## 2009. április 4., szombat

### Converting Integers to Base n

Problem/Question/Abstract:

How do I convert integers from Decimal to Base n and vice versa.

Solve 1:

unit BaseFunctions;
{Unit for conversion functions Dec_To_Base and Base_To_Dec.}
{These functions are designed to convert integers from Decimal to Base n}
{They can be used to create serial numbers for Compaq, etc.}
{See below for usage.}
{Written by Dave Murray, Nov 2000.}

interface

uses
SysUtils;

function Dec_To_Base(nBase, nDec_Value, Lead_Zeros: integer; cOmit: string): string;
function Base_To_Dec(nBase: integer; cBase_Value, cOmit: string): integer;

implementation

function Dec_To_Base(nBase, nDec_Value, Lead_Zeros: integer; cOmit: string): string;
{Function   : converts decimal integer to base n, max = Base36
Parameters : nBase      = base number, ie. Hex is base 16
nDec_Value = decimal to be converted
cOmit      = chars to omit from base (eg. I,O,U,etc)
Returns    : number in base n as string}
var
Base_PChar: PChar;
Base_String: string;
To_Del, Modulus, DivNo: integer;
temp_string: string;
i, nLen, Len_Base: integer;
begin
{initialise..}
Base_String := '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'; {max = Base36}
To_Del := 0;
Modulus := 0;
DivNo := nDec_Value;
result := '';
if (nBase > 36) then
nBase := 36; {max = Base36}
cOmit := UpperCase(cOmit);
{build string to fit specified base}
if not (cOmit = '') then
begin
{iterate thru' ommited letters}
nLen := Length(cOmit);
for i := 1 to nLen do
begin
To_Del := Pos(cOmit[i], Base_String); {find position of letter}
if (To_Del > 0) then
begin
{remove letter from base string}
Len_Base := Length(Base_String);
temp_string := Copy(Base_String, 0, To_Del - 1);
temp_string := temp_string + Copy(Base_String, To_Del + 1, Len_Base - To_Del);
Base_String := temp_string;
end; {if To_Del>0..}
end; {for i..}
end; {if not cOmit=''..}
{ensure string is required length for base}
SetLength(Base_String, nBase);
Base_PChar := PChar(Base_String);
{divide decimal by base & iterate until zero to convert it}
while DivNo > 0 do
begin
Modulus := DivNo mod nBase; {remainder is next digit}
result := Base_PChar[Modulus] + result;
DivNo := DivNo div nBase;
end; {while..}
{fix zero value}
if (Length(result) = 0) then
result := '0';
for i := 1 to (Lead_Zeros - Length(result)) do
result := '0' + result;
end; {function Dec_To_Base}

function Base_To_Dec(nBase: integer; cBase_Value, cOmit: string): integer;
{Function   : converts base n integer to decimal, max = Base36
Parameters : nBase       = base number, ie. Hex is base 16
cBase_Value = base n integer (as string) to be converted
cOmit       = chars to omit from base (eg. I,O,U,etc)
Returns    : number in decimal as string}
var
Base_PChar: PChar;
Base_String: string;
To_Del, Unit_Counter: integer;
temp_string: string;
i, nLen, Len_Base: integer;
begin
{initialise..}
Base_String := '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'; {max = Base36}
To_Del := 0;
Unit_Counter := nBase;
result := 0;
if (nBase > 36) then
nBase := 36; {max = Base36}
cOmit := UpperCase(cOmit);
cBase_Value := UpperCase(cBase_Value); {ensure uppercase letters}
{build string to fit specified base}
if not (cOmit = '') then
begin
{iterate thru' ommited letters}
nLen := Length(cOmit);
for i := 1 to nLen do
begin
To_Del := Pos(cOmit[i], Base_String); {find position of letter}
if (To_Del > 0) then
begin
{remove letter from base string}
Len_Base := Length(Base_String);
temp_string := Copy(Base_String, 0, To_Del - 1);
temp_string := temp_string + Copy(Base_String, To_Del + 1, Len_Base - To_Del);
Base_String := temp_string;
end; {if To_Del>0..}
end; {for i..}
end; {if not cOmit=''..}
{ensure string is required length for base}
SetLength(Base_String, nBase);
Base_PChar := PChar(Base_String);
{iterate thru digits of base n value, each digit is a multiple of base n}
nLen := Length(cBase_Value);
if (nLen = 0) then
result := 0 {fix zero value}
else
begin
for i := 1 to nLen do
begin
if (i = 1) then
unit_counter := 1 {1st digit = units}
else if (i > 1) then
unit_counter := unit_counter * nBase; {multiples of base}
result := result
+ ((Pos(Copy(cBase_Value, (Length(cBase_Value) + 1) - i, 1), Base_PChar) - 1)
* unit_counter);
end; {for i:=1..}
end; {else begin..}
end; {function Base_To_Dec}

end. {unit BaseFunctions}

Solve 2:

function Dec2Numb(N: Longint; A, B: Byte): string;
var
C: Integer;
{\$IFDEF RX_D4}
Number: Cardinal;
{\$ELSE}
Number: Longint;
{\$ENDIF}
begin
if N = 0 then
Result := '0'
else
begin
{\$IFDEF RX_D4}
Number := Cardinal(N);
{\$ELSE}
Number := N;
{\$ENDIF}
Result := '';
while Number > 0 do
begin
C := Number mod B;
if C > 9 then
C := C + 55
else
C := C + 48;
Result := Chr(C) + Result;
Number := Number div B;
end;
end;
if Result <> '' then
end;

function Numb2Dec(S: string; B: Byte): Longint;
var
I, P: Longint;
begin
I := Length(S);
Result := 0;
S := UpperCase(S);
P := 1;
while (I >= 1) do
begin
if S[I] > '@' then
Result := Result + (Ord(S[I]) - 55) * P
else
Result := Result + (Ord(S[I]) - 48) * P;
Dec(I);
P := P * B;
end;
end;

Code from RXLib library.