[Math] Converting from twos complement to decimal

arithmeticbinarydecimal-expansiondiscrete mathematics

I am currently reading a textbook and I can't seem to understand what the examples in the book did. I do believe it is an error with the book, but if not can someone explain?

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How come there is no negative sign in front of the final result?

Best Answer

$-2_{ten}=\begin {cases}-000000...000010_{two} \ \ \text{in signed binary}\\ \ \ \ 11111111...1110_{two} \ \ \text {in 2's complement binary}\\ \end{cases}$

In $2$'s complement binary the sign is expressed by the leading $1$'s.

Taking the absolute value of a negative number (leading $1$'s) in $2$'s complement binary is flipping the bits and then adding one.

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