Binary to Binary-Coded Decimal (BCD) Converter

Posted on December 10, 2013 by Daniel

A binary to binary-coded decimal, or BCD for short, is a method storing decimal numbers in binary form. The majority of the time a number in a logic design is stored as a binary number internally as to simplify math and logic operations and converted to a set of BCD numbers only when it needs to then be sent to something that requires it in decimal number form i.e. a display of some sort. The Verilog and VHDL code below is for an 8-bit binary to BCD decoder that gives and ones, tens and hundreds decimal place output for driving a display or other device.

The modules below take a 8-bit binary number on the number input and converts that number into three 4-bit BCD numbers, one for each decimal place. These 4-bit BCD numbers are still binary numbers but each one only goes from 0 to 9, even though 4-bits can go from 0 to 15, to represent the 10 possibilities of a decimal number.

CODE

Verilog

`timescale 1ns / 1ps

module bcd(number, hundreds, tens, ones);
   // I/O Signal Definitions
   input  [7:0] number;
   output reg [3:0] hundreds;
   output reg [3:0] tens;
   output reg [3:0] ones;
   
   // Internal variable for storing bits
   reg [19:0] shift;
   integer i;
   
   always @(number)
   begin
      // Clear previous number and store new number in shift register
      shift[19:8] = 0;
      shift[7:0] = number;
      
      // Loop eight times
      for (i=0; i<8; i=i+1) begin
         if (shift[11:8] >= 5)
            shift[11:8] = shift[11:8] + 3;
            
         if (shift[15:12] >= 5)
            shift[15:12] = shift[15:12] + 3;
            
         if (shift[19:16] >= 5)
            shift[19:16] = shift[19:16] + 3;
         
         // Shift entire register left once
         shift = shift << 1;
      end
      
      // Push decimal numbers to output
      hundreds = shift[19:16];
      tens     = shift[15:12];
      ones     = shift[11:8];
   end

endmodule

`timescale 1ns / 1ps

module bcd(number, hundreds, tens, ones);

// I/O Signal Definitions

input [7:0] number;

output reg [3:0] hundreds;

output reg [3:0] tens;

output reg [3:0] ones;

// Internal variable for storing bits

reg [19:0] shift;

integer i;

always @(number)

begin

// Clear previous number and store new number in shift register

shift[19:8] = 0;

shift[7:0] = number;

// Loop eight times

for (i=0; i<8; i=i+1) begin

if (shift[11:8] >= 5)

shift[11:8] = shift[11:8] + 3;

if (shift[15:12] >= 5)

shift[15:12] = shift[15:12] + 3;

if (shift[19:16] >= 5)

shift[19:16] = shift[19:16] + 3;

// Shift entire register left once

shift = shift << 1;

end

// Push decimal numbers to output

hundreds = shift[19:16];

tens = shift[15:12];

ones = shift[11:8];

end

endmodule

VHDL

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity bcd is
   Port ( 
      number   : in  std_logic_vector (7 downto 0);
      hundreds : out std_logic_vector (3 downto 0);
      tens     : out std_logic_vector (3 downto 0);
      ones     : out std_logic_vector (3 downto 0)
   );
end bcd;

architecture Behavioral of bcd is

begin

   bin_to_bcd : process (number)
      -- Internal variable for storing bits
      variable shift : unsigned(19 downto 0);
      
	  -- Alias for parts of shift register
      alias num is shift(7 downto 0);
      alias one is shift(11 downto 8);
      alias ten is shift(15 downto 12);
      alias hun is shift(19 downto 16);
   begin
      -- Clear previous number and store new number in shift register
      num := unsigned(number);
      one := X"0";
      ten := X"0";
      hun := X"0";
      
	  -- Loop eight times
      for i in 1 to num'Length loop
	     -- Check if any digit is greater than or equal to 5
         if one >= 5 then
            one := one + 3;
         end if;
         
         if ten >= 5 then
            ten := ten + 3;
         end if;
         
         if hun >= 5 then
            hun := hun + 3;
         end if;
         
		 -- Shift entire register left once
         shift := shift_left(shift, 1);
      end loop;
      
	  -- Push decimal numbers to output
      hundreds <= std_logic_vector(hun);
      tens     <= std_logic_vector(ten);
      ones     <= std_logic_vector(one);
   end process;

end Behavioral;

library IEEE;

use IEEE.STD_LOGIC_1164.ALL;

use IEEE.NUMERIC_STD.ALL;

entity bcd is

Port (

number : in std_logic_vector (7 downto 0);

hundreds : out std_logic_vector (3 downto 0);

tens : out std_logic_vector (3 downto 0);

ones : out std_logic_vector (3 downto 0)

);

end bcd;

architecture Behavioral of bcd is

begin

bin_to_bcd : process (number)

-- Internal variable for storing bits

variable shift : unsigned(19 downto 0);

-- Alias for parts of shift register

alias num is shift(7 downto 0);

alias one is shift(11 downto 8);

alias ten is shift(15 downto 12);

alias hun is shift(19 downto 16);

begin

-- Clear previous number and store new number in shift register

num := unsigned(number);

one := X"0";

ten := X"0";

hun := X"0";

-- Loop eight times

for i in 1 to num'Length loop

-- Check if any digit is greater than or equal to 5

if one >= 5 then

one := one + 3;

end if;

if ten >= 5 then

ten := ten + 3;

end if;

if hun >= 5 then

hun := hun + 3;

end if;

-- Shift entire register left once

shift := shift_left(shift, 1);

end loop;

-- Push decimal numbers to output

hundreds <= std_logic_vector(hun);

tens <= std_logic_vector(ten);

ones <= std_logic_vector(one);

end process;

end Behavioral;

Test Bench

LIBRARY ieee;
USE ieee.std_logic_1164.ALL;
USE ieee.numeric_std.ALL;
 
ENTITY TB_bcd IS
END TB_bcd;
 
ARCHITECTURE behavior OF TB_bcd IS 
 
   -- Component Declaration for the Unit Under Test (UUT)
   component bcd
      port(
         number   : in  std_logic_vector(7 downto 0);
         hundreds : out std_logic_vector(3 downto 0);
         tens     : out std_logic_vector(3 downto 0);
         ones     : out std_logic_vector(3 downto 0)
      );
   end component;
   
   --Inputs
   signal number   : std_logic_vector(7 downto 0) := (others => '0');

    --Outputs
   signal hundreds : std_logic_vector(3 downto 0);
   signal tens     : std_logic_vector(3 downto 0);
   signal ones     : std_logic_vector(3 downto 0);
 
BEGIN
 
   -- Instantiate the Unit Under Test (UUT)
   uut: bcd
      port map (
         number   => number,
         hundreds => hundreds,
         tens     => tens,
         ones     => ones
      );

   -- Stimulus process
   stim_proc: process
   begin      
      loop
         number <= std_logic_vector(unsigned(number) + 1);
         
         wait for 10 ns;
      end loop;
      
      wait;
   end process;

end;

LIBRARY ieee;

USE ieee.std_logic_1164.ALL;

USE ieee.numeric_std.ALL;

ENTITY TB_bcd IS

END TB_bcd;

ARCHITECTURE behavior OF TB_bcd IS

-- Component Declaration for the Unit Under Test (UUT)

component bcd

port(

number : in std_logic_vector(7 downto 0);

hundreds : out std_logic_vector(3 downto 0);

tens : out std_logic_vector(3 downto 0);

ones : out std_logic_vector(3 downto 0)

);

end component;

--Inputs

signal number : std_logic_vector(7 downto 0) := (others => '0');

--Outputs

signal hundreds : std_logic_vector(3 downto 0);

signal tens : std_logic_vector(3 downto 0);

signal ones : std_logic_vector(3 downto 0);

BEGIN

-- Instantiate the Unit Under Test (UUT)

uut: bcd

port map (

number => number,

hundreds => hundreds,

tens => tens,

ones => ones

);

-- Stimulus process

stim_proc: process

begin

loop

number <= std_logic_vector(unsigned(number) + 1);

wait for 10 ns;

end loop;

wait;

end process;

end;

36 thoughts on “Binary to Binary-Coded Decimal (BCD) Converter”

mike on April 7, 2014 at 6:46 pm said:

tnks for your code vhdl …it served me

Reply ↓
s on May 10, 2014 at 4:28 pm said:

vhdl code dont work, show error on alias num is shift(7 downto 0);
alias one is shift(11 downto 8);
alias ten is shift(15 downto 12);
alias hun is shift(19 downto 16);

Reply ↓
- Daniel on May 10, 2014 at 7:06 pm said:
  
  What was the specific error that it gave about those lines? and what software tools (IDE) are you using?
  
  Reply ↓
Siytek on December 30, 2014 at 11:33 am said:

Thanks for the info 🙂 nice clear implementation. Using this code, I created a decoder over at EDA Playground that takes a 14-bit decimal number (0 – 9999) and decodes it to 4 segments:
http://www.edaplayground.com/x/C4D
The code also works great on the DE0 board (Altera Cyclone III), where the only difference is the segment output is inverted to suit the boards active low hardware setup.

Reply ↓
MANJUNATH on January 7, 2015 at 8:08 pm said:

hai sir
i’m doing project on floating point numbers i want to convert decimal numbers to binary format. i request you to help me out in

thanking you
k.manjunath

Reply ↓
- Daniel on January 10, 2015 at 11:03 pm said:
  
  Do you want to convert to BCD to standard binary or BCD to floating point?
  
  Reply ↓
mohammad faizal on February 24, 2015 at 7:33 pm said:

hai sir
i’m doing project i want to convert decimal numbers to binary coded decimal format. i request you to help me out in verilog

thanking you
M.faizal

Reply ↓
- Daniel on February 25, 2015 at 10:02 am said:
  
  I don’t quite follow what you are asking, you provide more information?
  
  Reply ↓
  - mohammad faizal on February 25, 2015 at 10:39 am said:
    
    hai sir
    i’m doing project on floating point numbers i want to convert decimal numbers to bcd format. i request you to help me out in
    
    Reply ↓
Aksatha Selvam on February 26, 2015 at 3:33 am said:

Hello Sir,

I am doing a project on SPI master in slave out VHDL code. Can you please help me out in this please.

Reply ↓
- Daniel on February 26, 2015 at 9:38 am said:
  
  I would suggest you take a look at the OpenCores website at http://opencores.org/projects. They have many pre-made SPI modules that you could use.
  
  Reply ↓
mohammad faizal on March 2, 2015 at 12:13 am said:

hai sir
i’m doing project on floating point numbers i want to convert decimal numbers to bcd format. i request you to help me out in

Reply ↓
- Daniel on March 3, 2015 at 1:46 pm said:
  
  I would suggest asking a forum, you will get a quicker response and greater variety of help with your project. A few suggestions would be:
  
  http://www.edaboard.com/group128.html
  https://groups.google.com/forum/m/#!forum/comp.lang.verilog
  http://embdev.net/forum/fpga-vhdl-verilog
  
  Reply ↓
Satheesh on March 9, 2015 at 3:01 am said:

hai sir
i’m doing project on floating point numbers i want to convert Binary to decimal and decimal to binary , both using “floating point” values. I request you to help me out in this Sir..

thanking you,
Satheesh.R (M.E. VLSI)

Reply ↓
Elesar on March 23, 2015 at 3:29 pm said:

Hello,

I have some difficulties simulating the code. I think that it is because there is no input clock signal in the BCD block. I am using Xilinx ISE 9.1. Do you have any idea what shall I do to make it work?

Thank you in preliminary!

Reply ↓
- Daniel on March 23, 2015 at 5:30 pm said:
  
  The code for the Binary to BCD decoder is combinational logic (i.e. uses only AND, OR, ADDERS, … which don’t use clocks) but you do need to have some sort of timing controlling the input. If you look at the test bench above, you will notice that the inputs are changed (line #43) and then it waits for a period of time (line #45). This delay is to allow the changes on the inputs to ripple though all of the logic and show up on the output of the module. The amount of time that is required depends on what FPGA you are using/simulating. For an older Spartan 3 FPGA the time needs to be somewhere in the 30 ns range, where as a modern Spartan 6 is in the 10 ns range. The inputs can be controlled by a clock but the period of the clock would need to be longer than the time it takes for the changes to ripple through the logic. If the clock is to fast then the changes will have not made it to the output yet and when you attempt to read the output there will be invalid data.
  
  Let me know if this helps or if you are still having trouble.
  
  Reply ↓
  - Elesar on March 29, 2015 at 1:53 pm said:
    
    Hello Daniel,
    
    It looks that my problem with the simulation was because ISE9.1 doesn’t work properly on Windows 7. I installed ISE 14.7 and everything works fine now. I only have troubles with creating testbenches. In 9.1 there was no need of testbench, because the adding of input signals was made by graphic way. Can you recommend me tutorial on this matter?
    
    Best regards!
    
    Reply ↓
    - Daniel on March 29, 2015 at 8:36 pm said:
      
      The process for creating a test bench is very similar to creating an new VHDL entity. When you use the New Source Wizard you select VHDL Test Bench rather that VHDL Module and then associate that test bench with the module that you want to test. ISE will then generate most of the support code needed to implement the test bench and then you would just need to write some code to stimulate the inputs in the same manner that you would change the outputs of an VHDL module. The only difference is since this is a simulation you can use the wait for ##ns; or wait until X = 'Y'; rather than relying on the clock. I would suggest looking at some of the test benches that I have supplied with the various modules I’ve written and there is a good video showing and overview of the process at the link below.
      
      https://www.youtube.com/watch?v=vlb-SlfDNpY
      
      Reply ↓
robin on October 28, 2015 at 7:08 am said:

can we use and modify this for our project? this is a big help, and it works perfectly!

Reply ↓
Roberto Bolaños on October 29, 2015 at 1:57 am said:

Funciona a la perfección el de verilog!! Gracias!!

Reply ↓
Nihad on December 19, 2015 at 7:59 am said:

i am trying to convert 8 bit to 10 bit my verilog code is not working but vhdl is working can you please help me?
my verilog code is following:
module binbcd8(input[7:0] b,output reg[9:0] p);
reg[17:0] z;
integer i;
always@(b)
begin
z <=17'b0;
z[10:3] <=b;
for(i=0;i4)
z[11:8]<=z[11:8]+3;
else
z4)
z[15:12]<=z[15:12]+3;
else
z<=z;
z[17:1]<=z[16:0];
end
p4 then
z(11 downto 8):=z(11 downto 8)+3;
end if;
if z(15 downto 12)>4 then
z(15 downto 12):=z(15 downto 12)+3;
end if;
z(17 downto 1):=z(16 downto 0);
end loop;
p<=z(17 downto 8);

end process;
end Behavioral;

Reply ↓
- Daniel on January 1, 2016 at 5:33 pm said:
  
  I would suggest looking at Siytek code from the comment above at http://www.edaplayground.com/x/C4D. It is a 14 binary to BCD decoder that you can use.
  
  Reply ↓
Nihad on December 19, 2015 at 8:01 am said:

my verilog is following:
`timescale 1ns / 1ps
//////////////////////////////////////////////////////////////////////////////////
// Company:
// Engineer:
//
// Create Date: 16:28:08 12/19/2015
// Design Name:
// Module Name: binbcd8
// Project Name:
// Target Devices:
// Tool versions:
// Description:
//
// Dependencies:
//
// Revision:
// Revision 0.01 – File Created
// Additional Comments:
//
//////////////////////////////////////////////////////////////////////////////////
module binbcd8(input[7:0] b,output reg[9:0] p);
reg[17:0] z;
integer i;
always@(b)
begin
z <=17'b0;
z[10:3] <=b;
for(i=0;i4)
z[11:8]<=z[11:8]+3;
else
z4)
z[15:12]<=z[15:12]+3;
else
z<=z;
z[17:1]<=z[16:0];
end
p<=z[17:8];
end
endmodule

Reply ↓
Talha Shah on January 9, 2016 at 8:13 am said:

Thank you For Verilog Code

Reply ↓
Manikanta Kopparapu on February 10, 2016 at 11:16 pm said:

Hello sir I am doing project Fast architecture for decimal digit multiplication .I want code for binary to BCD converter and binary multiplier

Reply ↓
prakash on February 23, 2016 at 8:06 am said:

Hai sir
I’m doing project on “a high performance binary to BCD converter” ,i want clear details about this project, and why we using this project. Can u send me sir…..

Reply ↓
dumm_c on February 23, 2016 at 8:08 pm said:

Hi Daniel.

I tried the VHDL code and it works well. Thank you.
But can I modify your codes so it accepts a number up to 999?

Regards,
dummy_c

Reply ↓
- Daniel on February 23, 2016 at 9:09 pm said:
  
  Everything is free and opensource so feel free to modify and change as you wish. Siytek posted a link to a modified version of this that can handle 14 bits at http://www.edaplayground.com/x/C4D, it might we worth taking a look at.
  
  Reply ↓
  - dummy_c on February 23, 2016 at 9:36 pm said:
    
    Wow just what I am looking for!
    Since I will output it to 4 seven segments(using Nexys 3).
    And thank you so much for the fast response I really
    appreciate it Daniel.
    
    More power to your blog. 😀
    
    Reply ↓
Michael Correia on June 10, 2016 at 8:23 am said:

Thanks very much for this code! I’m making a Gameboy in VHDL and I wasn’t sure how to approach and instruction that converted the accumulator to BCD. I wanted to credit you in the bcd file but I don’t know your last name. Could you tell me your last name or another way you wish to be recognized?

Reply ↓
Pingback: Binary Coded Signals | Rise Fall Trading
debasish on May 14, 2017 at 1:38 am said:

what ise have you used to write this code

Reply ↓
- Daniel on May 14, 2017 at 4:35 am said:
  
  It was written in Xilinx ISE 13.2.
  
  Reply ↓
William30 on June 7, 2017 at 11:42 am said:

Hi, do you allow guest posting on deathbylogic.com ? 🙂 Let me know on my email

Reply ↓
Binary Today 5 on September 22, 2018 at 5:16 pm said:

This is really one of the best binary options trading posts I’ve read through
in ages.

Reply ↓
Harold.Julia on December 17, 2019 at 11:18 am said:

try to build the solid foundation of the bricks that others have taken, life will not be so hard.

Reply ↓

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Binary to Binary-Coded Decimal (BCD) Converter

CODE

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Test Bench

36 thoughts on “Binary to Binary-Coded Decimal (BCD) Converter”

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