In my article “7 Bits Are Not Enough for 2-Digit Accuracy” I showed how the relative spacing of decimal and binary floating-point numbers dictates when all conversions between those two bases round-trip. There are two formulas that capture this relationship, and I will derive them in this article. I will also show that it takes one more digit (or bit) of precision to round-trip a floating-point number than it does to round-trip an integer of equal significance.

Continue reading “Number of Digits Required For Round-Trip Conversions”