b; b[0..$-n])
      if(b && AofB(n-1,b[i+1..$]) return true;

   return false;
}

bool AofB(int n, bool[] bs)
{
   foreach(bool b; bs) if(b && --n == 0) return true;
   return false;
}

Basic Half-Adder

A, B : 1st 2nd bits
O, C : unit output and carry to next unit

O := A xor B;
C := A and B;

(A && B) || (A && C) || ... || (D && E) || (D && F) || (E && F)

#{x | x <- {A, B, C, D, E, F} | x} = 2

#{...}

{x | x <- {A, B, C, D, E, F} | x}