How do computers store neg binary numbers?

[_buddha]

Homework Statement

Which of the following numbers will be stored in an 8-bit computer as 11000001? This computer uses the 2's compliment convention.

a)-64 b)-63 c)63 d)64

Homework Equations

1's and 2's compliment

The Attempt at a Solution

The answer is -63 and after trial and error i get that answer, but I am just wondering what exactly happens to the actual number. This is what my understanding is, so since the first digit in the number is a 1, therefore its negative. And after converting it to its compliment i get 00111111, which equals to 63 in base 10. So therefore the answer is -63. Is this the correct way of handling this question?

 

[NobodySpecial]

Two's complement is slightly tricky to explain (http://en.wikipedia.org/wiki/Two's_complement) but very useful once you 'get' it

Possibly simpler explanation http://mathforum.org/library/drmath/view/54344.html

 

[Zryn]

You can also just add the bits together, except remembering that for 2's complement, the MSB is negative.

-1 * 128 + 1 * 64 + 0 * 32 + 0 * 16 + 0 * 8 + 0 * 4 + 0 * 2 + 1 * 1 = -128 + 64 + 1 = -63