Twos complement notation question?

Question

I have a quick question how do you do the two complement system,

For example say I have in two complement a $6$ which is $0110$ and $3$ which is $0011$ and I want to add

$6+(-3)$ I know what five is in binary but how do I find $-3$ is so that I can add them. That is my question I heard I have to find the complement and add 1.

Your binary for $5$ is not correct. – Ross Millikan Feb 19 '13 at 22:50 — Ross Millikan, Feb 19 '13 at 22:50
yes I meant six i got confused. – Fernando Martinez Feb 19 '13 at 22:54 — Fernando Martinez, Feb 19 '13 at 22:54

amWhy · Accepted Answer · 2013-02-19T23:00:06.117

5

Yes, you can "invert" the digits of 3 ($0 \to 1, 1 \to 0$) and ADD 1 to obtain -3 in two's complement. So 0011 is the base two representation of 3, and its complement (-3) is therefore 1100 + 1 = 1101.

Hence $6 + (-3) = 0110 + 1101 = 0011 = 3$ as desired.

edited Feb 19 '13 at 23:00

answered Feb 19 '13 at 22:46

amWhy

209,954

so you invert the digits of 0 and 1 to find the complement and then add 1 to find the negative. – Fernando Martinez Feb 19 '13 at 22:48
1

Inverting the digits gives ones' complement, not the twos' complement. – Ross Millikan Feb 19 '13 at 22:50
You invert digits, and add 1, to get two's complement. – amWhy Feb 19 '13 at 22:50
yes sorry I meant the complement. – Fernando Martinez Feb 19 '13 at 22:52
It takes a little getting used to. The more bits you use, the larger the numbers you can work with. – amWhy Feb 19 '13 at 22:58
yes that makes sense thanks – Fernando Martinez Feb 19 '13 at 23:01

score 2 · Answer 2 · answered Feb 19 '13 at 22:42

2

$5$ is $00000101$ and $3$ is $00000011$. The one's complement of $3$ is $11111100$ and the two's complement is one more: $11111101$. Adding gives $(1)00000010$, i.e. $2$ (fortunately).

answered Feb 19 '13 at 22:42

Hagen von Eitzen

374,180

but you do not need that many bits to 5 or 3 in binary or do you? – Fernando Martinez Feb 19 '13 at 22:56
@FernandoMartinez: no, you don't need that many, but we are prone to think of numbers having $8, 16, 32, or 64$ bits because that is what computers do. – Ross Millikan Feb 19 '13 at 23:06

Twos complement notation question?

2 Answers2