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Suppose I have the 2's complement, negative number 1111 1111 1011 0101 (0xFFBB5). How can I represent this as a decimal number in base 10?

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2 Answers 2

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If $x$ is an $n$ digit number written in two's complement, then $\tilde{} x +1 = -x$, where $\tilde{} x$ is the $n$-digit not of $x$. In your case, ~0xFFBB5 + 1 = 0x0044B = 1099, so your number is $-1099$.

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Here is the process to convert a negative two's complement number back to decimal:

(1) flip all the bits,

(2) add 1, and

(3) interpret the result as a binary representation of the magnitude and add a negative sign

So, for your example, we have:

$$1111~1111~1011~0101 \xrightarrow{(1)} 0000~0000~0100~1010 \xrightarrow{(2)} 0000~0000~0100~1011 \xrightarrow{(3)} -75$$

It looks like you wrote the wrong binary and meant:

$$1111~1111~1011~1011~0101 \xrightarrow{(1)} 0000~0000~0100~0100~1010 \xrightarrow{(2)} 0000~0000~0100~0100~1011 \xrightarrow{(3)} -1099$$

Of course, in Hex, you can invert all the bits and add 1 and take a negative magnitude.


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Great outline of strategy, and followed by applying it (perfect combination) +1 –  amWhy May 7 '13 at 0:16

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