. An n-bit adder can be constructed by cascading n full adders in series, with the carry into stage i, Ci , coming from the output of stage i − 1. The carry into stage 0, C0 , is 0. If each stage takes T nsec to produce its sum and carry, the carry into stage i will not be valid until iT nsec after the start of the addition. For large n the time required for the carry to ripple through to the high-order stage may be unacceptably long. Design an adder that works faster. Hint: Each Ci can be expressed in terms of the operand bits Ai − 1 and Bi − 1 as well as the carry Ci − 1 . Using this relation it is possible to express Ci as a function of the inputs to stages 0 to i − 1, so all the carries can be generated simultaneously
