In particular, have you a need to support a machine whose native
format is *not* IEEE-754?  There are few such machines left, and
if you *do* have such a need, I need to know, since right now the
plan is to desupport them in 8.5.

 From easiest to most difficult:

(1) If all you need is assurance that a number will be bit-for-bit
     the same on input that it was on output, format it to precisely
     seventeen decimal digits, no more, no less.  Either
         set ::tcl_precision 17; puts $theFloat
     or
         puts [format %.17g $theFloat]
     will do the trick.  (Caveat: This presumes that your sscanf
     and sprintf are standards-compliant.  Not all are.)  In 8.5,
     simply [puts $theFloat] will do just fine without messing
     with ::tcl_precision; the default value of tcl_precision
     becomes "as many digits as are needed to guarantee correct
     reconstruction of the number on input."

(2) If you need the number in binary because you're putting it
     to external media, then
         [binary format d $theFloat]
     will give the floating point number as a string of eight
     bytes in the native byte order.

(3) If you need a specific endianity,
     things get a trifle more complicated in 8.4.  You have to
     determine the machine's endianity:
         binary scan [binary format d 1.0] w test
         switch -exact [format %16lx $test] {
             3ff0000000000000 {
                 set big false
             }
             0000000000000f3f {
                 set big true
             }
             default {
                 error "machine does not have IEEE-754"
             }
         }
      Now, to write a float out big-endian:
          if {$big} {
             binary scan [binary format d $theFloat] W bits
          } else {
             binary scan [binary format d $theFloat] w bits
          }
          set result [binary format W $bits]
      Change the 'W' in the last line to a 'w' to write
      little-endian instead, or to write hexadecimal, change
      it to:
          puts [format %16x $bits]

      8.5 makes this process somewhat easier, because the [binary]
      command adds the 'q' and 'Q' format groups to format 'double's
      in a specific endianity.

I hope this has covered everything you need; feel free to
ask again if it hasn't.