Questions tagged [floating-point]

Approximate representation of numbers as a fixed number of digits multiplied by a logarithmic scale.

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382 views

Implications of truncation of numbers when converted into binary

I have been posed with a question whereby a computer truncates numbers to x number of digits. Due to this, if this computer is trying to store a decimal number which has a binary equivalent greater ...
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1answer
625 views

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes Floating point overflow. Negative floating point overflow. All 0's in the exponent ...
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Is Decimal (correctly-rounded arbitrary precision decimal floating point arithmetic) fixed-point, floating-point or something else?

The Decimal data type I am referring to is GNU MPFR(https://en.wikipedia.org/wiki/GNU_MPFR), or libmpdec (http://www.bytereef.org/mpdecimal/doc/libmpdec/index.html). I have been searching for ...
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Floating point substraction

if $x=1.0e38=1.0 * 10^{38}$ and $y=3.0$ i want to find $ (x-x)+y $ and $(x+y)-x$ i think the value of (x-x)+y will be just substract $x-x=0 + y=3.0 = 3.0$ but how can i perfom addition of different ...
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1answer
61 views

Computing an Expression

I am writing code to evaluate the following expression: $$ \frac{(a+b+c)!}{a! b! c!} $$ where $a$, $b$ and $c$ are on the range of $10$ to $500$. The result is going to be a floating point number. ...
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57 views

How does normalised floating point binary work with two's complement?

I'm doing AQA a-level computer science, and the specification for which states that: Exam questions on floating point numbers will use a format in which both the normalised mantissa and exponent are ...
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1answer
44 views

algorithm for correctly rounded floating point radix conversion

Is there any generic algorithm which implements a floating point radix conversion? Lets say we have a $p$-digit FP number $A = \sum_{i=0}^{p-1} A_i \beta^{e-i}$ in radix $\beta$ and with $0 \leq ...
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1answer
181 views

Floating point Euclidean norm optimization

Past few days I've been struggling with floating point number exercises, trying to learn how they work and what are their limitations. The exercise I've encountered today is as follows: The ...
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2answers
415 views

How to compute relative error for the rounding of floating point numbers when the rounded number is 0?

I have asked this question on Stack Overflow, I am asking it here in the hope to get more traction. The relative rounding error for a floating point number x is defined as $e_r = |\frac{(round(x) -...
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Using a 16-bit 2,s Complement normalised floating-point representation; 10-bit fractional mantissa and a 6-bit integer exponent: express 2.171875

So far I know how to normalize when you are given, say: 1111010010 Mantissa, and 000100 exponent and are told that it's a positive number: ...
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Can area-partitioning lose included points due to floating point precision?

I'm currently partitioning a big area $A$ into $n$ areas $B_i$ such that $$\bigcup_{i=1}^n B_i = A$$ I have geo-coordinates which I know are in $A$ (also with the finite precision of floats). ...
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Using half float to represent scaled short (int16), do I lose precision comparing to using double?

A device is generating 14-bit integer which is stored as int16 (short), a scaling process will then scale the data to value of order 10E-3. Does it then matter if I store these number with half float ...
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1answer
140 views

Computing the error bound of floating-point expression

How should I compute the maximum absolute and relative error of the following IEEE-754 floating-point expression? a.y + (x - a.x) * ((b.y - a.y) / (b.x - a.x)) ...
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Inverting an IEEE 754 double

While preparing for an exam I've come across this problem: Let $x$ be an IEEE 754 double precision number. Show that $$ \texttt{fl}(x * \texttt{fl}(1/x)) $$ has only 2 possible results ...
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When do you know whether an exponent represents a movement of the decimal point to the left?

I'm learning about floating point numbers and I don't quite understand when one should interpret an exponent as moving the decimal point to the left. By book shows an example of converting -10.5 ...
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How can a Number Represented without Normalization Technique?

Consider the following floating point Representation Mantissa is pure fraction in signed magnitude form . What is the representation of the binary number 1111.1111 $\times 2^{2} $ in hexadecimal ...
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How do the Guard, sticky, and round bits work and affect floating point Representation?

I've got a test on this tomorrow, my instructor's lectures aren't up, and the notes are ambiguous... Anyhow, we've been covering floating point operations, specifically addition, and he mentioned ...
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91 views

How to determine the range of a number represented in IEEE-754 format?

Given a format: say 12-bit floating point with sign bit, 5 - bit biased exponent and 6- bit significant with implied bit, how do i go about determining the range of ...
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Logarithms using digit recurrence, how many bits to store in a LUT?

In a known method for approximating logarithms the following decomposition is adopted (assuming $x \in [1,2)$): $$ log_2(x) = 1 + \sum_{j=1}^{+\infty} w_i log_2(1+2^{-j}) $$ Where all the ...
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Are floats abstract data types?

Source:https://en.wikipedia.org/wiki/Abstract_data_type Can we say that float data types (or all primitive data types or only integer) are abstract data types?
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Calculating sums of floating point numbers by hand

how do you calculate the sum of 2.6125 * 10^1 and 4.150390625 * 10-1 by hand, assuming A and B are stored in the 16-bit half precision. i cant figure out how to do this by hand with out losing most of ...
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1answer
357 views

Problem on Floating Point Representation

Consider the floating-point representation 31-24 : Exponent 23-0 : Mantissa The exponent is in 2's complement representation and mantissa is in the sign ...
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1answer
46 views

floating point normalised value of -1

I have, lets say, 8 bits mantissa and 4 bit exponent. Then, -1=1111 1111 there are no 0s so how can I normalise -1 in 2's complement form?
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NaN simple precision IEEE 754 [closed]

How many words exist in the format of the simple precision IEEE 754 standard to represent the NaN value?
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Write the smallest positive number that can be represented by the floating point system

Using a normalised floating point representation box with an 8-bit mantissa and a 4-bit exponent, both stored using two’s complement. (a) Write the smallest positive number that can be represented by ...
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1answer
556 views

Convert between IEEE 754-2008 decimal64 and IEEE double precision floating point number

I need to know the algorithm for converting between IEEE 754-2008 decimal64 and IEEE 754-1985 double precision floating point number. I have been working on this for the past 2 days and I match the ...
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1answer
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Product with floating point [closed]

I was studying the product with floating point and I saw this example. I made the translation, sorry if something is not grammatically correct. ![enter image description here][1]
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Doubt in definition of Float

Can anyone tell the meaning of the bold portion? Float: It is used to store decimal numbers (numbers with floating point value) with single precision.

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