I have a number in base $10$. The number is $N$. $N=-127$. Assuming $16$ bit 2's complement number representation, I need to convert $N$ to hexadecimal
I am not sure how to proceed. I know that the binary representation of $-127$ is $1000000001111111$. I am confused as to what the question is asking. Please help. Sorry for the tag.
Your expression for $-127$ is the sign-magnitude representation, not the two's complement representation. To get two's complement, you start with the representation for $+127$, which in $16$ bits is $0000\ 0000\ 0111\ 1111$. To negate it you complement each bit, getting $1111\ 1111\ 1000\ 0000$ and add $1$ to get $1111\ 1111\ 1000\ 0001$. Note that you can now add $127+(-127)$ and get $0$ if you ignore the carry out. That is one of the nice things about two's complement.
To convert this to hex, you can just convert each set of four bits, so the hex representation is $FF81$
binary. This isn't perfect given the tag description, but there doesn't appear to be any tag better suited to questions about $2$'s complements. (If there is a better tag, I would be pleased for thebinarytag to be replaced.) – Travis Willse Oct 01 '19 at 03:29