what does 2's complement mean exactly??

1.) 2's complement states that the numbering system were using will use this form for example
(0001)2 = (+1)10 (in 2's complement form)
(1111)2 = (-1)10 (in 2's complement form)

2.) does 2's complement just represent the negative value of a positive number? for example
(0001)2 = (+1)10 (in 2's unsigned form)<-- not 2's complement
(1111)2 = (-1)10 (in 2's complement form) <-- 2's complement

Quote:Original post by nuclear123
what does 2's complement mean exactly??

It means that the most significant bit is used to determine the number's signedness.

Quote:
1.) 2's complement states that the numbering system were using will use this form for example
(0001)2 = (+1)10 (in 2's complement form)
(1111)2 = (-1)10 (in 2's complement form)

Yes. A helpful trick is to flip the bits and add one when you have a negative number, so:

11112 since the most significant bit is set, we know this number is negative
00002 flip the bits
00012 add 1
Resulting in -110

Another example:
10012 MSB is set, this number is negative
01102 flip the bits
01112 add 1
Resulting in -710

Quote:
2.) does 2's complement just represent the negative value of a positive number? for example
(0001)2 = (+1)10 (in 2's unsigned form)<-- not 2's complement
(1111)2 = (-1)10 (in 2's complement form) <-- 2's complement

No. Remember that 2's complement is a way of interpreting a set of bits. The bits 11112 can be either -1 as a signed integer, or a 15 as an unsigned integer.

Take this inequality:

11112 > 01112 as unsigned integers evaluates to true since 15 > 7. However, as signed integers this evaluates to false since -1 < 7.

AFAIK the main reason is the simplicity with which addition and subtraction can be done in hardware. Think on the famous
12 + 12 = 102
and carry bit propagation.

Quote:Private message from nuclear123
how does a computer need to determine wether the first value is negative or the second value?

(0001)2 = (+1)10 (in 2's unsigned form)<-- unsigned
(1111)2 = (-1)10 (in 2's complement form) <-- 2's complement

how does it know that 0001 is unsigned form and 1111 is 2's complement negative, and not 1111 unsigned?

Anyway: The computer doesn't know. A computer doesn't distinguish a type from a set of bits. The type is inferred by the operations performed on those bits. For example, there are two assembler instructions for multiplying two (Intel 8088) 16-bit registers: mul (unsigned integer multiply), and imul (signed integer multiply).

So, in a 4-bit architecture using 2's complement,
00012 will always be interpreted as +110 using mul and imul, and
11112 will be interpreted as +1510 when using mul, but will be interpreted as -110 when using imul.