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This decimal format can also represent any binary fraction a/2 m, such as 1/8 (0.125) or 17/32 (0.53125). More generally, a rational number a / b , with a and b relatively prime and b positive, can be exactly represented in binary fixed point only if b is a power of 2; and in decimal fixed point only if b has no prime factors other than 2 and/or 5.
The Q notation is a way to specify the parameters of a binary fixed point number format. For example, in Q notation, the number format denoted by Q8.8 means that the fixed point numbers in this format have 8 bits for the integer part and 8 bits for the fraction part. A number of other notations have been used for the same purpose.
To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change 1 / 4 to a decimal, divide 1.00 by 4 (" 4 into 1.00 ...
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 ...
[1] The format is written with the significand having an implicit integer bit of value 1 (except for special data, see the exponent encoding below). With the 52 bits of the fraction (F) significand appearing in the memory format, the total precision is therefore 53 bits (approximately 16 decimal digits, 53 log 10 (2) ≈ 15.955). The bits are ...
Any such decimal fraction, i.e.: d n = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing d N by d N − 1 and replacing all subsequent 0s by 9s (see 0.999...). In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion.
The decimal number 0.15625 10 represented in binary is 0.00101 2 (that is, 1/8 + 1/32). (Subscripts indicate the number base .) Analogous to scientific notation , where numbers are written to have a single non-zero digit to the left of the decimal point, we rewrite this number so it has a single 1 bit to the left of the "binary point".
A template for displaying common fractions of the form int+num/den nicely. It supports 0–3 anonymous parameters with positional meaning. Template parameters [Edit template data] Parameter Description Type Status leftmost part 1 Denominator if only parameter supplied. Numerator if 2 parameters supplied. Integer if 3 parameters supplied. If no parameter is specified the template will render a ...