Decimal Values of 8-bit Hexadecimal Number 0xD1 | Conversion Homework Solution

[TranscendArcu]

Homework Statement

Write all the possible decimal values (3 of them) of the 8-bit hexadecimal number 0xD1.

The Attempt at a Solution

So I can write that D1 = D*16¹ + 1 * 16⁰ = 13*16 + 1 = 209

Can I also say that the most significant bit is reserved for sign? In that case, I think the D would indicate a negative value (is that right? What's the cutoff for positive/negative signed values in hexadecimal?) Thus, I would have: - (1 * 16⁰) = -1

The only other interpretation I can think of is to say that D1 is a complement, so I'd have to convert to binary and then convert to decimal. So:

D1 = 1101 0001, then I take all the places where the value is zero and add. Doing so gives: 2 + 4 + 8 + 32 = 46

I also have to add one to 46, I believe. So my answer is 47. Is that so?

 

[HallsofIvy]

"most significant bit reserved for sign"? What, exactly, is the statement of the problem? "Most significant bit" would refer to a memory location in a computer but the question you ask, converting a hexadecimal number to decimal, doesn't necessarily have anything to do with computers.

 

[SammyS]

Homework Statement

Write all the possible decimal values (3 of them) of the 8-bit hexadecimal number 0xD1.

The Attempt at a Solution

...

Can I also say that the most significant bit is reserved for sign? In that case, I think the D would indicate a negative value (is that right? What's the cutoff for positive/negative signed values in hexadecimal?) Thus, I would have: - (1 * 16⁰) = -1

If the most significant bit is used for the sign, then looking at D in binary 1101, indicates that 0xD1 is the negative of 0x51 ...

I think there's another way to interpret this number for the negative case --- in which the representation sort of wraps around zero like a mod function. What do you need to add to 0xD1 to get 0x100 ? ... 47. That would make this -47.