Subject: Binary Coded Decimals

61. *****
 Q: What are Binary Coded Decimals? How to convert them?

 A: Let us look at full integers only and skip the even more
difficult question of BCD reals and BCD operations.
     Decimal Hexa  BCD
        1      $1    1
        :      $9    9
       10      $A   ..
        :       :    :
       12      $C   ..
        :       :    :
       16     $10   10
       17     $11   11
       18     $12   12
        :       :    :
Consider the last value, that is BCD presentation of 12. The
corresponding hexadecimal is $12 (not $C as in normal decimal to
hexadecimal conversion). The crucial question is how to convert
12BCD to $12 (or its normal decimal equivalent 18). Here is my
sample code:
  type BCDType = array [0..7] of char;
  {}
  procedure StrToBCD (s : string; var b : BCDType);
  var i, p : byte;
  begin
    FillChar(b, SizeOf(b), '0');
    p := Length (s);
    if p > 8 then exit;
    for i := p downto 1 do b[p-i] := s[i];
  end;  (* strtobcd *)
  {}
  function BCDtoDec (b : BCDType; var ok : boolean) : longint;
  const Digit : array [0..9] of char = '0123456789';
  var i, k : byte;
      y, d : longint;
  begin
    y := 0;
    d := 1;
    ok := false;
    for i := 0 to 7 do begin
      k := Pos (b[i], Digit);
      if k = 0 then exit;
      y := y + (k-1) * d;
      if i < 7 then d := 16 * d;
    end; { for }
    ok := true;
    BCDtoDec := y;
  end;  (* bcdtodec *)
  {}
  {}
  procedure TEST;
  var i  : byte;
      b  : BCDType;
      x  : longint;
      ok : boolean;
      s  : string;
  begin
    s := '12';
    StrToBCD (s, b);
    write ('The BCD value : ');
    for i := 7 downto 0 do write (b[i], ' ');
    writeln;
    x := BCDtoDec (b, ok);
    if ok then writeln ('is ', x, ' as an ordinary decimal')
      else writeln ('Error in BCD');
  end;  (* test *)
  {}
  begin TEST; end.

Next we can ask, what if the BCD value is given as an integer.
Simple, first convert the integer into a string. For example in
the procedure TEST put
  Str (12, s);

Finally, what about converting an ordinary decimal to the
corresponding BCD but given also as a decimal variable.  For example
18 --> 12?
  function LHEXFN (decimal : longint) : string;
  const hexDigit : array [0..15] of char = '0123456789ABCDEF';
  var i : byte;
      s : string;
  begin
    FillChar (s, SizeOf(s), ' ');
    s[0] := chr(8);
    for i := 0 to 7 do
      s[8-i] := HexDigit[(decimal shr (4*i)) and $0F];
    lhexfn := s;
  end;  (* lhexfn *)
  {}
  function DecToBCD (x : longint; var ok : boolean) : longint;
  const Digit : array [0..9] of char = '0123456789';
  var hexStr : string;
  var i, k : byte;
      y, d : longint;
  begin
    hexStr := LHEXFN(x);
    y := 0;
    d := 1;
    ok := false;
    for i := 7 downto 0 do begin
      k := Pos (hexStr[i+1], Digit);
      if k = 0 then exit;
      y := y + (k-1) * d;
      if i > 0 then d := 10 * d;
    end; { for }
    ok := true;
    DecToBCD := y;
  end;  (* dectobcd *)
  {}
  procedure TEST2;
  var i    : byte;
      x10  : longint;
      xBCD : longint;
      ok   : boolean;
  begin
    x10 := 18;
    writeln ('The ordinary decimal value : ', x10);
    xBCD := DecToBCD (x10, ok);
    if ok then writeln ('is ', xBCD, ' as a binary coded decimal')
      else writeln ('Error in BCD');
  end;  (* test2 *)
  {}
  begin TEST; end.
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