Question

B.30 [15] <§B.6> This exercise is similar to Exercises B.28 and B.29, but this time calculate the relative speeds of a 64-bit adder using ripple carry only, ripple carry of 4-bit groups that use carry lookahead, ripple carry of 16-bit groups that use carry lookahead, and the carry-lookahead scheme from Exercise B.27.

Short answer

The relative speed is 128T.

Step-by-step solution

Define the concept.

The 64- bit adderhas the feature of carry propagating and carry generating.

For the carry propagating, the carry propagator (P) is used for propagating to the following state of this.

For carry generating, the carry generator (G) is used for generating the result query by not considering the carry of the input.

The computed sum of every 16-bit adder is represented by “S”.

The ripple carry adder is referred to as the digital circuit that can able to produce the arithmetical sum of the specified numbers. This also can construct by cascading the full adders. There is also a carry output from every full adder that is cascaded to the “carry input” of the following full adder in the sequence.

The “T” is referred to as the time unit.

In the Ripple carry adder one bit requires 2T time.

Determine the calculation.

In the Ripple carry adder one bit requires 2T time.

$\text{Hence,forthe64-bitripplecarryadder,thedelay=}\left(\text{64×2T}\right)\text{=128T}$

The new equation for the carry-look ahead logic (64- bit adder) that is implemented by the 16-bit adders, those are acted as the building block:

$\begin{array}{l}\text{C1=G0+}\left(\text{P0×c0}\right)\\ \text{C2=G1+}\left(\text{P1×G0}\right)\text{+}\left(\text{P1×P0×c0}\right)\\ \text{C3=G2+}\left(\text{P2×G1}\right)\text{+}\left(\text{P2×P1×G0}\right)\text{+}(\text{P2}\times \text{P1}\times \text{P0}\times \text{c0})\end{array}$

The diagram of the 64-bit adder by using the ripple-carry: