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2's complement without negative reference

Thread starter #1
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.

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


Active 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 :cool:
Thread starter #3
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.


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

Ian Rogers

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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...


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Most Helpful Member
Thats where i go wrong, i forget to ditch. TBH i havnt come across it for a while, most of what i have needed have been these plug and go sensors, talk about no need to think! This bio reactor is going to test me, i have all the kit except the special power unit and the main controller, Those run in at £6-£12K second hand. The reactors cost enough as it is, i just can justify spending money on something that in theory should be easy. The really hard part is finding the voltages!!

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