Conversions

Binary to Bcd- Bcd to Binary

Please check this site: http://www.doulos.com/knowhow/vhdl_designers_guide/models/binary_bcd/
The ideas of Bin to Bcd conversions can be found at this "old" document: XAPP029
A problem (with solution) based at this principle can be found here.

Its possible to convert a Binary to Bcd values (and the other way around), with a "slightly modified" 4-bit shift register
(one for each Bcd-number).

After the shift Before the shift

Bcd_x+1  (next bit)    Bcd_x   <= Bcd_x+1   (next bit) Bcd_x0             (0)            0      <=       0              (0)          0       hence    0 <= 0 * 2
0             (0)            2      <=       0              (0)          1       hence    2 <= 1 * 2
0             (0)            4      <=       0              (0)          2       hence    4 <= 2 * 2
0             (1)            6      <=       0              (0)          3       hence    6 <= 3 * 2
0             (1)            8      <=       0              (0)          4       hence    8 <= 4 * 2
1             (0)            0      <=       0              (1)          5       hence 10 <= 5 * 2
1             (0)            2      <=       0              (1)          6       hence 12 <= 6 * 2
1             (0)            4      <=       0              (1)          7       hence 14 <= 7 * 2
1             (1)            6      <=       0              (1)          8       hence 16 <= 8 * 2
1             (1)            8      <=       0              (1)          9       hence 18 <= 9 * 2

Layout for a x-bit binary to 5 digit Bcd converter.

	The principle in a Binary to Bcd conversion 0000 -0- 0000 -0- 0000 -0- 0000 -0- 0000 <= 11101110 0000 -0- 0000 -0- 0000 -0- 0000 -0- 0001 <= 11011100 0000 -0- 0000 -0- 0000 -0- 0000 -0- 0011 <= 10111000 0000 -0- 0000 -0- 0000 -0- 0000 -1- 0111 <= 01110000 0000 -0- 0000 -0- 0000 -0- 0001 -0- 0100 <= 11100000 0000 -0- 0000 -0- 0000 -0- 0010 -1- 1001 <= 11000000 0000 -0- 0000 -0- 0000 -1- 0101 -1- 1001 <= 10000000 0000 -0- 0000 -0- 0001 -0- 0001 -1- 1001 <= 00000000 0000 -0- 0000 -0- 0010 -0- 0011 -1- 1000 <= 00000000 0 0 2 3 8 11101110₂ = 128+64+32 +8+4+2 = 255 -16-1 = 238

	BcdDigit.vhd - The source code for the "slightly modified" shift register.