Converting numbers from arbitrary bases

Michael A. Cleverly - The other day someone on OpenACS.org asked [1 ] for a Tcl proc that would convert a base-62 number into a base-10 integer. I replied with a version I'd written. Here is a slightly expanded one. convert_number employs some Salt and Sugar which I quite like.

(One caveat is that base_n_to_decimal will either return an incorrect answer or generate an error for really large numbers that are > than 2147483647.)


 proc base_characters {base_n} {
     set base [list 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]
     if {$base_n < 2 || $base_n > 62} {
         error "Invalid base \"$base_n\" (should be an integer between 2 and 62)"    
     }
     return [lrange $base 0 [expr $base_n - 1]]
 }
 
 proc base_n_to_decimal {number base_n} {
     set base   [base_characters $base_n]
     # trim white space in case [format] is used
     set number [string trim $number]
     # bases 11 through 36 can be treated in a case-insensitive fashion
     if {$base_n <= 36} {
         set number [string toupper $number]
     }
     set decimal 0
     set power [string length $number]
 
     foreach char [split $number ""] {
         incr power -1
         set dec_val [lsearch $base $char]
         if {$dec_val == -1} {
             error "$number is not a valid base $base_n number"
         }
         set decimal [expr $decimal + $dec_val * int(pow($base_n,$power))]
     }
 
     return $decimal
 }  

 proc decimal_to_base_n {number base_n} {
     set base [base_characters $base_n]
     # trim white space in case [format] is used
     set number [string trim $number]
 
     if {![string is integer $number] || $number < 0} {
         error "$number is not a base-10 integer between 0 and 2147483647"
     }
 
     while 1 {
         set quotient  [expr $number / $base_n]
         set remainder [expr $number % $base_n]
         lappend remainders $remainder
         set number $quotient
         if {$quotient == 0} {
             break
         }
     }
 
     set base_n [list]
 
     for {set i [expr [llength $remainders] - 1]} {$i >= 0} {incr i -1} {
         lappend base_n [lindex $base [lindex $remainders $i]]
     }
 
     return [join $base_n ""]
 
 }
 
 proc convert_number {number "from" "base" base_from "to" "base" base_to} {
     return [decimal_to_base_n [base_n_to_decimal $number $base_from] $base_to]
 }

Bryan Steimel - same thing as above for the most part, just what I managed to put together .. hopefully its helpful to someone. usage is hopefully self explanatory .. [to_base <num> <base>] and vice versa


        variable base_chars "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
        proc to_base {number base} {
                variable base_chars
                if {$number==0} { 
                        return 0 
                } elseif {(($base>62) || ($base<2))} { 
                        return -code error "base: expected integer between 2 and 62, got '$base'"
                } 
                set nums [string range $base_chars 0 [expr $base - 1]] 
                set result ""
                while {$number > 0} { 
                        set result "[string index $nums [expr $number % $base]]${result}"
                        set number [expr int($number / $base)]
                }
                set result
        } 

        proc from_base {number base} {
                variable base_chars
                if {(($base>62) || ($base<2))} { 
                        return -code error "base: expected integer between 2 and 62, got '$base'"
                }
                set nums [string range $base_chars 0 [expr $base - 1]]  
                for {
                        set result 0 
                        set i 0
                        set len [string length $number]
                } {$i<$len} {
                        incr i
                } {     incr i
                        set result [expr $result * $base] 
                        set result [expr $result + [string first [string index $number $i] $nums]]  
                } 
                set result
        } 

LV I'm searching for a technique of transforming strings. The transformation is to take a string like "Abc" and transforming it into an ASCII string of base 2, and then code to do the reverse - to transform "0110000101101001" and so forth into a string of alphabetic (or whatever) characters. However, I don't know how clear that description is... Anyways, I'm trying to figure out exactly how to do this - do I need to use the above code along with binary, format and scan to accomplish what I'm aiming for?


FrankBannon - 2011-11-09 22:29:51

LV: you have helped me so many times I feel compelled to return the favor. One quick method to convert text to binary and back might be:

# text to binary
proc text_to_bin str {
        foreach s [split $str ""] {
                set dec [scan $s %c]
                set bin [decimal_to_base_n $dec 2]
                append output [format "%08s " $bin]        ;# pad to 8 bits
        }
        return $output
}

# binary to text
proc bin_to_text str {
        foreach s $str {
                append output [format "%c" [scan $s %b]]
        }
        return $output
}

set binary [text_to_bin Tickle]
        01010100 01101001 01100011 01101011 01101100 01100101
bin_to_text $binary
        Tickle