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pdclib:printing_floating_point_numbers [2025/08/21 13:46] – [Visualization] solarpdclib:printing_floating_point_numbers [2025/08/21 14:01] (current) – [Biased Exponent] solar
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 Instead of assuming two's complement to allow for positive and negative exponents, IEEE 754 uses //biased// exponents: The exponent bits are interpreted as unsigned integer, but to get the "real" exponent value, you need to //substract// the bias value, which is ''FLOAT_MAX_EXP - 1'', ''DBL_MAX_EXP - 1'', or ''LDBL_MAX_EXP - 1'', respectively. Instead of assuming two's complement to allow for positive and negative exponents, IEEE 754 uses //biased// exponents: The exponent bits are interpreted as unsigned integer, but to get the "real" exponent value, you need to //substract// the bias value, which is ''FLOAT_MAX_EXP - 1'', ''DBL_MAX_EXP - 1'', or ''LDBL_MAX_EXP - 1'', respectively.
  
 +=== Huh? ===
 +
 +Remember that IEEE 754 is a //floating point// standard. It makes //no// asumptions on the integer logic of the machine. What should the exponent be encoded at? Two's compliment? You don't know if the ALU supports that! So the exponent is stored unsigned. That means that the value ''1'' (1x10^0, or 1x2^0) is not stored with an exponent of all zeroes, but an exponent halfway between all zeroes (signifying denormals) and all ones (signifying INF / NaN).
 ==== Infinity ==== ==== Infinity ====
  
pdclib/printing_floating_point_numbers.1755776815.txt.gz · Last modified: by solar

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