RickRegan

I wanted to go back to the source, or at least as far as I could go (I didn't look to see if any of Von Neumann's papers covered it :) ). I know D. Goldberg's appendix covers this (pages 218-219), for the binary to decimal direction, for single-precision floating-point. But I wanted a simple example as well, and I. Goldberg's paper had that.

0.921875 is 921875/10^6 = 59/64, which is exactly representable in binary since 64 (2^6) is a power of two. So 1.921875 * 2^6 = 1 59/64 * 64 = 64 + 59 = 123.

Or as acqq pointed out, the bit representations are the same: 1.921875 = 1.111011 (using my converter at http://www.exploringbinary.com/binary-converter/ ), which is 123 (1111011) shifted right 6 bits.