Chapter 3, Problem 31E

a.

Explanation of Solution

Propagation delay for 2-input multiplexer:

• Look at the diagram (c) in Figure 3.12 of the text book.
• The 2-input decoder has the propagation delay of “2”.
• To generate a carry, it requires the propagation delay of “1”...

b.

Explanation of Solution

Propagation delay for 1-bit full-adder:

• Look at the Figure 3.15 of the text book.
• This figure provides the full-adder circuit.
• Only one AND gate and “2” OR gates are needed for one-bit adder.
• One OR gate is used for sum and another OR gate is used for carry...

c.

Explanation of Solution

Propagation delay for 4-bit adder:

• Look at the Figure 3.16 of the text book.
• The propagation delay for 1-bit adder is “3”.
• To obtain the 4-bit adder, four 1-bit adders are needed.
• Hence, the 4-bit adder consists of the propagation delay, which is “4” times greater than the propagation delay of 1-bit adder.
• The propagation delay of 4-bit adder is computed as follows,

$\begin{array}{c}\text{Propagation\&}\end{array}$

d.

Explanation of Solution

Propagation delay if 4-bit adder were extended to “32” bits:

• To obtain the 32-bit adder, eight 4-bit adders are needed.
• The propagation delay for 4-bit adder is “12”.
• Hence, the 32-bit adder consists of the propagation delay, which is “8” times greater than the propagation delay of 4-bit adder.
• The propagation delay of 32-bit adder is computed as follows,

$\begin{array}{c}\text{Propagation delay\&}\end{array}$