Chapter B, Problem 28E

Explanation of Solution

4-bit ripple carry adder:

Explanation:

The above diagram describes about the 4 bit ripple carry adder that calculates the relative performance between the ripple carry adders.

Here, the time unit is denoted by T.

The equation requires 2T time to generate and propagate the carry of each bit. Hence, it takes 8T time for the carry of 4 bit.

The time taken by each bit can be calculated as follows

$\text{T}\text{=}\text{0}\text{a3}\mathrm{...}\text{0}\text{b3}\mathrm{...}\text{0}\text{c0}$

For time T=0, $\text{T}\text{=}\text{0}\text{a3}\mathrm{..}\text{0}\text{b3}\mathrm{..}\text{0}\text{c0}$

For time T=2, $\text{T}\text{=}\text{2}\text{s0}\text{c1}$

For time T=4, $\text{T}\text{=}4\text{s1}\text{c2}$

For time T=6, $\text{T}\text{=}6\text{s2}\text{c3}$

For time T=8, $\text{T}\text{=}8\text{s3}\text{c4}$

Therefore, the ripple adder includes the path from a0, b0, c0 to s3, c4 with 8T time

4-bit ripple carry adder: