Chapter B, Problem 30E

Explanation of Solution

Ripple carry adder of 64-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

$\begin{array}{c}\text{Delay}\text{=}\text{64}\text{×}\text{2T}\\ \text{=}128\text{T}\end{array}$

Therefore, the delay for 64-bit ripple carry adder is 128T.

Ripple carry adder of 64-bit for 4-bit groups:

The number of blocks generated can be calculates as $\frac{64}{\text{4}}\text{=}16$.

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 16 blocks can be calculated as follows

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

Therefore, the time by 16 blocks is 32T.

The total delay can be calculated as follows

$\begin{array}{c}\text{Delay}\text{=}\text{1T}\text{+}32\text{T}\text{+}\text{1T}\\ \text{=}34\text{T}\end{array}$

Thus, the delay of 4-bit groups is 34T.

Ripple carry adder of 64-bit for 16-bit groups:

The number of blocks generated can be calculates as $\frac{64}{16}\text{=}4$.

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 16 blocks can be calculated as follows

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

Therefore, the time by 16 blocks is 8T