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

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Presentation transcript:

 Arithmetic circuit  Addition  Subtraction  Division  Multiplication

 = 0  = 1  = 1  = 10 One bit in sum Two bit in sum

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

XYCS

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

XYZCS

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

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

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

 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

 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.

 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

 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

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

 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.

 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.

 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.