Chapter 1, Problem 38CRP

Explanation of Solution

List all the bit patterns that could be used to represent the value $\frac{3}{8}$ using the floating point format described in figure $1.24$:

The process to encode the values using the 8-bit floating point format is,

• Convert the given value in the binary representation.
• Copy the bit pattern into the mantissa field from left to right start with 1.
• Copy the bit pattern into the mantissa field from left to right start with 1.
• The exponential field is determined by imagine the pattern of mantissa field with a radix at its left and obtain the original binary number by determining the number of bits and direction of radix that must be moved.
• The remaining three bits represent the exponential field that is shown in the below table.

Bit pattern	value
$111$	3
$110$	2
$101$	1
$100$	0
$011$	$-1$
$101$	$-2$
$001$	$-3$
$000$	$-4$

• When the given value is positive then the bit assigned on high order bit is 0, and when the given value is negative then the bit assigned on higher bit is 1.
• Convert the number $\frac{3}{8}$  into binary representation.

$\begin{array}{c}\frac{3}{8}=0\times \frac{1}{2}+1\times \frac{1}{4}+1\times \frac{1}{8}\\ =0\times \frac{1}{2^1}+1\times \frac{1}{2^2}+1\times \frac{1}{2^2}\\ ={\left(0.011\right)}_2\end{array}$

• The mantissa field from the left to right is $\mathrm{}$