2.  Arithmetic circuit  Addition  Subtraction  Division  Multiplication

3.  0 + 0 = 0  0 + 1 = 1  1 + 0 = 1  1 + 1 = 10 One bit in sum Two bit in sum

4.  A combinational circuit that performs the addition of two bits.  Two inputs and two outputs.  Augend and Addend  Sum and Carry

5. XYCS 0000 0101 1001 1110

7.  A combinational circuit that performs the addition of three input bits.  Three inputs and two outputs.  Sum and Carry

8. XYZCS 00000 00101 01001 01110 10001 10110 11010 11111

10.  Adders connected in cascade.  Carry output from one full adder connected to carry input of next full adder.

12.  Input carry 0110  A1011  B0011  Sum1110  Output carry0011

13.  Input carry in the least significant position is 0.  Simple in concept.  Long circuit delay.  Many gates in the carry path.

14.  Practical design with reduced delay.  For a n- bit ripple carry adder  The longest delay path is 2n + 2.  16 – bit ripple carry adder - delay is 34 gate delays

15.  Designed by a transformation of the ripple carry adder design in which the carry logic over fixed groups of bits of the adder is reduced to two-level logic.

16.  OR gate and one of the AND gates are removed to form each of the full adders to form the ripple carry adder.  Separate the parts of full adders not involving the carry propagation path from those containing the path.  First part of each full adder  partial full adder - PFA

17.  Two outputs  P i and G i  From each PFA to ripple carry path  One input CiCi  From the carry path to each PFA

18.  P i = A i XOR B i - Propagate function  G i = A i. B i - Generate function

19.  Whenever P i = 1  Incoming carry is propagated through bit position from C i+1.  Whenever P i = 0  carry propagation through bit position is blocked.

20.  Whenever G i = 1  Carry output from the position is 1.  Regardless of value of P i.  A Carry has been generated.  Whenever G i = 0  carry is not generated.  C i+1 is 0.  C i is also 0.

21.  Generate and propagate functions correspond exactly to the half adder.  Essential in controling the values in ripple carry path.  PFA generates sum function by XOR of incoming carry, C i and propagate function, P i.