In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often used in systems with very small and very large real numbers that require fast processing times. In general, a floating-point number is represented approximately with a fixed number of significant digits (the significand) and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:
significand
×
base
exponent
,
{\displaystyle {\text{significand}}\times {\text{base}}^{\text{exponent}},}
where significand is an integer, base is an integer greater than or equal to two, and exponent is also an integer.
For example:
1.2345
=
12345
⏟
significand
×
10
⏟
base
−
4
⏞
exponent
.
{\displaystyle 1.2345=\underbrace {12345} _{\text{significand}}\times \underbrace {10} _{\text{base}}\!\!\!\!\!\!^{\overbrace {-4} ^{\text{exponent}}}.}
The term floating point refers to the fact that a number's radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated as the exponent component, and thus the floating-point representation can be thought of as a kind of scientific notation.
A floating-point system can be used to represent, with a fixed number of digits, numbers of different orders of magnitude: e.g. the distance between galaxies or the diameter of an atomic nucleus can be expressed with the same unit of length. The result of this dynamic range is that the numbers that can be represented are not uniformly spaced; the difference between two consecutive representable numbers varies with the chosen scale.
Over the years, a variety of floating-point representations have been used in computers. In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the IEEE.
The speed of floating-point operations, commonly measured in terms of FLOPS, is an important characteristic of a computer system, especially for applications that involve intensive mathematical calculations.
A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers.
My attempt is approaching this problem like the mass spring model. Considering the buoyancy force as spring force. By doing so, we can have the typical mass-spring equation
𝑚 (𝑑^2 𝑥)/(𝑑𝑡^2 )+Fbuoyancy = 𝐹_𝑒𝑥𝑡
Then I can assuming the displacement a will be the sinusoidal function...
If we throw empty but sealed glass bottle in water it will float with 60% of it's volume above the surface of water.
What is average density of floating bottle and what is it's volume? Mass of bottle is 0.4 kg(mass of air inside of bottle is irelevant).
It's easy problem but I can't get right...
>>> from numpy import exp, pi
>>> exp(1j*pi)
(-1+1.2246467991473532e-16j)
The fact that the imaginary part of this is not zero is wrecking a fourier collocation scheme for a nonlinear PDE with periodic boundary conditions: the coefficient corresponding to the Nyquist frequency, which should be...
I am very new to C programming so am struggling with this question and how exactly to begin it, when we are doing this are we to use something like sprintf?
Thank you.
[Mentors’ note: no template as this thread had initially been misplaced in the technical forums and was moved here]
Summary:: Enclosed Cubic foot capsule passing between two bodies of different densities but questioned pressure.
You have a tub of fresh water 32 feet high sharing a wall with...
Let's say there's an object floating in liquid. The depth of the object below the surface is 𝑑 and its height above the water is ℎ. The density of the ball is 𝑝𝑏 and the density of the liquid is 𝑝𝐿. The pressure above the water is 𝑃𝑎𝑡𝑚.
I understand this situation when only the density of the...
My specific system will benefit from having the MOSFET base plate floating. Are there any downsides to leaving a MOSFET base plate floating? Are there any reasons not to?
Context: I'm building an off-grid, 100% solar powered home. I have a 12 kw solar array wired up to a Sol-Ark inverter and a Fortress 18.5 kwh lithium battery.
Question: What is the ideal grounding/earthing scheme?
Additional context: where I'm building, there is currently no requirement that...
Floating inside a closed spaceship, no windows, not knowing if I'm free falling near a gravity source or far away from any gravity source, are there any experiments that can be made, to determine if there is a gravity source near and if there is such an experiment, to determine the gravity...
I am planning to build my own laptop stand with an acrylic sheet. The final product should look like the one in the attached image (bottom right)
Material: most laptop stands are made with 6mm acrylic thickness, hence this is what I will use. Also I already have this material at home.
I am...
I find myself in a space with air but no gravity. Say at ISS. Can I suck myself forward by sucking a straw? It reminds me somehow of Feynman's sprinkler.
Also Mach looked at something like Feynman's sprinkler. Mach invented something alike. Four ex/inhalers of air, tubes, that are in/exhale air...
OK. I'm sure we're all in agreement that it is theoretically possible to float a cruise ship "in" a bucket of water, right? If not, maybe we need to sort that out first.
A couple of practical provisos to start:
Allow some leeway on what constitutes a Cruise Ship for our purposes. I submit that...
I am parsing data from an excel sheet using pandas ExcelFile class and read_excel function. I noticed that when reading the file, there are floating point errors in the results. For example, a cell that contains 25.15 will be 25.149999999999977 in the pandas data frame.
The value 25.15 in Excel...
Hi everyone,
I am working on the Fortran code to solve a magnetic field by using "Floating Random Walk" method.
I use a square domain for this case and show in the attachment. The external magnetic strength comes from left to right boundary.
Both top and bottom are assuming as insulation...
The two situations are shown in the figures alongside. The hollow sphere has a thick heavy rim that compensates for the air inside it - both spheres have the same mass ##m_B## and radius ##r_B##.
Since the bodies have the same mass ##m_B##, the mass of liquid displaced is the same ...
Now that is an evil question! The more interesting case looks like when the cylinder is upright, so that is what I focused on. I defined two coordinates; ##\theta##, the angular displacement of the cylinder from the vertical and ##d##, the distance between the point on the cylindrical axis which...
A Spherical buoy has a diameter of 2m and weighs 3kN. It is designed to be used in a variety or circumstances by it being floated in water and anchored to the floor with a chain. Draw the free body diagram and determine the following given that the volume of a sphere is,
Volume = πD3/6
The...
The dimensions of the bodies given in the problem are visual. Clearly bodies a and b are cubical whereas c is not. One side of b is twice the side of a. Both a and b are submerged to the same depth but what is the depth of submersion of c? Arranging bodies (by copying and pasting a on b and c...
My answer : Both pressures are equal, i.e. ##\boxed{P_A = P_B}##.
Reason : (1) The block of wood displaces an amount (mass) of liquid equal to its weight (archimedes' principle for floating bodies, or law of floatation). Hence we can imagine removing the block in the second case and filling it...
We understand that the crucial thing about the problem is that the volume of water present in the three containers are not the same. Also, we note that in each case the weight of the container is the total weight of its contents. (A student might be confused as to why should be so - after all...
Hello all
I was hoping someone could help shed some light on understanding an equation for floating bodies.
I am trying to work out the distance between B and M shown in the sketch below:-
I have been given the equation:-
BM = I/V
BM = is the distance from center of buoyancy to the meta...
Since they're all in the same liquid I'm assuming the buoyant forces would be the same on each block. But then I think about the volumes of the blocks, and them being different. I'm not sure if the block's volume would affect the buoyant force. Any help would be great, thanks!
Recently I chanced upon a video from the Royal Institution. The host has tried to replicate a piece of art by Jeff Koons (snapshot from video):
At Ri, they have tried to produce the same thing by balancing the ball filled with water, in a tank containing saturated saline water at the bottom...
I recall reading somewhere about when anything, (eg. cars on the road, balls in a flowing stream) tend to clump together on curves. I don't remember where I read it but I seem to think there was some principal involved. Has anyone ever heard of this before, or am I mistaken. Thanks.
I am trying to solve the equation like this,
from sympy.solvers import solve
from sympy import Symbol
import math
x = Symbol('x')
A, B, C, D = 0.59912051, 0.64030348, 263.33721367, 387.92069617
print(solve((A * x) + (B * math.sqrt(x**3)) - (C * math.exp(-x / 50)) - D, x , numerical = True))...
How can I find omega on an object that is floating on water which is moving up and down on the object? The problem goes by giving you a cylindrical object with radius r and height H, pw(density of water), pc(density of circle) and x(t)=a*cos(wt). I do not understand why pw*pi*r^2*dg=pc*pi*r^2Hg
Homework Statement
A conductor sphere of radius R without charge is floating half-submerged in a liquid with dielectric constant ##\epsilon_{liquid}=\epsilon## and density ##\rho_l##. The upper air can be considered to have a dielectric constant ##\epsilon_{air}=1##. Now an infinitesimal...
I'm interested in the following general question: Assume x,y,z is an axes system, and that the y-z plane is occupied by a conductive plate at a known potential V with respect to the earth. Now, a conductive material M of neutral global electrical charge is placed at some distance of the plate...
In this circuit i want generate the floatin voltage from the external supply connected by a load to drain of transistors (suppose this is constant). So for me is possible to command the gates without an auxiliary low voltage battery.
Taking advantage of the high sensitivity of the mosfet I...
Homework Statement
I have 4 resistive sensors thus I need to tie 4 floating current sources. Floating current source will give me output voltage linear to the resistance of a sensor. I know it is not the best solution but it is good enough.
Image provided:
Homework Equations
None
The Attempt...
Homework Statement
The surface of a liquid is just able to support the weight of a six-legged insect. The leg ends can be assumed to be spheres each of radius 3.2 × 10−5 m and the weight of the insect is distributed equally over the six legs. The coefficient of surface tension in this case is...
For many, many years (don't ask), I've been running into the classic example of the local reference frame: the man in the box who can't tell if he's floating free in space, or falling into a gravity well.
It occurs to me that if one is in a falling box, a mass released at the top of the box...
Homework Statement
Homework EquationsThe Attempt at a Solution
When air is evacuated , atmospheric pressure pushing down the cork is eliminated , cork should rise a little i.e option b) . This is incorrect .
What am I missing ?
I have been searching but I have not been able to find the information I am looking for. I want to build a "floating table" that is supported by one or more compression springs. When an object is added the table will lower by just a bit. As another object is stacked on top of the first one...
Anybody can help me?? The problem is when the value of (r1o = r, and r2o=r), the result will be infinite,,,what the the probably test for this case?? I can't test floating point numbers for equality ( if r == 0.5 and r == -0.5). But, when running this program without test floating point, it...
While waiting in the doctor’s office, I looked at a balloon sticker on the wall. That made me think (once again). Would it be possible to make something float without using your basic flotation stuff (helium and propellers mostly)? I was thinking in more of a futuristic themed way. Like magnets...
I recently watched a great video demonstrating the floating water bridge experiment:
At around 34 sec, you can see an electrostatic discharge before the water bridge forms. I've read that this is due to the electrostatic breakdown of air between the two beakers.This made me curious about the...
Hello, I am someone who has no experience in physics other than primary/high school and I have a quick simple question about something I can't wrap my mind around as a complete physics newbie. Please have understanding.
The question: let's say a train is standing still at a point in space (so...
Homework Statement
A 9 cm square wooden post (density=420kg/m3) is 1.3m long and floats in sweater (density=1029 kg/m3. How deep is the post submerged in the water? The picture shows a 9cm x 9cm cross section of the post.
Homework Equations
Fb=density of liquid x volume of liquid submerged x...
Homework Statement
A thin bi-convex lens with refractive index n has spherical surfaces with equal radii of curvature r and measured focal length f. The lens floats horizontally on the surface of liquid mercury so that its lower surface effectively becomes a spherical mirror. A point object on...
Homework Statement
This problem is found in The Exercises for the Feynman Lectures on Physics:
A flat steel plate floating on mercury is acted upon by three forces at three corners of a square of side 0.100 m. Find a single fourth force which will hold the plate in equilibrium. Give the...
Homework Statement
A 0.75-m rod has a uniform linear mass density of λ. A small mass m with negligible volume is attached to one end of the rod. The rod with the attached mass is placed in a container of unknown ﬂuid and after oscillating brieﬂy, comes to rest at its equilibrium position. At...
Elsewhere someone is planning to install Under Floor Heating (UFH) in a house that is prone to flooding. UFH systems typically comprise a layer of insulation then a layer of concrete screed with UFH pipes in it.
Given this recent news story...
We had a switch fail to close on the A phase of a floating wye connected capacitor bank. The C phase fuse was found to be bad and was replaced, however the B phase fuse then blew. The bad switch was then found and replaced. After that the system operated normally. The contractor said the...
im writing a 2d space simulator and in it i want to simulate rockets as well as things like space elevators and spaceguns to allow players to compare how each system works and compare pros and cons. one idea i want to include in that simulator is my own that i want to promote to the new...
Hello Forum,
In DC circuits, I understand that a ground is a point or an entire conductor where the electric potential is set to be V=0 and the potential V at any other point in the circuit is referenced to that.
How does the the concept of ground loops work? Why are they not desirable?
What...
OKay I just want to confirm...It is written everywhere that if , in a liquid, the upthrust acting on an object is equal to its weight, it will float...If we consider an object taken deep into a liquid, and somehow its weight becomes equal to the upthrust acting on it, then it would just stay at...
Hello!
I was hoping someone here could help me solve a real world problem. So my university pool has something called a bulkhead, which is basically a bridge that floats above the water so that people can walk across the shorter dimension of the rectangular pool (50 meters long, 25 yards wide)...