Question 10.28: Describe a n-bit binary ripple-carry adder showing typical c......

The parallel adder performs additions at a relatively high speed, since it adds the bits from each position simultaneously. However, its speed is limited by an effect called carry propagation or carry ripple, which can best be explained by considering the following addition:

\begin{array}{rrrr} &1 & 1 & 1 & \\ &0 & 1 & 1 & 1 \\ + & 0 & 0 & 1 \\ \hline &1 & 0 & 0 & 0 \end{array}

Addition of the LSB position produces a carry into the second position. This carry when added to the bits of the second position, produces a carry into the third position. The latter carry, when added to the bits of the third position, produces a carry into the last position. The key thing to notice is that the sum bit generated in the last position (MSB) depends on the carry that was generated by the addition in the first position (LSB).

The parallel adders covered so far are ripple-carry types in which the carry output of each full-adder stage is connected to the carry input of the next higher-order stage. The sum and carry outputs of any stage cannot be produced until the input carry occurs; this leads to a time delay in the addition process, as illustrated in Fig. 10.21. The carry propagation delay for each full-adder is the time from the application of the input carry until the output carry occurs, assuming that the P and Q inputs are present.

The input carry to the least significant stage has to ripple through all of the adders before a final sum is produced. A cumulative delay through all of the adder stages is a worst-case addition time. The total delay can vary depending on the carries produced by each stage. If two numbers are added such that no carries occur between stages, the add time is simply the propagation time through a single full-adder from the application of the data bits on the inputs to the occurrence of a sum output.