# Problem What is the range of a signed word in hexadecimal? # Process A word is a 2-byte or 16-bit number. In signed binary numbers, the MSB is usually the digit which indicates the sign of the number. Since the word is signed in this case, and since the most common representation of negative numbers in binary is Two's Complement, that means the MSB is 0 when the binary number is positive and 1 when the binary number is negative. It also means that the lowest number in our range is the Two's Complement of our highest number. $\overbracket{\underbracket{0}_\textrm{Sign}000_2}^{0_{16}}\overbracket{0000_2}^{0_{16}}\overbracket{0000_2}^{0_{16}}\overbracket{0000_2}^{0_{16}}$ $\begin{split} \textrm{Maximum}&=\overbracket{\underbracket{0}_\textrm{Sign}111_2}^{7_{16}}\overbracket{1111_2}^{\textrm F_{16}}\overbracket{1111_2}^{\textrm F_{16}}\overbracket{1111_2}^{\textrm F_{16}}\\ &=\boxed{7\textrm{FFF}_{16}} \end{split}$ $\begin{split}\textrm{Minimum}&=\overbracket{\underbracket{1}_\textrm{Sign}000_2}^{8_{16}}\overbracket{0000_2}^{0_{16}}\overbracket{0000_2}^{0_{16}}\overbracket{0000_2}^{0_{16}}\\ &=\boxed{8000_{16}} \end{split}$ # Answer `0x8000` to `0x7FFF`.