計算機組織與結構›Ch2 計算機算術(Arithmetic)第 4 題/共 26 題
4. IEEE 754、Floating-Point Representation
#CC-02-004中IEEE 754Floating-Point Representation
Given an IEEE754 single-precision representation format in the table below and the bias value as 127. Which of the following statements are correct?
| 8 bits | 23 bits |
|---|---|
| S | Exponent | Fraction |
| Values (single precision) Exp. | Fraction | Meaning |
|---|---|---|
| 0 | 0 | 0 |
| 0 | Non-zero | +/- de-normalized number |
| 1-254 | Anything | +/- floating-point number |
| 255 | 0 | +/- infinity |
| 255 | Non-zero | NaN (Not a number) |
參考答案與解析
(a) 錯誤:的biased exponent=、fraction為1後接22個0,皆與題目所述相符;但sign field只能是0或1,正確表示應為Sign=1(代表負數),題目寫成「Sign=-1」並非合法的IEEE754位元值,故此選項有誤。(b) 正確:,因指數()低於normalized最小值(-126),須以denormalized表示:,故exponent field全為0,fraction為0010110後接16個0,恰等於題目所給的001 0110 0000 0000 0000 0000,sign=0(數值為正)亦相符。(c) 正確:normalized最小exponent field=1,對應實際exponent=1-127=-126,配合最小mantissa=1.0,故最小正規化正數為。(d) 錯誤:denormalized數形式為,最小正denormalized數的fraction僅最低位為1(即),換算為正規化表示為,並非。
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