Question about 2's complement system

[Voltemand11]

I'm doing a first year university assignment, and one of the questions says "Convert the negative 12 bit binary integer -110110110100 to its 2?s complement form and assume you are storing it in a 16 bit binary representation.". I know that in 2's complement form if the number starts with a 0 it is positive and if it starts with a 1 it is negative. I was just wondering if I could simply change the -110110110100 to 1110110110100 with the 1 in front to represent the negative symbol and change it to 1000110110110100 since it is being stored in 16 bits, or if I have to convert the 110110110100 to a positive base 10 number and put the negative symbol in front of it so it would be -3508 in base 10 (I just used a number base calculator to get the 3508), and then convert that number into 2's complement form. It's mildly confusing to me, so any help would be greatly appreciated. Thanks.

[Tony]

Voltemand11 @ Thu Sep 23, 2010 9:12 pm wrote:

I know that in 2's complement form if the number starts with a 0 it is positive and if it starts with a 1 it is negative.

While true, there's more to it than that. What's the decimal value of 1000,0000 (two's complement, 8 bit integer).

Hint: it's not -0. http://en.wikipedia.org/wiki/Two's_complement

[Voltemand11]

Well I know the largest positive signed integer in 8 bits is 0111 1111, which is 127. If I convert that to a negative 2's complement integer it is 1000 0001 which is -127, so 1000 0000 would be -128.

[Tony]

Right. Which should answer

Voltemand11 @ Thu Sep 23, 2010 9:12 pm wrote:

I was just wondering if I could simply change the -110110110100 to 1110110110100 with the 1 in front to represent the negative symbol and change it to 1000110110110100

[Voltemand11]

Okay, so if I write 0110110110100 to denote +3508 in base 10, it's in 13 bits. I need to convert it to 2's complement to get the negative binary representation. If I use the rule where you start at the right of the binary number and go until you reach the first 1 and then flip every number after that, I get 1001001001100 which is -3508. But how do I put that into 16 bits?

[Tony]

Voltemand11 @ Fri Sep 24, 2010 12:57 pm wrote:

it's in 13 bits

Perhaps this is the point where you want to make it 16 bits long.

[Voltemand11]

Voltemand11 wrote:

But how do I put that into 16 bits?

I'm just not sure how to do that. Can I just add zeros after the 1 denoting the negative until there is 16 bits?

[Tony]

Voltemand11 @ Fri Sep 24, 2010 12:57 pm wrote:

+3508 in base 10, it's in 13 bits.

The number is positive.

You can't just add 0s to two's complement, as we've already established with
0000,0000
1000,0000
example.

[Voltemand11]

Okay, I think I've found the solution. In 16 bits +3508 would be 0000110110110100. If I convert it to -3508 it would be 1111001001001100. Thanks for your help, it was greatly appreciated!