Maury Markowitz Posted January 21, 2022 Share Posted January 21, 2022 I'm curious about the passage on page 8-45 of De Re where it's talking about the memory representation of FP. The last two examples are: Number: 37.0 = 37 * 100**0 Format: 40 37 00 00 00 00 (exponent= 40+0) Number: -460312 = -46.0312 * 100**2 Format: C2 46 03 12 00 00 (exponent= 80+40+2) So I'm wondering what the rule is here... is it simply that the exponent is changed until the leftmost digit of the mantissa is non-zero? Does this imply that anything with exponent 100**0 ... 100**4 (40 ... 44) is directly readable? IE: Number: 123456.0 = 12.3456 * 100**4 Format: 44 12 34 56 00 00 (exponent= 40+4) Quote Link to comment Share on other sites More sharing options...

ClausB Posted January 21, 2022 Share Posted January 21, 2022 What do you mean by 1 hour ago, Maury Markowitz said: directly readable ? Quote Link to comment Share on other sites More sharing options...

stepho Posted January 22, 2022 Share Posted January 22, 2022 Storing the exponent with an offset is common - even in the IEEE floating point representation used in the current CPU's. For C2 46 03 12 00 00 the exponent is C2 . The top bit is the sign (ie $80 means negative). So we remove the top bit, leaving $42. Then we remove the offset of $40, to leave $02. The mantissa is 46 03 12, which is BCD for 46.0312 (implied decimal point is just after the first byte of the mantissa). Treating the exponent and mantissas as BCD, this gives us 46.0312 * 100^2 = 46.0312 * 10000 = 460312 . Remembering the sign, we now have -460312 . 40 12 34 56 00 00 therefore reads as 12.34560000 * 100^0 = 12.34560000 41 12 34 56 00 00 therefore reads as 12.34560000 * 100^1 = 1234.560000 42 12 34 56 00 00 therefore reads as 12.34560000 * 100^2 = 123456.0000 43 12 34 56 00 00 therefore reads as 12.34560000 * 100^3 = 12345600.00 44 12 34 56 00 00 therefore reads as 12.34560000 * 100^4 = 1234560000 3F 12 34 56 00 00 therefore reads as 12.34560000 * 100^-1 = 0.1234560000 3E 12 34 56 00 00 therefore reads as 12.34560000 * 100^-2 = 0.0012345600 and so on 3 Quote Link to comment Share on other sites More sharing options...

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