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The true significand of normal numbers includes 23 fraction bits to the right of the binary point and an implicit leading bit (to the left of the binary point) with value 1. Subnormal numbers and zeros (which are the floating-point numbers smaller in magnitude than the least positive normal number) are represented with the biased exponent value ...
The significand [1] (also coefficient, [1] sometimes argument, [2] or more ambiguously mantissa, [3] fraction, [4] [5] [nb 1] or characteristic [6] [3]) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include ...
In the IEEE standard the base is binary, i.e. =, and normalization is used.The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits).
A signed (meaning positive or negative) digit string of a given length in a given radix (or base). This digit string is referred to as the significand, mantissa, or coefficient. [nb 1] The length of the significand determines the precision to which numbers can be represented. The radix point position is assumed always to be somewhere within the ...
Mantissa (/ m æ n ˈ t ɪ s ə /) may refer to: . Mantissa (logarithm), the fractional part of the common (base-10) logarithm Significand (also commonly called mantissa), the significant digits of a floating-point number or a number in scientific notation
For example, a significand of 8 000 000 is encoded as binary 0111 1010000100 1000000000, with the leading 4 bits encoding 7; the first significand which requires a 24th bit (and thus the second encoding form) is 2 23 = 8 388 608.
Thus, only 10 bits of the significand appear in the memory format but the total precision is 11 bits. In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (log 10 (2 11) ≈ 3.311 decimal digits, or 4 digits ± slightly less than 5 units in the last place).
"Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction. In the case where the significand is considered to be an integer and definition 2 is used, the "integer" spoken of is made up of the digits that appear after the decimal point." The bolded part is what I added.