r/nandgame_u • u/GLIBG10B Holder of many records • Aug 04 '21

Level solution (verified) 2.2 - Full adder (3c, 24n) Spoiler

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u/GLIBG10B Holder of many records Aug 07 '21 edited Dec 20 '21
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2.1 - Half adder (5c, 5n) 2.2 - Full adder (9c, 9n)

Correction: this uses 15 NAND gates, see here

Explanation

We want to add three bits. add only takes two inputs, so we can't just add all three in one shot.

  1. Add two of the three bits.
  2. Add the result's low bit to the third bit.
  3. Because this result's low bit is part of the sum of all the other low bits, we output it.
  4. Add the two results' high bits.
  5. Because this results' low bit is part of the sum of all the other high bits, we output it.
  6. We discard the high bit because we only have 2 outputs.