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A full-adder is a combinational circuit (memory-less) that forms the arithmetic sum of two input bits...

A full-adder is a combinational circuit (memory-less) that forms the arithmetic sum of two input bits (say a and b) and a carry in (Cin, so three input bits total). The full-adder provides two outputs in the form of the (S)um and the carry out (Cout). The input bits a and b represent the terms to be added, but the full-adder needs to also consider the carry in bit, too.

  1. Construct a truth table for the Full-Adder
  2. Construct a K-Map for the sum output (S) and derive the most reduced Boolean equation from your map.
  3. Construct a K-Map for the carry out (Cout) and derive the most reduced Boolean equation from your map.
  4. Using Boolean Algebra, prove that S can be expressed as the XOR of the three inputs. Said another way, show the steps in Boolean Algebra that prove:

S = a XOR b XOR c

  1. Using algebraic manipulation (like in the previous problem), prove that:

Cout = ab + (a XOR b)*Cin

  1. Draw the circuit for the full-adder in Logisim (Or otherwise); copy and paste a screen shot here.
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