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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).
1001 + 1000 = 10001 9 + 8 = 17 10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit.
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 .
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:
The original binary value will be preserved by converting to decimal and back again using: [58] 5 decimal digits for binary16, 9 decimal digits for binary32, 17 decimal digits for binary64, 36 decimal digits for binary128. For other binary formats, the required number of decimal digits is [h]
A binary encoding is inherently less efficient for conversions to or from decimal-encoded data, such as strings (ASCII, Unicode, etc.) and BCD. A binary encoding is therefore best chosen only when the data are binary rather than decimal. IBM has published some unverified performance data. [2]
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
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.