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In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number (Burks [11] et al.) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part.
To derive the value of the floating-point number, the significand is multiplied by the base raised to the power of the exponent, equivalent to shifting the radix point from its implied position by a number of places equal to the value of the exponent—to the right if the exponent is positive or to the left if the exponent is negative.
The integer n is called the exponent and the real number m is called the significand or mantissa. [1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation.
Several earlier 16-bit floating point formats have existed including that of Hitachi's HD61810 DSP of 1982 (a 4-bit exponent and a 12-bit mantissa), [2] Thomas J. Scott's WIF of 1991 (5 exponent bits, 10 mantissa bits) [3] and the 3dfx Voodoo Graphics processor of 1995 (same as Hitachi).
Exponent: 11 bits; Significand precision: 53 bits (52 explicitly stored) The sign bit determines the sign of the number (including when this number is zero, which is signed). The exponent field is an 11-bit unsigned integer from 0 to 2047, in biased form: an exponent value of 1023 represents the actual zero. Exponents range from −1022 to ...
The exponent field is an 8-bit unsigned integer from 0 to 255, in biased form: a value of 127 represents the actual exponent zero. Exponents range from −126 to +127 (thus 1 to 254 in the exponent field), because the biased exponent values 0 (all 0s) and 255 (all 1s) are reserved for special numbers ( subnormal numbers , signed zeros ...
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
The encoding scheme for these binary interchange formats is the same as that of IEEE 754-1985: a sign bit, followed by w exponent bits that describe the exponent offset by a bias, and p − 1 bits that describe the significand. The width of the exponent field for a k-bit format is computed as w = round(4 log 2 (k)) − 13. The existing 64- and ...