問(wèn)題描述
浮點(diǎn)數(shù)有 32 位二進(jìn)制數(shù)，雙精度數(shù)有 64 位二進(jìn)制數(shù)嗎?文檔太難理解了.
Does a float have 32 binary digits and a double have 64 binary digits? The documentation was too hard to make sense of.
所有位都轉(zhuǎn)換為有效數(shù)字嗎?還是小數(shù)點(diǎn)的位置占用了一些位?
Do all of the bits translate to significant digits? Or does the location of the decimal point take up some of the bits?
推薦答案
float: 32 bits (4 bytes) 其中23 bits用于尾數(shù)(大約 7 個(gè)十進(jìn)制數(shù)字).8 位用于指數(shù)，因此浮點(diǎn)數(shù)可以使用這 8 位將小數(shù)點(diǎn)向右或向左移動(dòng)".這樣做可以避免在尾數(shù)中存儲(chǔ)大量零，如 0.0000003 (3 × 10-7) 或 3000000 (3 × 107).有 1 位用作符號(hào)位.
float: 32 bits (4 bytes) where 23 bits are used for the mantissa (about 7 decimal digits). 8 bits are used for the exponent, so a float can "move" the decimal point to the right or to the left using those 8 bits. Doing so avoids storing lots of zeros in the mantissa as in 0.0000003 (3 × 10-7) or 3000000 (3 × 107). There is 1 bit used as the sign bit.
double:64 位(8 字節(jié))，其中 52 位 用于尾數(shù)(大約 16 位十進(jìn)制數(shù)字).11位用于指數(shù)，1位為符號(hào)位.
double: 64 bits (8 bytes) where 52 bits are used for the mantissa (about 16 decimal digits). 11 bits are used for the exponent and 1 bit is the sign bit.
由于我們使用二進(jìn)制(只有 0 和 1)，所以當(dāng)數(shù)字非零時(shí)，尾數(shù)中的一位隱含為 1(浮點(diǎn)數(shù)和雙精度數(shù)都使用此技巧).
Since we are using binary (only 0 and 1), one bit in the mantissa is implicitly 1 (both float and double use this trick) when the number is non-zero.
此外，由于所有內(nèi)容都是二進(jìn)制(尾數(shù)和指數(shù))，因此轉(zhuǎn)換為十進(jìn)制數(shù)通常不準(zhǔn)確.像 0.5、0.25、0.75、0.125 這樣的數(shù)字被精確存儲(chǔ)，但 0.1 不是.正如其他人所說(shuō)，如果您需要精確存儲(chǔ)美分，請(qǐng)不要使用 float 或 double，使用 int、long、BigInteger 或 BigDecimal.
Also, since everything is in binary (mantissa and exponents) the conversions to decimal numbers are usually not exact. Numbers like 0.5, 0.25, 0.75, 0.125 are stored exactly, but 0.1 is not. As others have said, if you need to store cents precisely, do not use float or double, use int, long, BigInteger or BigDecimal.
來(lái)源:
http://en.wikipedia.org/wiki/Floating_point#IEEE_754:_floating_point_in_modern_computers
http://en.wikipedia.org/wiki/Binary64
http://en.wikipedia.org/wiki/Binary32
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