Rounding (roundoff) error is a phenomenon of digital computing resulting from the computer's inability to represent some numbers exactly. Specifically, a computer is able to represent exactly only integers in a certain range, depending on the word size used for integers.
Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.
Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; Rounding to a specified Rounding to integerTie-breakingDouble rounding
Rounding Computer Science Rounding Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter simpler or Rounding to a specified Rounding to integerTie-breakingDouble rounding
'Floating-point can also represent fractions between powers of 2: 0.750=1.5×2−1' But wait a minute. ...
Apologies for the confusing explanation. Let's step through how the computer actually represents that number in floating point representation and s...
Why is a floating point called that way? What is floating about it?
Great question. The floating part is the decimal (between the whole part and the fractional part), as floating point representation can both repres...
I was experimenting with this in Swift using doubles and floats. I wrote: var result2: Double = 0.1 ...
Funnily enough, yes. A number like 0.1 isn't easy store, because it's difficult to turn into a power of two. You see when you tell your computer to...
I realized there is a pattern in binary numbers 00000 00001 00010 00011 00100 00101 00110 00111 0100...
Nice observation! If you look at the period between changing phases (1 -> 0 or 0 -> 1), you'll see you get exactly 2^i which corresponds to the ith...
I didn't understand how floating point representation number like 0.375 in wrtten in binary.It's get...
There are 3 parts of a floating-point representation (using the IEEE-754 standard). The first bit is used to determine the sign of the number, 0 is...
Why do modern computers only use 64 bits? Can't they use as many bits as they want? Since more bits ...
Hello! This subject gets pretty deep, but it boils down to bit and computer architecture. 64 bits is 8^2 so 8 bytes, and as we learned a few lesson...
Why Doesn't an 8-bit calculator experience round off error to the same degree as a 64-bit computer m...
Your computer being a 64-bit machine doesn't really have anything to do with the number format, rather it describes its ability to store computatio...
are there some other programming scenarios when 2^1024 = infinity?
In JavaScript, Math.pow(2, 1024) is Infinity due to the limitations of how numbers are stored in JavaScript. However, those limitations vary by lan...
shouldn't max value be 32 because 0 is redundant? If there are 5 bits to store a value plus one more...
Nice observation as this is what has been done in practice! However, one small modification is that a 6-bit number often ranges from -32 to 31. Thi...
I didn't understand the bar over the 3 what was that for ?
The bar is sometimes used in mathematics to show that the numbers below the bar repeat periodically. So in this case it means the 3 keeps repeating...
In computer science, a scale factor is a number used as a multiplier to represent a number on a different scale, functioning similarly to an exponent in mathematics.
A scale factor is used when a real-world set of numbers needs to be represented on a different scale in order to fit a specific number format.
Although using a scale factor extends the range of representable values, it also decreases the precision, resulting in rounding error for certain calculations.
