Richard Suchenwirth 2002-07-06 - Every string standing for a number has to be understood relative to its base. We're most familiar with base 10 (the decimal system), where e.g. 123 stands for
1*10^2 + 2*10^1 + 3*10^0
and in computery the bases 2 (binary), 8 (octal), and 16 (hexadecimal) are also fairly common, but any integer could function as a base as long as we have enough distinct digits. If you want to experiment with other bases, here are two routines that convert a number to and from a different base, up to 62 (base64 uses a very different sequence of digits, so I didn't go that far)
Note also that signs are preserved (unlike computery habit to have octals and hexadecimals as unsigned, resp. sign-extended):
proc base {base number} {
set negative [regexp ^-(.+) $number -> number]
set digits {0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N
O P Q R S T U V W X Y Z a b c d e f g h i j k l m n o p
q r s t u v w x y z}
set res {}
while {$number} {
set digit [expr {$number % $base}]
set res [lindex $digits $digit]$res
set number [expr {$number / $base}]
}
if $negative {set res -$res}
set res
}
proc frombase {base number} {
set digits {0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N
O P Q R S T U V W X Y Z a b c d e f g h i j k l m n o p
q r s t u v w x y z}
set negative [regexp ^-(.+) $number -> number]
set res 0
foreach digit [split $number ""] {
set decimalvalue [lsearch $digits $digit]
if {$decimalvalue<0 || $decimalvalue >= $base} {
error "bad digit $decimalvalue for base $base"
}
set res [expr {$res*$base + $decimalvalue}]
}
if $negative [set res -$res]
set res
}Category Mathematics - Arts and crafts of Tcl-Tk programming