Chapter B, Problem 29E

Explanation of Solution

Ripple carry adder of 16-bit:

The time unit is denoted by T.

In ripple carry adder, 2T time is required to generate and propagate the carry of each bit.

The delay can be calculated as follows

$\begin{array}{c}\text{Delay}\text{=}\text{16}\text{×}\text{2T}\\ \text{=}\text{32T}\end{array}$

Therefore, the delay for 16-bit ripple carry adder is 32T.

Ripple carry adder of 16-bit for 4-bit groups:

The number of blocks generated can be calculates as $\frac{\text{16}}{\text{4}}\text{=}\text{4}$.

In ripple carry adder, 2T time is required to generate and propagate the carry of each bit.

The time taken by single block is 2T and then the time taken by 4 blocks can be calculated as follows

$\begin{array}{c}\text{time}\text{taken}\text{=}\text{4}\text{×}\text{2T}\\ \text{=}\text{8T}\end{array}$

Therefore, the time by 4 blocks is 8T