Computer-Organisation/Number-System/Floating-Point-Encoding-(%E6%B5%AE%E7%82%B9%E6%95%B0%E7%BC%96%E7%A0%81)

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Computer-Organisation/Number-System/Floating-Point-Encoding-(%E6%B5%AE%E7%82%B9%E6%95%B0%E7%BC%96%E7%A0%81)

Abstract § Based on the IEEE 754 Standard sign 0 for positive, 1 for negative exponent by default -127 with all bits set to 0 mantissa takes the binary behind the decimal place after normalisation (the yellow circle part) Reliable precision is 7 decimal digits Approximation of Real Number § mantissa gives the precision From 1 to 2 (2^0-2^1), there are 23 bits of mantissa used for precision after decision point For 2 to 4 (2^1-2^2), there are 22 bits of mantissa used for precision after decision point, one of the bit is used to present the whole number before decimal point With every range of 2, the precision after the decimal point is reduced by 2 Thus, the precision of the number after decimal point is getting worse as the number getting bigger Normalised Number § The range of real numbers between 0 and smallest Normalised Number isn’t covered, covered by Subnormal Number (Denormalized Number) The 1 is implicit when exponent isn’t 0.

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