
## Section16.6Exercises

###### 1

Using IEEE 754 32-bit format, what decimal number would the bit pattern $\hex{00000000}_{16}$ represent, ignoring the special case of “zero value”.

Solution

1. Compute $s\text{,}$ $e+127\text{,}$ and $f\text{.}$

\begin{align*} s &= \binary{0}\\ e + 127 &= \binary{00000000}_{2}\\ e &= -127_{10}\\ f &= \binary{00000000000000000000000} \end{align*}
2. Finally, plug these values into Equation (16.5.1). (Remember to add the hidden bit.)

\begin{align*} (-1)^0 \times 1.00\dots 00 \times 2^{-127} &= \mbox{a very small number}\\ &\ne 0.0 \end{align*}

so we do need the special case.

###### 2

Convert the following decimal numbers to 32-bit IEEE 754 format by hand:

1. $1.0$

2. $-0.1$

3. $2016.0$

4. $0.00390625$

5. $-3125.3125$

6. $0.33$

7. $-0.67$

8. $3.14$

1. $\hex{3f80 0000}$

2. $\hex{bdcc cccd}$

3. $\hex{44fc 0000}$

4. $\hex{3b80 0000}$

5. $\hex{c543 5500}$

6. $\hex{3ea8 f5c3}$

7. $\hex{3f2b 851f}$

8. $\hex{4048 f5c3}$

###### 3

Convert the following hexadecimal numbers to decimal by hand using the 32-bit IEEE 754 format:

1. $\hex{4000 0000}$

2. $\hex{bf80 0000}$

3. $\hex{3d80 0000}$

4. $\hex{c180 4000}$

5. $\hex{42c8 1000}$

6. $\hex{3f99 999a}$

7. $\hex{42f6 e666}$

8. $\hex{c259 48b4}$

1. $+2.0$

2. $-1.0$

3. $+0.0625$

4. $-16.03125$

5. $100.03125$

6. $1.2$

7. $123.449997$

8. $-54.320999$