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.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/713a63bd-641c-4c05-ab81-1b90f5f9d4c8/result_image/1561940635.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011546Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=529c8347adc9305f9b62f768edd5d2b0cdb17dcf37bef413473704e00d6aa33d)
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.