Number Systems and Circuits for AdditionBinary AdditionSlide 3Binary AddersBinary Half-Adder CircuitBinary Full-Adder CircuitSlide 7Number Systems and Circuits for AdditionLecture 5Section 1.5 Wed, Jan 19, 2005Binary AdditionAddition of binary digits produces a sum bit and a carry bit.p q sum carry1 1 0 11 0 1 00 1 1 00 0 0 0Binary AdditionThe sum bit is p q.The carry bit is p q.Binary AddersA binary half-adder adds two bits and produces a sum bit and a carry bit.A binary full-adder adds two bits and a carry-in bit and produces a sum bit and a carry-out bit.Binary Half-Adder CircuitDesign circuits for p q and p q.Consolidate them into one circuit, if possible.Binary Full-Adder CircuitInput Outputp q c-in s c-out1 1 1 1 11 1 0 0 11 0 1 0 11 0 0 1 00 1 1 0 10 1 0 1 00 0 1 1 00 0 0 0 0Binary Full-Adder CircuitUse two half-adders to add the bits two at a time.Add p and q, producing s1 and c1.Add c-in and s1, producing s and c2.Add c1 and c2, producing c-out.•c1 c2 produces c-out.Design the
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