Chapter B, Problem 32E

Explanation of Solution

Block diagram for carry save adder with 16-bit:

Explanation:

The above diagram carry save adder with 16-bit and includes 16 number of 1-bit adders for adding the 16 bits. The partial product is 16 intermediate terms M15, M14…M0 and the multiplicand ANDed is 16 multiplier bits m15, m14…m0.

Block diagram for carry look ahead adder with 16-bit:

Explanation:

• The above diagram describes about the 16 bit carry look ahead adder that includes 16 numbers of 1-bit full adders to add the 16 bits.
• It includes carry generator, carry propagator and sum.
  • Carry generator denoted by G is used for generating the output query without depending on input query.
  • Carry propagator denoted by P is used for propagating the next state.

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