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Questions tagged [binary-arithmetic]

30 questions
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2 answers

Function that spreads input

I'd like to know if there is a function $f$ from n-bit numbers to n-bit numbers that has the following characteristics: $f$ should be bijective Both $f$ and $f^{-1}$ should be calculable pretty fast $f$ should return a number that has no…
fuz
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5 answers

Is 2**x faster to compute than exp(x)?

Forgive the naïveté that will be obvious in the way I ask this question as well as the fact that I'm asking it. Mathematicians typically use $\exp$ as it's the simplest/nicest base in theory (due to calculus). But computers seem to do everything in…
isomorphismes
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10
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8 answers

Represent a real number without loss of precision

Current floating point (ANSI C float, double) allow to represent an approximation of a real number. Is there any way to represent real numbers without errors? Here's an idea I had, which is anything but perfect. For example, 1/3 is…
incud
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10
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1 answer

Computing the number of bits of a large power of integer

Given two integers $x$ and $n$ in binary representation, what is the complexity of computing the bit-size of $x^n$? One way to do so is to compute $1+\lfloor \log_2(x^n)\rfloor=1+\lfloor n\log_2(x)\rfloor$ by computing an approximation of…
Bruno
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8
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3 answers

Finding maximum and minimum of consecutive XOR values

Given an integer array (maximum size 50000), I have to find the minimum and maximum $X$ such that $X = a_p \oplus a_{p+1} \oplus \dots \oplus a_q$ for some $p$, $q$ with $p \leq q$. I have tried this process: $\text{sum}_i = a_0 \oplus a_1 \oplus …
palatok
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6
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3 answers

Converting function to bitwise only?

I have a function to count upper bits of a 32 bit value. So if a number is 11100011111..., the result is 3 as there are 3 ones in the most significant place before a 0 is hit. I need to convert the function to use only bitwise operations (no if…
Anonymous
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6
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1 answer

How does binary addition work?

I find binary confusing. I have watched minecraft redstone videos on binary adders, real binary adders, diagrams, etc and yet I have not learned much at all. How does electrons flowing through wires made of gold "add/subtract" to make numbers…
AMDG
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6
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3 answers

What circuit depth is required to add?

If we suppose that we are given two numbers $a$ and $b$ to add, what circuit depth do we require to add them? I'm wondering if $a$ and $b$ are $O(n)$, and thus the amount of bits required to store $a$ and $b$ are $O(\log_2(n))$, how much time and/or…
Matt Groff
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2 answers

Isn't std::bernoulli_distribution inefficient? Designing a bit-parallel Bernoulli generator

C++11 has a convenient Bernoulli RNG, illustrated at http://en.cppreference.com/w/cpp/numeric/random/bernoulli_distribution . However, distilling an entire random integer into a single random bit seems inefficient when the expectation parameter $p$…
Igor Markov
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5
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1 answer

Double-nested loop with bitwise operation

I have this little exercise: for ( i = 0; i < 2 * n; i += 2 ) for ( j = 1; j <= n; j <<= 1 ) if ( j & i ) foo (); (j <<= 1 means j = (j << 1), where << is the bitwise left shift operator. & is the bitwise and operator.) I am supposed to…
Machta
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5
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2 answers

Are there algorithms or circuits that can implement addition without the need for carry flags

Let two numbers $x,y$ be represented in some digit form (binary, octal, ...): $(x_1 x_2 x_3 \ldots)$ and $(y_1 y_2 y_3 \ldots)$. Can we add those numbers such that we do not need to carry over: $x_i = x_i+y_i + c(x_{i-1},y_{i-1})$ where…
user13675
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2 answers

Minimizing the full adder - where did this XOR come from?

When minimizing the full adder, I don't understand why $A(\bar{B}\bar{C} + BC)$ reduces to $A\overline{(B\oplus{C})}.$ $(\bar{B}\bar{C} + BC)\to (B\oplus{C})$ is partially decipherable, but why is $(B\oplus{C})$ inverted to…
Tyler
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4
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1 answer

Computing the rank of a multiset after inserting another element

What is the procedure for computing the rank of a multiset after inserting an element? For instance, lets say we have a set $S = (0,1)$ containing $n = 2$ distinct elements. The multiset $M = (1,1)$ has rank $5$ because there are $4$ multisets less…
tshar
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2 answers

Japanese Multiplication simulation - is a program actually capable of improving calculation speed? Or am I doomed from the start?

On SuperUser, I asked a (possibly silly) question about processors using mathematical shortcuts and would like to have a look at the possibility at the software application of that concept. I'd like to write a simulation of Japanese Multiplication…
user17734
4
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1 answer

Bitarithmetrics to Base X

I've got the following theoretical problem which puzzles me a bit: I can obtain a string of n bytes (as octets, one byte = one octet = eight bits) of random data. I need to preserve the randomness while reducing the base from 256 to x where x is…
hakre
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