Answer
$\begin{aligned} \text { a. } 10101000 &=\left(1 \times 2^{3}\right)+\left(1 \times 2^{5}\right)+\left(1 \times 2^{7}\right) \\ &=8+32+128 \\ &=168 \text { as an unsigned integer value } \end{aligned}$
$\begin{aligned} \text { b. } 10101000 &=\left(1 \times 2^{3}\right)+\left(1 \times 2^{5}\right) \\ &=8+32 \\ &=40 \end{aligned}$
This is the value of the magnitude portion of the number. The left-most bit represents the sign bit. In this example, it is a $1,$ which is a
negative sign.
$$
=-40 \text { as a signed integer value }
$$
Work Step by Step
$\begin{aligned} \text { a. } 10101000 &=\left(1 \times 2^{3}\right)+\left(1 \times 2^{5}\right)+\left(1 \times 2^{7}\right) \\ &=8+32+128 \\ &=168 \text { as an unsigned integer value } \end{aligned}$
$\begin{aligned} \text { b. } 10101000 &=\left(1 \times 2^{3}\right)+\left(1 \times 2^{5}\right) \\ &=8+32 \\ &=40 \end{aligned}$
This is the value of the magnitude portion of the number. The left-most bit represents the sign bit. In this example, it is a $1,$ which is a
negative sign.
$$
=-40 \text { as a signed integer value }
$$
