Answer
$Answer\ of\ a:$
$\begin{aligned} \text +0.25 &=0.01 \text { in binary } \\ &=0.1 \times 2^{-1} \text { in scientific notation } \end{aligned}$
so the base is $+0.1$ and the exponent is $-1 .$
$\ \ \ \ \ =0\ \underbrace{100000000}_{\text { mantissa }} \qquad \underbrace{1\ 00001}_{\text { exponent }}$
---
$Answer\ of\ b:$
$\begin{aligned}-32\ 1 / 16 &=-100000.0001 \\ &=-0.1000000001 \times 2^{6} \\ &= 1\ \underbrace{100000000}_{\text { mantissa }} \qquad \underbrace{0\ 00110}_{\text { exponent }} \end{aligned}$
Note that the last 1 in the mantissa was not stored because there was not
enough room. The loss of accuracy that results from limiting the number
of digits available is called a truncation error.
Work Step by Step
$Answer\ of\ a:$
$\begin{aligned} \text +0.25 &=0.01 \text { in binary } \\ &=0.1 \times 2^{-1} \text { in scientific notation } \end{aligned}$
so the base is $+0.1$ and the exponent is $-1 .$
$\ \ \ \ \ =0\ \underbrace{100000000}_{\text { mantissa }} \qquad \underbrace{1\ 00001}_{\text { exponent }}$
---
$Answer\ of\ b:$
$\begin{aligned}-32\ 1 / 16 &=-100000.0001 \\ &=-0.1000000001 \times 2^{6} \\ &= 1\ \underbrace{100000000}_{\text { mantissa }} \qquad \underbrace{0\ 00110}_{\text { exponent }} \end{aligned}$
Note that the last 1 in the mantissa was not stored because there was not
enough room. The loss of accuracy that results from limiting the number
of digits available is called a truncation error.
