Chapter 2.4, Problem 2.51PP

A.

Explanation of Solution

Calculation of binary representation:

• From the problem 2.46, the binary value of “$\frac{\text{1}}{\text{10}}$” is represented by “0.000110011[0011]…….₂”.
• From the given question, here determine an approximation value of “x'” by using IEEE round-to-even mode.
  • So, at the non-terminating sequence for “$\frac{\text{1}}{\text{10}}$”, it shows that “2” bits to the right of the rounding position are “1”

B.

Explanation of Solution

Calculation of decimal value representation:

• From the part A, after subtracting “x' – 0.1”, the binary value representation is “0.0000000000000000000000000[1100]”.
  • Comparing this to be binary representation of “$\frac{\text{1}}{\text{10}}$”, then it is approximately gives ${\text{2}}^x$

C.

Explanation of Solution

Time for computed clock after “100” hours:

The time for computed clock after “100” hours are shown below:

From the part B, the time computed by the software is “$\text{2}\text{.38 }\times {\text{ 10}}^{\text{-8}}\times \text{ 100 hours}$”.

In general, 1 hour = $\text{ 60 }\times \text{ 60}$ seconds. Then $\text{2}\text{.38 }\times {\text{ 10}}^{\text{-8}}\times \text{ 100 }\times \text{ 60}\times \text{60}$.

From the given question, the counter is increment at “0

D.

Explanation of Solution

Calculation of prediction:

From the given question, a Scud travels at around 2,000 meters per second.

From the part C, the time is “0.086” seconds...