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The sum of the exponent bias (127) and the exponent (1) is 128, so this is represented in the single-precision format as 0 10000000 10010010000111111011011 (excluding the hidden bit) = 40490FDB [27] as a hexadecimal number. An example of a layout for 32-bit floating point is and the 64-bit ("double") layout is similar.
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.
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).
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 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 ...
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).
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.
When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.