NAND Equivalents | A Drop In The Digital Ocean

These are the sixteen selection patterns from here implemented in terms of S7:
nand-equivalents

In terms of familiar functions, S7 is NAND. So all sixteen selections written as NAND functions would be:


  S0   (NAND (NAND $1 (NAND $1 $1)) (NAND $1 (NAND $1 $1)))
  S1   (NAND (NAND (NAND $1 $1) (NAND $2 $2)) (NAND $1 (NAND $1 $1)))
  S2   (NAND (NAND (NAND $1 $1) $2) (NAND $1 (NAND $1 $1)))
  S3   (NAND $1 $1)
  S4   (NAND (NAND $1 (NAND $1 $2)) (NAND $1 (NAND $1 $1)))
  S5   (NAND $2 $2)
  S6   (NAND (NAND (NAND $1 $1) $2) (NAND $1 (NAND $1 $2)))
  S7   (NAND $1 $2)
  S8   (NAND (NAND $1 $2) (NAND $1 $2))
  S9   (NAND (NAND $1 $2) (NAND (NAND $1 $1) (NAND $2 $2)))
 S10   (NAND (NAND $1 $2) (NAND $2 $2))
 S11   (NAND $1 (NAND $1 $2))
 S12   (NAND (NAND $1 $1) (NAND $1 $1))
 S13   (NAND (NAND $1 $1) $2)
 S14   (NAND (NAND $1 $1) (NAND $2 $2))
 S15   (NAND $1 (NAND $1 $1))))

 Note that S10 can also be written more simply as $1 and S12 as $2.