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I understand that unsigned representation does not have negative numbers but I am stuck with a question, I have to convert B which is a hex value to decimal and it is a unsigned representation. Now I am getting confused with, If it is an unsigned representation then why does it binary is 1011 ? There shouldn't be a 1 at the MSB. Please help me clear out the concept.


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up vote 3 down vote accepted

I suspect your puzzlement results from one or both of the following:

First, the MSB is is the most significant bit of the entire machine word, whose size in bits is usually a multiple of $8$; the 1 at the beginning of 1011 would only be the MSB if you were using $4$-bit words, which I don't think has been done for several decades at least. That it's the first bit in the textual representation of the number is just due to the fact that we leave off leading zeros in textual representations.

Second, and perhaps more importantly, that the representation is unsigned doesn't mean that the MSB is 0. Rather, it means that the MSB is used like all the other bits for representing a value, (namely the value $2^{l-1}$, where $l$ is the number of bits in the word), instead of having a special meaning for representing the sign.

For example, the range of an $8$-bit signed integer is $-128_{10}$ to $127_{10}$, corresponding to hexadecimal representations 80 to 7F, respectively; the range of an $8$-bit unsigned integer is $0_{10}$ to $255_{10}$, corresponding to hexadecimal representations 00 to FF, respectively. The hexadecimal representation FF of the value $255$ is an example of an unsigned representation with MSB 1.

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Thanks alot. Cleared alot of my false concepts :) – Fahad Uddin Aug 28 '11 at 16:44

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