$$ 2^30+ 2^29+...+2^1+2^0=2^31-1 $$

With the an adverse sign, the the smallest number is $$1-2^31$$However the following source says otherwise. It says the smallest worth is $$ -2^31$$ on the 3rd page.

You are watching: What is the smallest negative integer

https://www.uio.no/studier/emner/matnat/cg-tower.com/MAT-INF1100/h12/kompendiet/kap4.pdf

What am ns doing wrong here?

binary

re-superstructure

cite

follow

asked Jul 25 "18 at 13:44

Ali KıralAli Kıral

7511 silver- badge99 bronze title

$\endgroup$

include a comment |

## 4 answer 4

energetic oldest Votes

3

$\begingroup$

You are assuming the representation is signed-magnitude, i m sorry is a valid depiction of an adverse numbers. Your answer is exactly for that representation. Most computers use two"s complement, which allows one an ext negative value. The most an unfavorable value is $1$ adhered to by $31$ zeros and also represents $-2^-31$. The motivation is that you have the right to do arithmetic in two"s complement without worrying around whether numbers are positive or an unfavorable and the comes the end right, simplifying the design of the chip.

re-publishing

mention

follow

answer Jul 25 "18 in ~ 13:55

Ross MillikanRoss Millikan

357k2626 yellow badges236236 silver- badges423423 bronze title

$\endgroup$

0

include a comment |

2

$\begingroup$

The smallest an adverse number is a $1$ adhered to by $31$ zeros i m sorry is understood as $-2^31.$ since twos" match is basically arithmetic modulo $2^32,$ it would certainly be equally logical to interpret it as $2^31.$ The negative value is preferred so that the an adverse integers are precisely those v a $1$ as the most far-reaching bit.

re-publishing

mention

follow

answer Jul 25 "18 in ~ 13:51

saulspatzsaulspatz

50.7k66 gold badges2828 silver badges5959 bronze title

$\endgroup$

0

include a comment |

2

$\begingroup$

Your calculation in itself is correct. However, over there are an ext efficient methods to represent an unfavorable integers than sign & magnitude, i m sorry is the an approach you use. Such methods include "two"s complement", which is in fact defined in the connect you provided. When they create that the smallest an adverse integer we have the right to represent is $-2^31$ they refer to the much more efficient methods, and not the naive method. I imply you proceed to read the section about two"s complement and also maybe then it will certainly all make an ext sense.

re-superstructure

cite

monitor

answer Jul 25 "18 in ~ 13:55

Dean GurvitzDean Gurvitz

56744 silver- badges2121 bronze badges

$\endgroup$

1

include a comment |

2

$\begingroup$

In the two"s match representation,

$$\beginalign000&\to0\\001&\to1\\010&\to2\\011&\to3\\100&\to-4\\101&\to-3\\110&\to-2\\111&\to-1\endalign$$

In this representation, the values are in increasing order (except because that the $3/-4$ jump), therefore that practically the same adder have the right to be provided for unsigned and signed additions/subtractions.

re-superstructure

point out

follow

answered Jul 25 "18 in ~ 14:01

user65203user65203

$\endgroup$

2

include a comment |

## your Answer

Thanks because that contributing an answer to cg-tower.comematics stack Exchange!

Please be sure to*answer the question*. Provide details and share your research!

But *avoid* …

Use cg-tower.comJax to layout equations. Cg-tower.comJax reference.

To learn more, check out our advice on writing good answers.

See more: Ll Cool J Luv You Better Lyrics, Luv U Better

Draft saved

Draft discarded

### Sign up or log in

authorize up using Google

sign up making use of Facebook

sign up using Email and Password

send

### Post together a guest

surname

email Required, but never shown

### Post together a guest

name

Required, but never shown

post Your price Discard

By clicking “Post your Answer”, girlfriend agree to our terms of service, privacy policy and also cookie plan

## Not the prize you're looking for? Browse various other questions tagged binary or asking your own question.

Featured on Meta

associated

0

assessing the decimal indistinguishable of binary numbers in; sign and also magnitude, one's complement and two's match

0

Bitwise Operations and the specify name Convention the their operator

1

Signed magnitude Binary number come Hexadecimal

3

converting $\frac27$ come a binary number in a $32$ bit computer

1

Minimum variety of bits come represent an unfavorable number

0

Binary number in compact type

0

smallest number that can be save in a 32 little fixed allude system suspect the radix suggest is in the middle?

warm Network concerns more hot concerns

concern feed

subscribe to RSS

concern feed To i ordered it to this RSS feed, copy and also paste this URL right into your RSS reader.

cg-tower.comematics

agency

ridge Exchange Network

site architecture / logo © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.9.23.40291

cg-tower.comematics ridge Exchange works finest with JavaScript allowed

her privacy

By clicking “Accept every cookies”, girlfriend agree stack Exchange can store cookie on your an equipment and disclose details in accordance through our Cookie Policy.