<< Chapter < Page Chapter >> Page >

Twos complement representation

  • Ones Complement

The ones complement of a number is represented by flipping the number's bits one at a time. For example, the value 01001001 becomes 10110110.

Suppose you are working with B-bit numbers. Then the ones complement for the number N is 2 B size 12{2 rSup { size 8{B} } } {} -1 -N

  • Twos complement

The twos complement of a number N in a B-bit system is 2 B size 12{2 rSup { size 8{B} } } {} -N.

There is a simple way to calculate a twos complement value: invert the number's bits and then add 1.

For a concrete example, consider the value 17 which is 00010001 in binary. Inverting gives 11101110. Adding one makes this 11101111.

  • Twos Complement Representation

Like sign magnitude, twos complement representation uses the most significant bit as a sign bit, making it easy to test whether an integer is positive or negative. It differs from the use of the sign-magnitude representation in the way that the other bits are interpreted.

Consider an n-bit integer. A, in twos complement representation. If A is positive, then the sign bit an-1 is zero. The remaining, bits represent the magnitude of the number in the same fashion as for sign magnitude:

A = i = 0 n 2 a i 2 i size 12{A= Sum cSub { size 8{i=0} } cSup { size 8{n - 2} } {a rSub { size 8{i} } 2 rSup { size 8{i} } } } {} If a n 1 = 0 size 12{a rSub { size 8{n - 1} } =0} {}

The number zero is identified as positive and therefore has a 0 sign bit and a mag­nitude of all 0s. We can see that the range of positive integers that may he repre­sented is from 0 (all of the magnitude bits are 0) through- 1 (all of the magnitude bits are 1). Any larger number would require more bits.

For a negative number A (A<0), the sign bit,is one. The remain­ing n-1 bits can take on any one of a n 1 2 n 1 size 12{a rSub { size 8{n - 1} } 2 rSup { size 8{n - 1} } } {} values. Therefore, the range of negative integers that can be represented is from -1 to - 2 n 1 size 12{2 rSup { size 8{n - 1} } } {}

This is the convention used in twos complement representation, yielding the following expression for negative and positive numbers:

A = 2 n 1 a n 1 + i = 0 n 2 a i 2 i size 12{A= - 2 rSup { size 8{n - 1} } a rSub { size 8{n - 1} } + Sum cSub { size 8{i=0} } cSup { size 8{n - 2} } {a rSub { size 8{i} } 2 rSup { size 8{i} } } } {}

The range of A is from - 2 n 1 size 12{2 rSup { size 8{n - 1} } } {} to 2 n 1 size 12{2 rSup { size 8{n - 1} } } {} -1.

Example: Using 8 bit to represent

+50= 0011 0010

-70=1011 1010

Converting between different bit lengths

The rule for twos complement integers is to move the sign hit to the new leftmost position and fill in with copies of the sign bit. For positive numbers, fill in with zeros, and for negative numbers, till in with ones.

For example:

+18 = 00010010

+18 = 00000000 00010010

-18 = 10010010

-18 = 11111111 10010010

3. integer arithmetic

3.1 negation

In sign-magnitude representation, the rule for forming the negation of an integer is simple: Invert the sign bit.

In twos complement representation, the negation of an integer can he formed with the following rules:

1. Take the Boolean complement of each bit of the integer (including the sign bit). That is. set each 1 to 0 and each 0 to 1.

2. Treating the result as an unsigned binary integer, add 1.

This two-step process is referred to as the twos complement operation, or the taking of the twos complement of an integer


Negation Special Case 1:

0 = 00000000

Bitwise not 11111111

Add 1 to LSB +1

Result 1 00000000

Overflow is ignored, so: - 0 = 0

Negation Special Case 2:

-128 = 10000000

bitwise not 01111111

Add 1 to LSB +1

Result 10000000

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
with the given example MOV BX,AX describe the sequence that will be followed using instruction state diagram
Gireesh Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Computer architecture. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10761/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Computer architecture' conversation and receive update notifications?