二進位轉BCD碼的硬體實現

http://people.ee.duke.edu/~dwyer/courses/ece52/Binary_to_BCD_Converter.pdf

BCD碼這種編碼形式利用了四個位元來儲存一個十進位的數碼，使二進位和十進位之間的轉換得以快捷的進行。

要介紹的是二進位轉BCD碼的硬體實現，採用左移加3的演算法，具體描述如下：

（此處以8-bit 二進位碼為例）

1、左移要轉換的二進位碼1位元

2、左移之後，BCD碼分別置於百位、十位、個位

3、如果移位後所在的BCD碼列大於或等於5，則對該值加3

4、繼續左移的過程直至全部移位元完成

舉例：將十六進位碼0xFF轉換成BCD碼

Shift and Add-3 Algorithm

1. Shift the binary number left one bit.

2. If 8 shifts have taken place, the BCD number is in the Hundreds, Tens, and Units column.

3. If the binary value in any of the BCD columns is 5 or greater, add 3 to that value in that BCD column.

4. Go to 1.

 Here is a Verilog module for this truth table.

module add3(in,out);
input [3:0] in;
output [3:0] out;
reg [3:0] out;

always @ (in)
 case (in)
 4'b0000: out <= 4'b0000;
 4'b0001: out <= 4'b0001;
 4'b0010: out <= 4'b0010;
 4'b0011: out <= 4'b0011;
 4'b0100: out <= 4'b0100;
 4'b0101: out <= 4'b1000;
 4'b0110: out <= 4'b1001;
 4'b0111: out <= 4'b1010;
 4'b1000: out <= 4'b1011;
 4'b1001: out <= 4'b1100;
 default: out <= 4'b0000;
 endcase
endmodule

Here is a structural Verilog module corresponding to the logic diagram.

module binary_to_BCD(A,ONES,TENS,HUNDREDS);
input [7:0] A;
output [3:0] ONES, TENS;
output [1:0] HUNDREDS;
wire [3:0] c1,c2,c3,c4,c5,c6,c7;
wire [3:0] d1,d2,d3,d4,d5,d6,d7;

assign d1 = {1'b0,A[7:5]};
assign d2 = {c1[2:0],A[4]};
assign d3 = {c2[2:0],A[3]};
assign d4 = {c3[2:0],A[2]};
assign d5 = {c4[2:0],A[1]};
assign d6 = {1'b0,c1[3],c2[3],c3[3]};
assign d7 = {c6[2:0],c4[3]};
add3 m1(d1,c1);
add3 m2(d2,c2);
add3 m3(d3,c3);
add3 m4(d4,c4);
add3 m5(d5,c5);
add3 m6(d6,c6);
add3 m7(d7,c7);
assign ONES = {c5[2:0],A[0]};
assign TENS = {c7[2:0],c5[3]};
assign HUNDREDS = {c6[3],c7[3]};

endmodule