## 二进制到BCD码转换

### 1. 理论基础
在单片机里面，如：显示个温度值，这时，要取一个数的个位、十位、百位，可以用/和 %（求商和求余）来解决。
但是，在FPGA里面用求商和求余将会非常消耗资源，这样就必须用到二进制转BCD码了，这里介绍一种简单的加3移位算法。
注：B代表二进制，D代表十进制，0x代表十六进制，BCD为BCD码,下同。

{{ :b2bcd.png |}}

1、加3移位法

以二进制数（0000_101 Xn）B＝（10+Xn）D为例，

串行输入三位后，（0101）B＝5（D）

左移一位后：（0000_101Xn）B＝（10+Xn）D

如果（0000_101Xn）B直接输出显示为：

当Xn＝0时，0000_1010＝0x0A。此为错误的BCD码。

采用加3移位法，修正移位结果：

串行输入三位后，结果大于4

（0101）B＝5（D）

加3：（0101）B+（0011）B＝（1000）B   --十进制表示：5+3＝8

再左移一位后：

（1000Xn）B＝ （0001_000Xn）BCD 

对应十进制显示：1 Xn

每四位BCD码对应一位十进制数，即：（10+Xn）D，转换成功

注：Xn为下一位串行输入的二进制数。



### 2. 代码
<code python>
module binary2bcd(binary_data,tens,ones);
input [4:0] binary_data;
output reg [3:0] tens;
output reg [3:0] ones;

always @*
case(binary_data)
    5'd0: 
        begin
            tens = 4'd0;
            ones = 4'd0;
        end
    5'd1:
        begin
            tens = 4'd0;
            ones = 4'd1;
        end
    5'd2:
        begin
            tens = 4'd0;
            ones = 4'd2;
        end
    5'd3:
        begin
            tens = 4'd0;
            ones = 4'd3;
        end
    5'd4:
        begin
            tens = 4'd0;
            ones = 4'd4;
        end
    5'd5:
        begin
            tens = 4'd0;
            ones = 4'd5;
        end
    5'd6:
        begin
            tens = 4'd0;
            ones = 4'd6;
        end
    5'd7:
        begin
            tens = 4'd0;
            ones = 4'd7;
        end
    5'd8:
        begin
            tens = 4'd0;
            ones = 4'd8;
        end
    5'd9:
        begin
            tens = 4'd0;
            ones = 4'd9;
        end
    5'd10: 
        begin
            tens = 4'd1;
            ones = 4'd0;
        end
    5'd11:
        begin
            tens = 4'd1;
            ones = 4'd1;
        end
    5'd12:
        begin
            tens = 4'd1;
            ones = 4'd2;
        end
    5'd13:
        begin
            tens = 4'd1;
            ones = 4'd3;
        end
    5'd14:
        begin
            tens = 4'd1;
            ones = 4'd4;
        end
    5'd15:
        begin
            tens = 4'd1;
            ones = 4'd5;
        end
    5'd16:
        begin
            tens = 4'd1;
            ones = 4'd6;
        end
    5'd17:
        begin
            tens = 4'd1;
            ones = 4'd7;
        end
    5'd18:
        begin
            tens = 4'd1;
            ones = 4'd8;
        end
    5'd19:
        begin
            tens = 4'd1;
            ones = 4'd9;
        end
    5'd20: 
        begin
            tens = 4'd2;
            ones = 4'd0;
        end
    5'd21:
        begin
            tens = 4'd2;
            ones = 4'd1;
        end
    5'd22:
        begin
            tens = 4'd2;
            ones = 4'd2;
        end
    5'd23:
        begin
            tens = 4'd2;
            ones = 4'd3;
        end
    5'd24:
        begin
            tens = 4'd2;
            ones = 4'd4;
        end
    5'd25:
        begin
            tens = 4'd2;
            ones = 4'd5;
        end
    5'd26:
        begin
            tens = 4'd2;
            ones = 4'd6;
        end
    5'd27:
        begin
            tens = 4'd2;
            ones = 4'd7;
        end
    5'd28:
        begin
            tens = 4'd2;
            ones = 4'd8;
        end
    5'd29:
        begin
            tens = 4'd2;
            ones = 4'd9;
        end
    5'd30:
        begin
            tens = 4'd3;
            ones = 4'd0;
        end
    5'd31:
        begin
            tens = 4'd3;
            ones = 4'd1;
        end
endcase

/*
integer i;

always @(binary_data)
begin
    tens = 4'd0;
    ones = 4'd0;
    
    for (i=7; i >= 0; i=i-1)
    begin
        if (tens>=5)
            tens = tens +3;
        if (ones >= 5)
            ones = ones +3;
        tens = tens << 1;
        tens[0] = ones[3];
        ones = ones << 1;
        ones[0] = binary_data[i];
    end
end
*/

endmodule

</code>