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Given a decimal number, it can be split into two pieces of about the same size, each of which is converted to binary, whereupon the first converted piece is multiplied by 10 k and added to the second converted piece, where k is the number of decimal digits in the second, least-significant piece before conversion.
However, decimal fixed-point and decimal floating-point formats are still important and continue to be used in financial, commercial, and industrial computing, where the subtle conversion and fractional rounding errors that are inherent in binary floating point formats cannot be tolerated.
This template is for quickly converting a decimal number to binary. Usage Use {{Binary|x|y}} where x is the decimal number and y is the decimal precision (positive numbers, defaults displays up to 10 digits following the binary point).
In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal (BID) encoding, it is encoded as a binary number.
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 .
Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine.
The following functions in C convert between binary numbers and their associated Gray codes. While it may seem that Gray-to-binary conversion requires each bit to be handled one at a time, faster algorithms exist. [60] [55] [nb 1]
0110 (decimal 6) AND 1011 (decimal 11) = 0010 (decimal 2) Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above: 0110 (decimal 6) AND 0001 (decimal 1) = 0000 (decimal 0) Because 6 AND 1 is zero, 6 is divisible by two and therefore even.