How did we get the Incrementer equations?

Full Adder equations:

Sum = A xor B xor Cin

Cout = AB or Cin A or Cin B = AB or Cin (A or B)Let B = 0, Cin = 1 so that Sum = A + 1. Then equations simplify to: SUM = A xor 1 xor 0 = A xor 1 = A’  Cout = 0 or 1 (A or 0) = A.

If we want an “En” input, then we want SUM = A if En=0, else SUM = A+1 if En = ‘1’. Filling in the above equations: SUM = A En’ or A’ En = A xor En Cout = A En (note that Cout = 0 if En = 0).

The “Cout” of one bit becomes the “En” signal for the next bit!!!!

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