ieee 754 - Is it 52 or 53 bits of floating point precision? -

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i keep on seeing nonsense 53 bits of precision in 64-bit ieee floating point representation. please explain me how in world bit stuck 1 in contributes numeric precision? if had floating point unit bit0 stuck-on 1, of course know produces 1 less bit of precision normally. sensibilities on this?

further, exponent, scaling factor without mantissa, specifies leading bit of number is, no leading bit ever used. 53th bit real 19th hole. merely (useful) crutch aid human mind , logic accessing such values in binary. claim otherwise double counting.

either books , articles claiming 53rd bit nonsense wrong, or idiot. stuck bit stuck bit. let's hear arguments contrary.

the mathematical significand1 of ieee-754 64-bit binary floating-point object has 53 bits. encoded combination of 52-bit field exclusively significand , information exponent field indicates whether 53rd bit 0 or 1.

since main significand field 52 bits, people refer significand 52 bits, sloppy terminology. significand field not contain information significand, , complete significand 53 bits.

it not true leading bit of significand never used (as other 1). when encoding of exponent zero, leading bit of significand 0 instead of more frequent 1.

1 “significand” preferred term, not “mantissa.” significand linear, mantissa logarithmic.


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