Hubbry Logo
Base 50Base 50Main
Open search
Base 50
Community hub
Base 50
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Base 50
Base 50
Base 50
View on Wikipedia
from Wikipedia

Honda 50cc engine
The Honda 50cc was first offered in the Honda Super Cub seen here.
Production1958-present
Assembly15 countries worldwide
ClassMotorcycle, scooter, moped, ATV, ATC, pit bike, dirt bike and various power sport machines.
EngineHorizontal 49–124 cc (3.0–7.6 cu in) 4-stroke air-cooled single
Transmission3- or 4-speed automated manual with wet multi-plate centrifugal clutch
Weight2–3 kg (4.4–6.6 lb) (dry)
RelatedLifan Group

A Base 50 engine is a generic term for engines that are reverse-engineered from the Honda 49 cc (3.0 cu in) air-cooled four-stroke single cylinder engine. Honda first offered these engines in 1958, on their Honda Super Cub 50. Honda has offered variations of this engine continuously, in sizes up to 124 cc (7.6 cu in), since its introduction. The Honda Super Cub has been produced in excess of 100,000,000 units, the most successful motorized vehicle in history.[1] With multiple manufactures utilizing clones of the Honda 50 engine for current mopeds, scooters, small motorcycles and power sport machines, it is the most produced engine in history.

The engines are usually identical in form, fit and function to Honda 50cc engines and the parts are usually interchangeable with genuine Honda parts.

The term Base 50 has originated from the importation of modern styled, small Pit Bikes that use the Honda CRF50 as a base for design. Base 50's have also been known as Chondas, a gang term due to influx of Honda clone engines being primarily from China. The name, a portmanteau of "Chinese" or "clone", and "Honda", is seldom used in direct sales marketing.

Intellectual property infringement

[edit]

Honda has a presence in China and shares manufacturing facilities with local industry, as required by Chinese local content trade law. Despite this, Honda has never pursued infringements regarding patents or intellectual property specifically regarding the Honda 50 or Base 50 engines, as the patents for said engines exceed 30 years.[2] Honda has pursued legal action against Lifan regarding other business practices, including Lifans use of Hongda for marketing motorcycles.[3] Honda also won a patent lawsuit in 2007 regarding a separate infringement for the sale of the Lifan LF100T motorcycle[4]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Base 50

View on Grokipedia
from Grokipedia
Base 50 is a that uses a (base) of 50, employing 50 distinct symbols as digits to represent values, with each position in a number signifying a power of 50. Unlike common bases such as 10 () or 16 (), base 50 has remained largely theoretical or confined to specialized applications, with its primary historical implementation occurring in computing rather than everyday arithmetic. The system gained practical use in the IBM SQUOZE encoding scheme, where it enabled efficient packing of symbols into machine words on early IBM computers. In the IBM SQUOZE system, introduced in 1958 with the SCAT assembler on the SHARE Operating System for the , base 50 facilitated compression of alphanumeric identifiers and symbols. A could encode six characters from a 50-symbol alphabet (including uppercase letters A–Z, digits 0–9, and special characters such as space, =, #, /, %, +, &, -, @, *, $, ,, and .), plus two flag bits. This was achieved by splitting the six characters into two groups of three, with each group treated as a three-digit number in base 50 (for example, characters A, B, C encoded as A × 50² + B × 50 + C), then combining the results into the word. This approach exploited the fact that 50⁶ is less than 2³⁶, requiring fewer bits than a full six-bit-per-character representation and saving storage on memory-constrained machines like the IBM 709, 7090, and 7094. The encoding treated character strings as positional numbers in base 50, converting them to binary for storage and reversing the process for retrieval. For instance, the string "SQUOZE" was packed into a 34-bit value within a , demonstrating the system's efficiency for in early and . This differs markedly from similar schemes like DEC RADIX-50 (also known as DEC Squoze), which used a 40-character set (equivalent to octal 50, or 40 decimal) and packed three characters into 16 bits on DEC systems. IBM's base 50 thus represented a distinct adaptation tailored to its hardware architecture. Beyond its role in IBM SQUOZE, base 50 has seen minimal adoption in other contexts and remains uncommon compared to more widespread . Its significance lies primarily in illustrating early techniques for data compaction in computing, where larger allowed denser representation of restricted symbol sets within fixed word sizes.

Introduction and basics

Definition and properties

Base 50 is a with a of 50. In this system, each represents a power of 50, and the value of a number is the sum of its digits multiplied by the corresponding powers of 50, where each digit is an from 0 to 49. This requires exactly 50 distinct symbols (digits) to represent all possible values in each position. Mathematically, the value vv of a base-50 number with digits dm,dm−1,…,d1,d0d_m, d_{m-1}, \dots, d_1, d_0 (where dm≠0d_m \neq 0) is given by v=∑k=0mdk⋅50kv = \sum_{k=0}^{m} d_k \cdot 50^k with 0≤dk<500 \leq d_k < 50. The are : 500=150^0 = 1, 501=5050^1 = 50, 502=250050^2 = 2500, 503=12500050^3 = 125000, and so on. The number of digits required to represent a positive integer NN in base 50 is ⌊log⁡50N⌋+1\lfloor \log_{50} N \rfloor + 1. In specialized computing contexts, base-50 representations have been applied to efficiently encode data using sets of 50 symbols treated as digits in this .

Comparison to common bases

Base 50 differs markedly from common due to its large of 50, which exceeds (base 2), (base 8), (base 10), and (base 16), while being slightly less than sexagesimal (base 60) used historically for time and angles. In terms of information density, each base 50 digit represents one of 50 possible values, yielding approximately \log_2(50) \approx 5.64 bits per digit—substantially higher than 's 1 bit per digit, 's \approx 3.32 bits per digit, and 's exact 4 bits per digit. This higher density means base 50 can represent a given numerical magnitude with fewer digits than smaller-base systems. For large numbers of magnitude around , base 50 requires roughly n / \approx n / 1.699 \approx 0.588n digits, compared to n digits in (or approximately 0.833n digits in ). Practically, the reduced digit count offers efficiency in specialized contexts like historical data packing (e.g., IBM SQUOZE, which used base-50 encoding to fit six characters into 34 bits), but the need for 50 distinct symbols makes it far less convenient for human use than bases with fewer digits, such as or .

Representation of numbers

In base 50 , numbers are represented as sequences of digits ranging from 0 to 49, where each digit's position indicates a power of 50. The rightmost digit corresponds to 50^0 (the units place), the next digit to the left corresponds to 50^1, and so on, with the value of the number being the sum of each digit multiplied by its respective power of 50. The leftmost digit carries the highest . typically includes a subscript "50" to specify the , such as 10_{50}, which equals 1 × 50^1 + 0 × 50^0 = 50 in . Digits 0 through 9 can use standard , but digits 10 through 49 lack universal single symbols and are commonly denoted by their decimal equivalents, often placed in parentheses or separated by delimiters to avoid ambiguity with adjacent digits. For example, the decimal number 592 can be represented as (11)(42)_{50}, interpreted as 11 × 50^1 + 42 × 50^0 = 550 + 42 = 592. Small values up to 49 are represented identically to their forms (e.g., 1_{50} to 49_{50}), while values from 50 onward require . For instance:
  • 50 (decimal) is 10_{50}
  • 99 (decimal) is 1(49)_{50} = 1 × 50 + 49 = 99
  • 2500 (decimal) is 100_{50} = 1 × 50^2 + 0 × 50^1 + 0 × 50^0 = 2500
  • 2601 (decimal) is 111_{50} = 1 × 50^2 + 1 × 50^1 + 1 × 50^0 = 2500 + 50 + 1 = 2601
Larger numbers follow the same principle, with additional positions for higher powers of 50. Zero is represented simply as 0 (or 0_{50}), and leading zeros do not alter the numerical value but may appear in fixed-length or encoding contexts to maintain consistent digit counts. In specialized applications like the IBM SQUOZE scheme, symbols are mapped to base-50 digit values (0-49), and groups of characters are treated as —for example, three symbols A, B, C are encoded as A × 50^2 + B × 50 + C—demonstrating practical use of this representation for data compaction.

History and usage

Origins and early references

Base 50 as a with a of 50 and 50 distinct digits lacks documented origins in ancient or pre-modern numeral systems. Historical numeral systems from ancient civilizations, such as the that used with cuneiform symbols for powers of 60, show no evidence of a base 50 positional scheme. Unlike the well-attested in , in , or in many cultures, base 50 does not appear in historical records as a standard for everyday or mathematical use. While some languages and feature numeral systems described as base-50, these are typically additive rather than fully positional with 50 distinct symbols; for instance, certain employ an additive base 50 for with . Similarly, numeral systems in the include base-50 structures, but these are unusual and influenced by body-part metaphors without constituting a full positional system with unique digits for 0 through 49. The positional base 50 thus remains primarily a theoretical construct, rarely adopted historically as a complete numeral system. Its earliest practical references emerge in , where radix-50 encodings were developed to efficiently pack symbols in limited memory, as seen in specialized schemes on early IBM machines. These computing applications are discussed further in later sections.

Computing applications

Base 50 encoding was employed in early computing as a data packing mechanism, particularly through 's SQUOZE format introduced in 1958 for the computer. SQUOZE packed six characters from a set of 50 symbols, plus two flag bits, into a single , with the character data occupying 34 bits. This scheme leveraged base-50 representation to achieve efficient storage, as six base-50 digits fit within 34 bits (since 50⁶ < 2³⁴). The format was primarily used for in —contributing to the historical practice of restricting external symbols to six characters with a limited character set—and for compactly representing combined source and , including symbol tables, on . It is distinct from DEC's Radix-50 encoding, which despite its name is a base-40 system (50 in equals 40 in ) and uses different packing for .

Modern and hypothetical uses

In contemporary contexts, base 50 has no widespread or standardized adoption as a and remains primarily theoretical or illustrative in nature. It appears occasionally as an example in software libraries designed for arbitrary-base numeral handling and conversion. For instance, the mXparser mathematical expression parser and evaluator library supports base 50 representations, using it in tutorial examples to demonstrate parsing and evaluation of numbers in , such as through expressions like base(50, 1, 2, 3, 49). Hypothetical discussions of high-radix systems (including base 50) sometimes arise in explorations of that leverage for data compaction or , though base 50 itself is not highlighted as a primary or implemented choice in such proposals. No prominent contemporary implementations in computing, , or other fields are documented, and it continues to lack practical everyday or industrial use.

Digit sets and encodings

IBM SQUOZE was a base-50 encoding scheme introduced in 1958 with the SCAT assembler in the SHARE Operating System for the , and later employed on the and 7094 machines. It provided a compact representation of , primarily for in programs, by packing six characters into one (with two bits reserved for flags). The scheme used a fixed set of 50 characters: the 26 A–Z, the 10 , the space character, and the 13 special characters =, #, /, %, ), +, &, -, @, *, $, ,, and .. Each character was mapped to a unique value from 0 to 49 according to its position in this alphabet. Six characters ABCDEF were encoded using the formula (A×502+B×50+C)×217+(D×502+E×50+F)(A \times 50^{2} + B \times 50 + C) \times 2^{17} + (D \times 50^{2} + E \times 50 + F) where A–F are the decimal values of the characters in the base-50 alphabet. This grouped the characters into two triplets, each converted to a base-50 value (maximum 124,999, which fits in as 217=131,0722^{17} = 131{,}072), then combined by and adding the second, yielding a 34-bit data value. By exploiting the fact that 50 requires approximately 5.64 bits per character (versus the 6 bits used in standard ), SQUOZE saved two bits per , enabling denser storage of symbolic information. This packing method supported efficient handling of that combined , , and , which were processed by loaders to produce on these early .

Gurmukhi-based encoding

One proposed variant for representing base 50 employs the to define its digit set. This encoding combines all characters from the with the standard (੦ through ੯) to form a collection of 50 distinct symbols, each corresponding to a value from 0 to 49. This approach appears in as an illustrative example of adapting an Indic script for high-radix , though it remains theoretical and lacks widespread adoption or detailed implementation records. It demonstrates the potential flexibility of using established to supply sufficient for larger bases beyond conventional Latin or .

Other proposed or custom digit sets

In the absence of a standardized for , custom approaches for representing values beyond the conventional and A–Z () vary widely and remain ad hoc. Some modern implementations, such as certain online base converters, extend the set using lowercase letters (e.g., a through n for values 36 through 49) to provide the additional 14 symbols needed. Other extensions may draw from punctuation or typographical symbols, though no universal or dominant convention has emerged. For bases exceeding 36 in general, no universal convention exists, and selections are typically ad hoc, sometimes relying on multi-character representations per to avoid needing more than 36 unique symbols. Challenges include ensuring and distinctiveness to prevent confusion in handwritten or displayed forms, as well as compatibility across different contexts or computing environments. As a result, base 50 lacks a dominant digit set beyond specialized historical encodings like IBM SQUOZE (covered separately) and remains largely theoretical or context-specific rather than widely adopted.

Mathematical aspects

Place value and positional notation

In a with , the value of each digit depends on its position relative to the radix point, with each position representing a successive power of 50. The rightmost digit occupies the 50^0 place (value 1), the digit immediately to its left occupies the 50^1 place (value 50), followed by 50^2 = 2500, 50^3 = 125000, 50^4 = 6250000, and so on for higher places. Any number in base 50 can be expressed using the general formula for applied to base b=50b = 50: for a sequence of digits dndn−1…d1d0d_n d_{n-1} \dots d_1 d_0 (where each dkd_k is an integer from 0 to 49), the value is dn×50n+dn−1×50n−1+⋯+d1×501+d0×500d_n \times 50^n + d_{n-1} \times 50^{n-1} + \dots + d_1 \times 50^1 + d_0 \times 50^0. This sum of digit contributions weighted by powers of the base yields the total value in . This mechanism contrasts with , such as , where symbol values are independent of order and position carries no multiplicative significance. In positional base 50, enables efficient representation of arbitrarily large numbers using a fixed set of 50 distinct digits, though custom symbols are typically required beyond the standard 0–9 due to the high .

Conversion to and from base 10

Conversion to and from base 10 Converting numbers between and base 50 follows the standard algorithms for with any . In base 50, digits range from 0 to 49, and each position represents a power of 50. To convert a number from base 50 to , multiply each digit by the appropriate power of 50 (starting with 50050^0 for the rightmost digit) and sum the results. This method yields the directly. For example, consider a base 50 number with digits 1, 10, 0 (written as 1,10,0 where 10 denotes the digit value ten). The conversion is 1×502+10×501+0×500=2500+500+0=30001 \times 50^2 + 10 \times 50^1 + 0 \times 50^0 = 2500 + 500 + 0 = 3000 in base 10. Another example: digits 2, 30 (as 2,30) gives 2×501+30×500=100+30=1302 \times 50^1 + 30 \times 50^0 = 100 + 30 = 130 in base 10. To convert a number from to base 50, repeatedly divide the number by 50 and record the , which become the base 50 digits from least to most significant (reading remainders from bottom to top). Continue until the is 0. For example, to convert 3000 (base 10) to base 50:
3000 ÷ 50 = 60 remainder 0
60 ÷ 50 = 1 remainder 10
1 ÷ 50 = 0 remainder 1
The remainders give digits 1, 10, 0 in base 50 (most significant first), equivalent to 1×502+10×501+0×500=30001 \times 50^2 + 10 \times 50^1 + 0 \times 50^0 = 3000. Another example, 130 (base 10):
130 ÷ 50 = 2 remainder 30
2 ÷ 50 = 0 remainder 2
The digits are 2, 30 in base 50. These methods apply generally to base 50 as a , regardless of the specific digit symbols used in encodings such as IBM SQUOZE or Gurmukhi variants (detailed in the digit sets sections). Remainders or digit values above 9 are simply the integer values 10 through 49.

Arithmetic operations in base 50

Arithmetic operations in base 50 are performed using the standard algorithms for , with carries and occurring whenever a column sum or difference reaches or exceeds the . Addition proceeds column by column from right to left. The in each position are added, along with any carry from the right, and if the total is 50 or greater, the after dividing by 50 is written as the digit in that position while the is carried to the next higher position. This process mirrors addition in but uses 50 as the threshold for carrying. For example, consider adding the base-50 numbers 1,49₅₀ (representing 1×50¹ + 49×50⁰) and 0,2₅₀ (2×50⁰). In the units place, 49 + 2 = 51; since 51 = 1×50 + 1, write 1 and carry 1. In the next place, 1 + 0 + 1 (carry) = 2. The result is 2,1₅₀. uses a similar right-to-left approach, with required when the top digit is smaller than the bottom digit in a column. Borrowing adds 50 to the current digit (equivalent to reducing the next higher digit by 1) before subtracting. For instance, subtracting 0,3₅₀ from 1,2₅₀: in the , 2 < 3, so borrow 1 from the fifties place (making it 0 and adding 50 to the units, yielding 52 - 3 = 49); the fifties place becomes 0 - 0 = 0 after borrowing. The result is 0,49₅₀. Multiplication follows the , producing by multiplying one number's digits by each digit of the other and shifting left accordingly, then adding those partial products using base-50 addition rules (including carries when partial sums ≥50). Carries are handled at each stage of adding the partial products. For example, multiplying the single-digit base-50 numbers 2₅₀ and 30₅₀ (where 30₅₀ represents the digit with value 30) yields 2 × 30 = 60 (in ). Converting 60 to base 50 gives 60 = 1 × 50 + 10, so write 10 and carry 1 to the next higher place (resulting in 1,10₅₀). Larger multi-digit cases extend this process with multiple partial products added in base 50. Because base 50 has a large , carries and borrows occur less frequently than in smaller bases when digits are moderate, though they become significant with larger digit values (near 49). The operations remain fully consistent with principles.

Comparison with other bases

Advantages and disadvantages

The primary advantage of base 50 as a is its high information density, which enables large numbers to be represented with significantly fewer digits than in lower-radix systems such as . This compactness stems from the larger value per , a general property of high-radix systems that can reduce the length of representations in applications prioritizing storage or transmission efficiency. However, base 50 presents substantial disadvantages for human use. It requires memorizing and distinguishing 50 distinct symbols, imposing a heavy cognitive burden compared to bases with fewer digits, such as the 10 used in . Arithmetic operations become more complex due to the large size of required , which grow quadratically with the and hinder manual computation. Base 50 also lacks the favorable divisibility properties of certain other bases, such as base 12 (with divisors 2, 3, 4, 6) or (highly composite), limiting its convenience for fractional representations involving a wide range of denominators. In contrast to theoretical optimal radices near e ≈ 2.718 (with as the most efficient integer base in terms of radix economy) or human-preferred ranges around 8–12 (balancing digit count, symbol learning, and arithmetic ease), base 50 falls far from these ideals and remains largely theoretical.

Relation to high-radix systems

Base 50 is an example of a with a large of 50, placing it among systems that use significantly more distinct digits than common bases such as 10 () or 16 (). High-radix numeral systems, including base 60, have historical precedence in . The sexagesimal system (base 60), originating in , employed with powers of 60 to support advanced mathematical and astronomical computations, benefiting from 60's high divisibility for representing fractions. Related high-radix approaches in computing include base 64, which appears in modern encoding schemes (such as base64 for ) and specialized using 64 symbols, though these are typically encoding mechanisms rather than general for arithmetic. Very high remain largely theoretical or niche outside computing encodings, as the requirement for numerous distinct symbols limits , while their primary appeal lies in minimizing for representation or achieving specific efficiencies in machine-oriented applications.

References

  1. https://hackaday.com/2016/11/22/squoze-your-data/
  2. https://handwiki.org/wiki/SQUOZE
  3. https://r-knott.surrey.ac.uk/IntegerReps/intreps.html
  4. https://math.tools/calculator/base/10-50
  5. https://math.stackexchange.com/questions/4780579/on-the-non-equivalency-of-information-density-between-radices
  6. https://www.informit.com/articles/article.aspx?p=2221791
  7. https://dl.acm.org/doi/10.1145/320964.320968
  8. https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_numerals/
  9. https://pure.mpg.de/rest/items/item_1586644/component/file_1878151/content
  10. https://www.cambridge.org/core/journals/iranian-studies/article/metaphorical-use-of-body-parts-in-forming-counting-expressions-evidence-from-tati-language-group/630FE363E1873FD9B4FE136AB84BC759
  11. https://mathparser.org/mxparser-tutorial/various-numeral-systems/
  12. https://arxiv.org/pdf/2306.02378
  13. https://numerals.fandom.com/wiki/List_of_number_systems
  14. https://online.math.uh.edu/Math2303-unpaid/ch1/s14/2303-Section-14.pdf
  15. https://www.inchcalculator.com/base-converter/
  16. https://www.cut-the-knot.org/blue/SysTable.shtml
  17. https://openstax.org/books/contemporary-mathematics/pages/4-4-addition-and-subtraction-in-base-systems
  18. https://openstax.org/books/contemporary-mathematics/pages/4-5-multiplication-and-division-in-base-systems
  19. https://www.lenovo.com/ch/en/glossary/what-is-radix/
  20. https://www.probabilisticworld.com/numeral-systems-everything-you-need-to-know/
  21. https://mathoverflow.net/questions/479253/what-is-the-mixed-radix-numeral-system-of-best-radix-economy
  22. https://www.scienceabc.com/eyeopeners/why-we-should-already-use-base-12-instead-of-base-10.html
  23. https://math.stackexchange.com/questions/446664/what-is-the-most-efficient-numerical-base-system
  24. https://steven-varga.ca/site/radix64/
  25. https://vorakl.com/articles/stream-encoding/
Add your contribution
Related Hubs
User Avatar
No comments yet.