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In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [ 1 ] [ 2 ] It is also known as the shift-and-add -3 algorithm , and can be implemented using a small number of gates in computer hardware, but at the expense of high latency .
Use: {{Hexadecimal|x}} where x is the decimal number to be converted to a hexadecimal. Decimals and fractions will be rounded down. Decimals and fractions will be rounded down. The number is, by default, formatted with a final subscript 16 to display the base.
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
Algorithms, with code, for correctly rounded conversion from binary to decimal and decimal to binary are discussed by Gay, [59] and for testing – by Paxson and Kahan. [ 60 ] Hexadecimal literals
Each of these number systems is a positional system, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hexadecimal weights are powers of 16. To convert from hexadecimal or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example:
Horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a i coefficients are the digits of the base-x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.
The Luhn mod N algorithm is an extension to the Luhn algorithm (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered base. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of N ...
This scheme can also be referred to as Simple Binary-Coded Decimal (SBCD) or BCD 8421, and is the most common encoding. [12] Others include the so-called "4221" and "7421" encoding – named after the weighting used for the bits – and "Excess-3". [13]