# Questions tagged [computer-arithmetic]

For questions concerning finite precision arithmetic in computers and other related concepts.

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### How to generate Maximum Min-SW gray code?

I'm trying to generate Maximum min-SW gray code for structured light described in this paper. Can someone help to understand how to generate this 10 bit gray code?
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### Identify all the RAW data dependencies in the following code.

Identify all the RAW data dependencies in the following code. Which dependencies are data hazards that will be resolved by forwarding? Which dependencies are data hazards that will cause a stall? ...
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### Floating point approximation to logarithms by powers and bit counting?

Earlier I both asked questions and found some interesting sources on the internet of how to do approximate division by combining and counting number of 0s following most significant bit in denominator....
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### Relativistiv kinetic energy and floating point

My function is $E(v)=mc^2(\frac{1}{\sqrt{1-v^2/c^2}} - 1)$, (c=3e8, m=1) and I have to calculate it for values of v between 1e-6 and 2.99e8. The point of this problem is floating point precision. For ...
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### Is there any way to predict the amount of “carries” one could get by doing a sum?

https://en.m.wikipedia.org/wiki/Carry_(arithmetic) Definition of carry in Wikipedia I'm guessing the answer is no but just to be sure I wanted to know of there is a way to predict the amount of ...
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### Division-free Krylov methods?

I have been using various Krylov subspace methods for a long time, especially conjugate gradient. I'm wondering if there is some way to modify the algorithms to postpone / avoid the divisions that ...
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### What is the symbol for a a result that overflows?

Suppose we have an unsigned $8$ bit number (min=$0$, max=$255$). the result of "$200 + 200$" overflows to $144$ the result of "$100 - 200$" (under?)overflows to $156$ Is there are mathematical ...
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### Hanek payne trigonometric range reduction detailed analysis of loss of significance.

I'm struggling to understand what is the actual problem described as "loss of significance" when a trigonometric range reduction argument is performed. I was trying to perform the analysis by myself ...
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### Concatenation of languages and multiplying strings

I'm having a hard time understanding concatenation of languages. I'm trying to understand how the following can be possible: |L1L2| $\neq$ |L1| * |L2| That is, the number of strings in the language ...
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### Machine numbers in a 32-bits (binary digits) computer?

I'm currently studying Numerical Analysis with the book "Numerical Analysis: Mathematics of Scientific Computing" by Kincaid. In this book, the authors have introduced a computer called "Marc-32" ...
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In section 5.3. of the following book an analysis of carry propagation in the ripple carry adder is performed. However the statistical analysis doesn't particularly convince me. Specifically at the ...
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### truncation in two's complment

My textbook gives an example of truncating a signed number in two's complement from 4 bits to 3 bits. It truncates -4 to 4. I am little confused by this, because the binary representation of -4 is ...
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### Mathematical Properties of Logical Shift

Many programming languages feature a logical shift operator, such as $(x >> n)$, where the bits of $x$ are shifted $n$ steps to the right (or left, $<<$), and the "vacated" bit positions ...