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26 NAND Gates

Consider a smaller subproblem,

f = AB + BC + CD  // 3 pairs

  = $\overline{\overline{AB + BC + CD}}$

  = $\overline{{\overline{AB}.\overline{BC}.\overline{CD}}}$

So we can realize f in 4 NAND Gates, each for $\overline{AB}$, $\overline{BC}$, $\overline{AC}$ and f.

We can generalize the formula as " number of pairs + 1 (for f)"  NAND gates to realize a similar kind of function.

Now, in f = AB+BC+CD+DE+................+YZ , we have 25 pairs. So we require 26 NAND gates.

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