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Number Systems and Circuits for Addition

Explore binary addition principles and design binary half-adder and full-adder circuits. Learn to handle carry bits for accurate computation.

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Number Systems and Circuits for Addition

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  1. Number Systems and Circuits for Addition Lecture 5 Section 1.5 Thu, Jan 26, 2006

  2. Binary Addition • Addition of binary digits produces a sum bit and a carry bit.

  3. Binary Addition • The sum bit is p q. • The carry bit is p  q.

  4. Binary Adders • A 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.

  5. Binary Half-Adder Circuit • Design circuits for p q and p  q. • Consolidate them into one circuit, if possible.

  6. Binary Full-Adder Circuit

  7. Binary Full-Adder Circuit • Use 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 circuit.

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