Eight-bit two’s complement question

Question

Consider an 8-bit two’s complement register R. What are the least and greatest decimal integers that can be stored in R? Help would be much appreciated.

@Amzoti Is the least 00000000 and the greatest 11111111 ? I'm not entirely sure what the "register R" means. — kiasy, Dec 18 '13 at 02:42
It means "you have 8 bits, what's the biggest and smallest number you can store in it, assuming you're using two's complement". The name of the register doesn't really matter. — Henry Swanson, Dec 18 '13 at 02:43
The greatest cannot be 11111111, because the sign bit is set to 1, so it represents a negative number. — Stephen Montgomery-Smith, Dec 18 '13 at 02:43
Klazy haha. @Amzoti can you check my comment on the answer please ? — kiasy, Dec 18 '13 at 02:45

score 3 · Accepted Answer · answered Dec 18 '13 at 02:43

3

You have 8 bits, so you can store $256 = 2^8$ distinct integers. Since you are using two's complemnt, the range is $-128..127$. You store $127$ as $01111111$ and $-128$ as $10000000$.

A register is just high-speed non-addressable memory near the CPU. The registers are used as caches for high-speed computation.

answered Dec 18 '13 at 02:43

ncmathsadist

49,383

So would the greatest be be 10000000 and smallest 00000000 ? – kiasy Dec 18 '13 at 02:44
see pp.22ff in http://www.ncssm.edu/~morrison/froobles/c0.pdf – ncmathsadist Dec 18 '13 at 02:45
I'm confused. Is my answer correct? – kiasy Dec 18 '13 at 02:49
Do you know how two's complement works? – ncmathsadist Dec 18 '13 at 12:33
very helpful, thanks ! – kiasy Dec 18 '13 at 19:44

Eight-bit two’s complement question

1 Answers1