Answer
The 10 bits would be represented as 9 bits for the magnitude and the
leftmost bit for the sign. To represent the magnitude, we must rewrite
300 as the sum of powers of $2,$ as we did in the previous question.
$300=256+32+8+4$
$\quad=2^{8}+2^{5}+2^{3}+2^{2}$
$\quad=100101100$ in 9 bits
To make it a negative value, we must add a 1 bit (the negative sign) to
the leftmost position of the number.
$\begin{aligned}-300 &=1100101100 \\ 254 &=128+64+32+16+8+4+2 \\ &=2^{7}+2^{6}+2^{5}+2^{4}+2^{3}+2^{1} \\ &=01111110 \text { to } 9 \text { bits of accuracy for the magnitude } \end{aligned}$
To make it a $+254,$ we must add a 0 (the $+$ sign $)$ to the leftmost position
of the number.
$+254=001111110$
Work Step by Step
The 10 bits would be represented as 9 bits for the magnitude and the
leftmost bit for the sign. To represent the magnitude, we must rewrite
300 as the sum of powers of $2,$ as we did in the previous question.
$300=256+32+8+4$
$\quad=2^{8}+2^{5}+2^{3}+2^{2}$
$\quad=100101100$ in 9 bits
To make it a negative value, we must add a 1 bit (the negative sign) to
the leftmost position of the number.
$\begin{aligned}-300 &=1100101100 \\ 254 &=128+64+32+16+8+4+2 \\ &=2^{7}+2^{6}+2^{5}+2^{4}+2^{3}+2^{1} \\ &=01111110 \text { to } 9 \text { bits of accuracy for the magnitude } \end{aligned}$
To make it a $+254,$ we must add a 0 (the $+$ sign $)$ to the leftmost position
of the number.
$+254=001111110$
