# 2's complement without negative reference

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#### Beau Schwabe

##### Active Member
Ok, so I had a REALLY dumb epiphany and I just want to make sure I'm not missing anything.

To make things simple I'll use 4 bits.

I have a number that ranges from 7 to -8 with 0 or -1 being center.
I want to convert that to a number that ranges from 0 to 15 with 7 or 8 being center.

In the past I would check the MSB; if it was a "0" then I would ADD 8; if it was a "1" I would SUBTRACT 8 ... without really even thinking what was going on.

Looking at this closer, all I need to do is invert the MSB and I'm done. No adding or subtracting required. Am I understanding that correctly? Even up to 32 Bit numbers?

Going in reverse, that might make for a really slick way to generate a 2's complement output.

Code:
2's Complement:       Desired Output:
0000 = 0                   8
0001 = 1                   9
0010 = 2                   10
0011 = 3                   11
0100 = 4                   12
0101 = 5                   13
0110 = 6                   14
0111 = 7                   15
1000 = -8                   0
1001 = -7                   1
1010 = -6                   2
1011 = -5                   3
1100 = -4                   4
1101 = -3                   5
1110 = -2                   6
1111 = -1                   7

#### Grossel

##### Well-Known Member
Not sure get this problem rigth, but have you thaught that if you just simply invert MSB then you would get the output result. No adding, no substraction - only make one bit oposite

#### Beau Schwabe

##### Active Member
have you thaught that if you just simply invert MSB then you would get the output result
... Right ... simply XORing the MSB is all that is needed.... before I would just do a compare on the MSB and then based on that actually do an addition or subtraction. Like I said it was a "REALLY dumb epiphany" on my part getting from point A to point B

EDIT: Hey, we are all human and sometimes it takes something obvious right in front of our face... I just wanted to share.

#### large_ghostman

##### Well-Known Member
Completely messes with my head this! One of those things that you get easy or you DONT!!

#### Ian Rogers

##### User Extraordinaire
Forum Supporter
2's complement is easy enough..

Micro's do not do negative numbers end of!! So programmers make it happen... we'll do 4 bit.

1111 = -1 Why!! because 0000 - 1 = 1111 ( which is actually 15 ).. 2's complement is the programming way to say negative..

1 is 0001 complemented ( this is the actual term for inversion ) you get 1110.. If you add 2 you get to get back to zero, so its obviously represents -2.. To make things right you have to add one.. complement once to invert then complement the LSBit with carry!!! or in other words 2's complement.. Programmers just subtract from max + 1 to get it positive...

16 - 1111 = 1.. BUT!! All this is superfluous as we are dealing with negative numbers, so we can just add them ie

1010 + 1110 = 1000 .. Or in English 10 + -2 = 8... Just remember to ditch the MSBit...