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The alignment of two decimal numbers (for example 1.3 + 27.08) is a simple, exact shift. Conversion to a character form or for display (e.g., to a text-based format such as XML, or to drive signals for a seven-segment display) is a simple per-digit mapping, and can be done in linear (O(n)) time.
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]
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.
In particular, the examples are simple particular cases (simple values exactly representable in binary, without an exponent part). This section is also probably off-topic: this is not an article about conversion, and conversion from decimal using decimal arithmetic (as opposed to conversion from a character string) is uncommon.
A decimal floating-point number can be encoded in several ways, the different ways represent different precisions, for example 100.0 is encoded as 1000×10 −1, while 100.00 is encoded as 10000×10 −2. The set of possible encodings of the same numerical value is called a cohort in the standard. If the result of a calculation is inexact the ...
Most decimal fractions (or most fractions in general) cannot be represented exactly as a fraction with a denominator that is a power of two. For example, the simple decimal fraction 0.3 (3 ⁄ 10) might be represented as 5404319552844595 ⁄ 18014398509481984 (0.299999999999999988897769…). This inexactness causes many problems that are ...
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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.