radix
Let an agent explain radix and positional notation, convert numbers between bases, describe common bases in computing and history, and separate other senses of radix.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain radix and positional notation, convert numbers between bases, describe common bases in computing and history, and separate other senses of radix.
The number of unique digits, including zero, used to represent numbers in a positional numeral system, also called the base, such as ten for decimal, two for binary, eight for octal, sixteen for hexadecimal and sixty for the Babylonian system; the radix determines place values and is used in computing, mathematics and number representation, with the word also denoting a root in botany and linguistics.
What it is for: The base of a numeral system.
It can be explain radix and place value; convert between bases; describe common bases; separate other senses.
Distinguishing features
Positive integer
Defines place value
Computing relevance
Historical variety
What it looks like
Not physical; a positive integer defining a numeral system.
How it is recognised
Number of digits in a positional system
Decimal ten, binary two, hexadecimal sixteen
A root in botany or a word root are other senses
Related models
is a kind of - category
is a kind of - category
is related to - arithmetic in bases
is related to - naming in decimal
In practice
Families and kinds
decimal radix
binary, octal and hexadecimal radices
sexagesimal and other historical radices
mixed radix systems
non-integer and negative radices
Standards and regulation
Mathematical and computing notation conventions
Standards for number representation in software
Failure modes and hazards
Confusing digit strings across bases
Conversion errors
Confusing radix senses
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Define What a radix is.
Concepts.
Definition
Radix and place value.
Definition
Definition.
- What is a radix, and how does it determine place values in positional notation? definition
- Is the numeral base, a botanical root or a word root meant? boundary
Bases
Common bases.
Bases
Bases.
- Why are binary, octal and hexadecimal used in computing, and why is decimal common in daily life? definition
- What are mixed radix systems such as time and angles? definition
Convert Converting bases.
Practice.
Calculate
Base conversion.
Calculate
Conversion.
- What is this number in another base, and how is the conversion done? action
- How are fractions represented in other bases? definition
Arithmetic
Arithmetic in bases.
Arithmetic
Arithmetic.
- How are addition, subtraction and multiplication performed in binary or hexadecimal? action
- How does radix affect divisibility tests? definition
Computing Radix in computing.
Applications.
Representation
Number representation.
Representation
Representation.
- How do computers represent integers and floating point numbers with radix two, and what is a radix point? definition
- What is radix sort? definition
Notation
Notation and prefixes.
Notation
Notation.
- How are bases indicated in programming languages and mathematics? provenance
- Which pitfalls arise in reading numeric literals? provenance
Learn History and teaching.
Education.
History
History of bases.
History
History.
- How did positional systems with different radices develop, from Babylonian sexagesimal to Hindu-Arabic decimal? provenance
- Which cultures used other bases? provenance
Teach
Teaching.
Teach
Teaching.
- How can radix and base conversion be taught? action
- Which misconceptions arise? provenance
What the second pass must settle
- Should each base be a separate entry?
- How should conversion tools be linked?
- How should historical systems be linked?