I've been experimenting with the idea of using 2-adic expansions of numbers to efficiently do division on computers. For instance, if you have the 8-bit integer, 171(0b10101011), multiplied by 3 truncates to 1(in full it's 0b1000000001, which as an 8-bit number simply equals 1), meaning that it's effectively 1/3 in this number system. My question is if there's a way to convert this truncated number back to a fraction without simply multiplying it with every number until you find the one that equals one. Further, if I multiply two of these fractions together, is it possible to determine whether the result is a fraction or a whole number?
2026-03-30 17:55:17.1774893317
Converting a 2-adic expansion to a fraction
32 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPUTER-SCIENCE
- What is (mathematically) minimal computer architecture to run any software
- Simultaneously multiple copies of each of a set of substrings of a string.
- Ackermann Function for $(2,n)$
- Algorithm for diophantine equation
- transforming sigma notation into harmonic series. CLRS A.1-2
- Show that if f(n) is O(g(n) and d(n) is O(h(n)), then f(n) + d(n) is O(g(n) + h(n))
- Show that $2^{n+1}$ is $O(2^n)$
- If true, prove (01+0)*0 = 0(10+0)*, else provide a counter example.
- Minimum number of edges that have to be removed in a graph to make it acyclic
- Mathematics for Computer Science, Problem 2.6. WOP
Related Questions in P-ADIC-NUMBER-THEORY
- How does one define an inner product on the space $V=\mathbb{Q}_p^n$?
- Can $\mathbb{Z}_2$ be constructed as the closure of $4\mathbb{Z}+1$?
- Number of points in reduction of a p-adic analytic manifold.
- How do I translate functions on the Prufer 2-group between functions on the $2^n$ roots of unity and the dyadic fractions modulo 1?
- Hensel Lemma and cyclotomic polynomial
- orbit representatives for the group of unipotent matrix acting on the set of skew-symmetric matrices
- Homomorphic images of $p$-adic integers
- Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$
- What do the elements of the affinoid algebra $A=K\langle x, y\rangle/(y-\pi x)$ look like?
- Find $\frac{a}{b} \in \mathbb{Q}$ such that $ |\,\frac{a}{b} - \sqrt{2}|_3 < \epsilon $
Related Questions in BINARY
- What is (mathematically) minimal computer architecture to run any software
- Produce solutions such that $k$&$x$ $=$ $k$,in a range ($0$,$n$)
- Solve an equation with binary rotation and xor
- Number of binary sequences with no consecutive ones.
- Recurrence with $\lfloor n/2 \rfloor$
- Converting numbers to different bases
- Why does the decimal representation of (10^x * 10^y) always suffix the same representation in binary?
- Period of a binary sequence
- Contradiction in simple linear regression formula
- From unary to binary numeral system
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?