Python binary decimal converter calculator free download
Create python binary decimal converter calculator free download program that takes a decimal floating point number and displays its binary representation and vice versa: L2 as well as just say "Invalid input" or similar. Here however a possible base may extend beyond just the decimal digits, so it is no longer possible to rely on zero to nine only and their associated character codes, thus the "digit" is now identified by indexing into an array of digits, thereby enabling "A" to follow "9" without character code testing.
The original routine was intended for usages in the hundreds of millions of calls, so this version would be unsuitable! In handling this, the exponent part was added to DD python binary decimal converter calculator free download who knows, the result may produce a zero DD as in " Few numbers are presented with more than sixteen fractional digits, but I have been supplied data supposedly on electric power consumption via the national grid with values such as 1.
It is better to risk one only, at the end. In a more general situation the text would first have to be scanned to span the number part, thus incurring double handling. The codes for hexadecimal, octal and binary formats do not read or write numbers in those bases, they show the bit pattern of the numerical storage format instead, and for floating-point numbers this is very different.
Note the omitted high-order bit in the normalised binary floating-point format - a further complication. Rather than mess about with invocations, the test interprets the texts firstly as base ten sequences, then base two. It makes no complaint over encountering the likes of "" when commanded to absorb according to base two.
The placewise notation is straightforward: Note again that a decimal value in binary is almost always a recurring sequence and that the exact decimal value of the actual binary sequence in the computer of finite length is not the same as the original decimal value. In this draft, the task does not give any guidelines for handling precision. So we will use 99 places after the decimal point and trim any trailing zeros and the decimal point, for integer case.
Also, since J does not have a "Decimal floating point number" data type, we will use a list of characters to represent a decimal or binary number this corresponds roughly with the relevant feature set of REXX which seems to have had a strong influence on this draft of this taskand use internal mantissa,exponent representations during the conversion. Well, I am no expert in OCaml, and my code may seem a bit messy, but I actually took a rather naive aproach Anyway, the program seems to work, but the algorithm s can probably be improved.
After reading the discussion, I took into account the suggestion that the program should perform conversions from any base to any other base. The binary to number conversion is easy because it's supported by Racket. Racket only supports the number to binary conversion for integer numbers, so we multiply the original number by a power of two, to get all the binary digits, and then we manipulate the string to place the point in the correct place. Bases up to 62 will just use decimal digits along with upper and lowercase Latin letters.
This REXX program is a modified version of the original program which can handle any base no limitand the original program did more extensive error checking. Bases that are negative are also supported python binary decimal converter calculator free download won't be explained here.
By far the easiest way to do this is to use Tcl's built-in handling of IEEE arithmetic, converting the IEEE representation into the string representation we want and vice versa by simple string manipulations. Adapting the code to work with IEEE python binary decimal converter calculator free download floats is left as an exercise for the reader, as is dealing with the trickier special cases of the infinities and NaN.
Create account Log in. Page Discussion Edit History. Decimal floating point number to binary From Rosetta Code. Decimal floating point number to binary is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Decimal floating-point DFP arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal base fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions common in human-entered data, such as measurements or financial information and binary base-2 fractions.
The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers This wider range can dramatically slow the accumulation of rounding errors during successive calculations; for example, the Kahan summation algorithm can be used in floating point to add many numbers with no python binary decimal converter calculator free download accumulation of rounding error.
Early mechanical uses of decimal floating point are evident in the abacusslide rulethe Smallwood calculatorand some other calculators that support entries in scientific notation. In the case of the mechanical calculators, the exponent is often treated as side information that is accounted for separately.
Inthe IEEE released IEEEa standard for computing with decimal floating point, which lacked a specification for how floating-point data should be encoded for interchange with other systems. This was subsequently addressed in IEEEwhich standardized the encoding of decimal floating-point data, albeit with two different alternative methods.
Fujitsu also has Sparc processors with DFP in hardware. Microsoft Cor. The IEEE standard definesand bit python binary decimal converter calculator free download floating-point representations.
Like the binary floating-point formats, the number is divided into a sign, an exponent, and a significand. Unlike binary floating-point, numbers are not necessarily normalized; values with few significant digits have multiple possible representations: When the significand is zero, the exponent can be any value at all. The exponent python binary decimal converter calculator free download were chosen so that the range available to normalized values is approximately symmetrical.
Since this cannot be done exactly with an even number of possible exponent values, the extra value was given to Emax. The 30 possible combinations are encoded in a 5-bit field, along with special forms for infinity and NaN. If the most significant 4 bits of the significand are between 0 and 7, the encoded value begins as follows:. If the leading 4 bits of the significand are binary or decimal 8 or 9the number begins as follows:.
The leading bit s in the above is a sign bit, and the following bits xxx in the above encode the additional exponent bits and the remainder of the most significant digit, but the details vary depending on the encoding alternative used.
The final combinations are used for infinities and NaNs, and are the same for both alternative encodings:. In the latter cases, all other bits python binary decimal converter calculator free download the encoding are ignored. Thus, it is possible to initialize an array to NaNs by filling it with a single byte value. While the encoding can represent larger significands, they are illegal and the standard requires implementations to treat them as 0, if encountered on input.
As described above, the encoding varies depending on whether the most significant 4 bits of the significand are in the range 0 to 7 2 to 2or higher 2 or 2. If the 2 python binary decimal converter calculator free download after the sign bit are "00", "01", or "10", then the exponent field consists of the 8 bits following the sign bit the 2 bits mentioned plus 6 bits of "exponent continuation field"and the significand is the remaining 23 bits, with an implicit leading 0 bit, shown here in parentheses:.
This includes subnormal numbers where the leading significand digit is 0. If the 2 bits after the sign bit are "11", then the 8-bit exponent field is shifted 2 bits to the right after both the sign bit and the "11" bits thereafterand the represented significand is in the remaining 21 bits.
In this case there is an implicit that is, not stored leading 3-bit sequence "" in the true significand:. The "11" 2-bit sequence after the sign bit indicates that there is an implicit "" 3-bit prefix to python binary decimal converter calculator free download significand. Note that the leading bits of the significand field do not encode the most significant decimal digit; they are simply part of a larger pure-binary number.
Decimal64 and Decimal operate analogously, but with larger exponent continuation and significand fields. In this version, the significand is stored as a series of decimal digits. The leading digit is between 0 and 9 3 or 4 binary bitsand the rest of the significand uses the densely packed decimal DPD encoding. Unlike the binary integer significand version, where the exponent changed position and came before the significand, this encoding combines the leading 2 bits of the exponent and the leading digit 3 or 4 bits of the significand into the five bits that follow the sign bit.
This is followed by a fixed-offset exponent python binary decimal converter calculator free download field. Finally, the significand continuation field made of 2, 5, or python binary decimal converter calculator free download bit decletseach encoding 3 decimal digits. If the first two bits after the sign bit are "00", "01", or "10", then those are the leading bits of the exponent, and the three bits after that are interpreted as the leading decimal digit 0 to 7: If the first two bits after the sign bit are "11", then the second two bits are the leading bits of the exponent, and the last bit is prefixed with "" to form the leading decimal digit 8 or The usual rule for performing floating-point arithmetic is that the exact mathematical value is calculated,  and the result is then rounded to the nearest representable value in the specified precision.
This is in fact the behavior mandated for IEEE-compliant computer hardware, under normal rounding behavior and in the absence of exceptional conditions. For ease of presentation and understanding, 7-digit precision will be used in the examples. The fundamental principles are the same in any precision.
A simple method to add floating-point numbers is to first represent them with the same exponent. In the example below, the second number is shifted right by 3 digits. We proceed with the usual addition method:. This is nothing other than converting to scientific notation. This is the true result, the exact sum of the operands. It will be rounded to 7 digits and then normalized if necessary. The final result is:.
Note that the low 3 digits of the second operand are essentially lost. This is round-off error. Python binary decimal converter calculator free download extreme cases, the sum of two non-zero numbers may be equal to one of them:. Another problem of loss of python binary decimal converter calculator free download occurs when two close numbers are subtracted. In extreme cases, the final result may be zero even though an exact calculation may be several million. This cancellation illustrates the danger in assuming that all of the digits of a computed result are meaningful.
Dealing with the consequences of these errors are topics in numerical analysis. To multiply, the significands are multiplied, while the exponents are added, and the result is rounded and normalized. There are no cancellation or absorption problems with multiplication or division, though small errors may accumulate as operations are performed repeatedly. In practice, the way these operations python binary decimal converter calculator free download carried out in digital logic can be quite complex.
From Wikipedia, the free encyclopedia. Floating-point formats IEEE bit: Single binary32decimal32 bit: Double binary64decimal64 bit: Quadruple binarydecimal bit: Booth's multiplication algorithm and Division algorithm. Handbook of Floating-Point Arithmetic 1 ed. Retrieved from " https: Computer arithmetic Floating point.