#####################################################################
 # procedures to show internal IEEE standard "double" representation #
 #####################################################################
 
 # big endian code
 
 proc floatToBinarBigEndian {d} {
     binary scan [binary format d $d] B* v
     set sign [string index $v 0]
     set exponent [string range $v 1 11]
     set mantissa [string range $v 12 end]
     return [list $sign $mantissa $exponent]
 }
 
 proc binarToFloatBigEndian {sign mantissa exponent} {
     if {$sign != "0" && $sign != "1"} {
 	error "bad sign \"$sign\""
     }
     if {[string length $mantissa] != 52} {
 	error "bad mantissa \"$mantissa\""
     }
     if {[string length $exponent] != 11} {
 	error "bad exponent \"$exponent\""
     }
     set v [binary format B64 $sign$exponent$mantissa]
     binary scan $v d v
     return $v
 }

 # little endian code

 proc __reverse__ {s} {
     for {set i [string length $s]} {$i>=0} {incr i -1} {
         append sr [string index $s $i]
     }
     return $sr
 }

 proc floatToBinarLittleEndian {d} {
     binary scan [binary format d $d] b* v
     set v [__reverse__ $v]
     set sign [string index $v 0]
     set exponent [string range $v 1 11]
     set mantissa [string range $v 12 end]
     return [list $sign $mantissa $exponent]
 }

 proc binarToFloatLittleEndian {sign mantissa exponent} {
     if {$sign != "0" && $sign != "1"} {
 	error "bad sign \"$sign\""
     }
     if {[string length $mantissa] != 52} {
 	error "bad mantissa \"$mantissa\""
     }
     if {[string length $exponent] != 11} {
 	error "bad exponent \"$exponent\""
     }
     set v [binary format b64 [__reverse__ $sign$exponent$mantissa]]
     binary scan $v d v
     return $v
 }

 # platform independent procedures #

 proc floatToBinar {d} {
     global tcl_platform
     switch $tcl_platform(byteOrder) {
         "bigEndian" {return [floatToBinarBigEndian $d]}
         "littleEndian" {return [floatToBinarLittleEndian $d]}
         default {return -code error "unknown byteOrder \"$tcl_platform(byteOrder)\""}
     }
 }

 proc binarToFloat {sign mantissa exponent} {
     global tcl_platform
     switch $tcl_platform(byteOrder) {
         "bigEndian" {return [binarToFloatBigEndian $sign $mantissa $exponent]}
         "littleEndian" {return [binarToFloatLittleEndian $sign $mantissa $exponent]}
         default {return -code error "unknown byteOrder \"$tcl_platform(byteOrder)\""}
     }
 }

 proc floatToBinarTest {value sign mantissa exponent} {
     set r [floatToBinar $value]
     if {
         [lindex $r 0] != $sign ||
         [lindex $r 1] != $mantissa ||
         [lindex $r 2] != $exponent
     } {
         return -code error "this machine is not IEEE floating point compliant"
     }
 }

 # Some tests

 floatToBinarTest  1.0      0 0000000000000000000000000000000000000000000000000000 01111111111
 floatToBinarTest -1.0      1 0000000000000000000000000000000000000000000000000000 01111111111

 # An example why you should put braces around "expr" argument

 set tcl_precision 12
 set pi [expr {acos(-1.0)}]
 floatToBinarTest $pi           0 1001001000011111101101010100010001000010110100011000 10000000000
 floatToBinarTest [expr {$pi}]  0 1001001000011111101101010100010001000010110100011000 10000000000
 floatToBinarTest [expr $pi]    0 1001001000011111101101010100010001000010111011101010 10000000000

 # the 17 digits string representation is exact

 set tcl_precision 17
 set pi [expr {acos(-1.0)}]
 floatToBinarTest $pi           0 1001001000011111101101010100010001000010110100011000 10000000000
 floatToBinarTest [expr {$pi}]  0 1001001000011111101101010100010001000010110100011000 10000000000
 floatToBinarTest [expr $pi]    0 1001001000011111101101010100010001000010110100011000 10000000000 

 puts [binarToFloat 0 1001001000011111101101010100010001000010110100010111 10000000000] ;# 3.1415926535897927
 puts [binarToFloat 0 1001001000011111101101010100010001000010110100011000 10000000000] ;# 3.1415926535897931
 puts [binarToFloat 0 1001001000011111101101010100010001000010110100011001 10000000000] ;# 3.1415926535897936 

 puts [binarToFloat 0 1001001000011111101101010100010001000010110100010111 10000000000] ;# 3.1415926535897927
 puts [binarToFloat 0 1001001000011111101101010100010001000010110100011000 10000000000] ;# 3.1415926535897931
 puts [binarToFloat 0 1001001000011111101101010100010001000010110100011001 10000000000] ;# 3.1415926535897936 

 # Special representations

 binarToFloat 0 0000000000000000000000000000000000000000000000000000 00000000000        ;# 0.0
 binarToFloat 0 0000000000000000000000000000000000000000000000000001 00000000000        ;# 4.9406564584124654e-324
 binarToFloat 0 1111111111111111111111111111111111111111111111111111 00000000000        ;# 2.2250738585072009e-308
 binarToFloat 0 0000000000000000000000000000000000000000000000000000 00000000001        ;# 2.2250738585072014e-308
 binarToFloat 0 0000000000000000000000000000000000000000000000000000 11111111110        ;# 8.9884656743115795e+307
 binarToFloat 0 1111111111111111111111111111111111111111111111111111 11111111110        ;# 1.7976931348623157e+308
 binarToFloat 0 0000000000000000000000000000000000000000000000000000 11111111111        ;# inf
 binarToFloat 1 0000000000000000000000000000000000000000000000000000 11111111111        ;# -inf
 binarToFloat 0 1111111111111111111111111111111111111111111111111111 11111111111        ;# nan
 binarToFloat 1 1111111111111111111111111111111111111111111111111111 11111111111        ;# nan
----
As the code above is quite capable of recognizing itself, it will only work if your platform uses the IEEE format as its native representation of floating point numbers. Tcl depends on the C language for this matter, and ISO C does not require floating point numbers to adhere to any specific format. See also [IEEE binary float to string conversion].
----
[[ [Computers and real numbers] ]]