binary-to-bcd converter
DESCRIPTION
Binary-to-BCD Converter. Discussion DS-4.1. Shift and Add-3 Algorithm. S1. Shift the binary number left one bit. 22. If 8 shifts have taken place, the BCD number is in the Hundreds , Tens , and Units column. 33. If the binary value in any of the BCD columns is 5 or greater, - PowerPoint PPT PresentationTRANSCRIPT
Binary-to-BCD Converter
Discussion DS-4.1
Shift and Add-3 Algorithm S1. Shift the binary number left one bit.22. If 8 shifts have taken place, the BCD number is in the
Hundreds, Tens, and Units column.33. If the binary value in any of the BCD columns is 5 or greater,
add 3 to that value in that BCD column.44. Go to 1.
Operation Hundreds Tens Units Binary HEX F F Start 1 1 1 1 1 1 1 1
Operation Hundreds Tens Units Binary HEX F F Start 1 1 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1 1 1 Shift 2 1 1 1 1 1 1 1 1 Shift 3 1 1 1 1 1 1 1 1 Add 3 1 0 1 0 1 1 1 1 1 Shift 4 1 0 1 0 1 1 1 1 1 Add 3 1 1 0 0 0 1 1 1 1 Shift 5 1 1 0 0 0 1 1 1 1 Shift 6 1 1 0 0 0 1 1 1 1 Add 3 1 0 0 1 0 0 1 1 1 1 Shift 7 1 0 0 1 0 0 1 1 1 1 Add 3 1 0 0 1 0 1 0 1 0 1 Shift 8 1 0 0 1 0 1 0 1 0 1 BCD 2 5 5
Steps to convert an 8-bit binary number to BCD
Truth table for Add-3 Module
A3 A2 A1 A0 S3 S2 S1 S0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 X X X X 1 0 1 1 X X X X 1 1 0 0 X X X X 1 1 0 1 X X X X 1 1 1 0 X X X X 1 1 1 1 X X X X
C
A3 A2 A1 A0
S3 S2 S1 S0
A3 A2 A1 A0 S3 S2 S1 S0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 X X X X 1 0 1 1 X X X X 1 1 0 0 X X X X 1 1 0 1 X X X X 1 1 1 0 X X X X 1 1 1 1 X X X X
K-Map for S3
A3 A2
A1 A0
00 01 11 10
00
01
11
10
1 1
11
1
X
S3 = A3+ A2 * A0+ A2 * A1
X X X
X
X
C1
C2
C3
C4C6
C5C7
B7
0
0 B6 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0P9 P8
8-bit binary input
BCD output
hunds tens units
Binary-to-BCDConverter
S3
C1
C2
C3
C4C6
C5C7
B7
0
0 B6 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0P9 P8
8-bit binary input
BCD output
hunds tens units
1 1 1 1 1 1 1 1
1 0 1 0
1 0 0 0
1 1 0 0 0 1
1 0 0 1 0 0 1 1
1 0 0 1 0 1 0 1 0 1
1 1
2 5 5
Hex FF
Binary-to-BCDConverter
Structural Solution
Operation Tens Units Binary
B 5 4 3 2 1 0
HEX 3 F
Start 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1
Shift 2 1 1 1 1 1 1
Shift 3 1 1 1 1 1 1
Add 3 1 0 1 0 1 1 1
Shift 4 1 0 1 0 1 1 1
Add 3 1 1 0 0 0 1 1
Shift 5 1 1 0 0 0 1 1
Shift 6 1 1 0 0 0 1 1
BCD 6 3 P 7 4 3 0
z 13 10 9 6 5 0
Steps to convert a 6-bit binary number to BCD
1. Clear all bits of z to zero2. Shift B left 3 bits
z[8:3] = B[5:0];3. Do 3 times if Units >4 then add 3 to Units (note: Units = z[9:6]) Shift z left 1 bit4. Tens = P[6:4] = z[12:10] Units = P[3:0] = z[9:6]
C1
C2
C30
0 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0
6-bit binary input
BCD output
tens units
1 1 1 1 1 1
1 0 1 0
1 0 0 0
1 1 0 0 0 1 1
6 3
Hex 3F
Operation Tens Units Binary
B 5 4 3 2 1 0
HEX 3 F
Start 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1
Shift 2 1 1 1 1 1 1
Shift 3 1 1 1 1 1 1
Add 3 1 0 1 0 1 1 1
Shift 4 1 0 1 0 1 1 1
Add 3 1 1 0 0 0 1 1
Shift 5 1 1 0 0 0 1 1
Shift 6 1 1 0 0 0 1 1
BCD 6 3 P 7 4 3 0
z 13 10 9 6 5 0
binbcd6.vhd
-- Title: Binary-to-BCD Converterlibrary IEEE;use IEEE.std_logic_1164.all;use IEEE.std_logic_unsigned.all; entity binbcd6 is port ( B: in STD_LOGIC_VECTOR (5 downto 0); P: out STD_LOGIC_VECTOR (6 downto 0) );end binbcd6;
architecture binbcd6_arch of binbcd6 isbegin bcd1: process(B) variable z: STD_LOGIC_VECTOR (12 downto 0);
begin for i in 0 to 12 loop
z(i) := '0'; end loop; z(8 downto 3) := B; for i in 0 to 2 loop
if z(9 downto 6) > 4 then z(9 downto 6) := z(9 downto 6) + 3; end if; z(12 downto 1) := z(11 downto 0);
end loop;
P <= z(12 downto 6); end process bcd1; end binbcd6_arch;
Operation Tens Units Binary
B 5 4 3 2 1 0
HEX 3 F
Start 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1
Shift 2 1 1 1 1 1 1
Shift 3 1 1 1 1 1 1
Add 3 1 0 1 0 1 1 1
Shift 4 1 0 1 0 1 1 1
Add 3 1 1 0 0 0 1 1
Shift 5 1 1 0 0 0 1 1
Shift 6 1 1 0 0 0 1 1
BCD 6 3 P 7 4 3 0
z 13 10 9 6 5 0
C1
C2
C30
0 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0
6-bit binary input
BCD output
tens units
1 1 1 1 1 1
1 0 1 0
1 0 0 0
1 1 0 0 0 1 1
6 3
Hex 3F
binbcd6.vhd (cont.)
Operation Tens Units Binary
B 5 4 3 2 1 0
HEX 3 F
Start 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1
Shift 2 1 1 1 1 1 1
Shift 3 1 1 1 1 1 1
Add 3 1 0 1 0 1 1 1
Shift 4 1 0 1 0 1 1 1
Add 3 1 1 0 0 0 1 1
Shift 5 1 1 0 0 0 1 1
Shift 6 1 1 0 0 0 1 1
BCD 6 3 P 7 4 3 0
z 13 10 9 6 5 0
C1
C2
C30
0 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0
6-bit binary input
BCD output
tens units
1 1 1 1 1 1
1 0 1 0
1 0 0 0
1 1 0 0 0 1 1
6 3
Hex 3Fbinbcd6.vhd
-- Title: Binary-to-BCD Converter
library IEEE;
use IEEE.std_logic_1164.all;
use IEEE.std_logic_unsigned.all;
entity binbcd is
port (
B: in STD_LOGIC_VECTOR (7 downto 0);
P: out STD_LOGIC_VECTOR (9 downto 0)
);
end binbcd;
8-Bit Binary-to-BCD Converter binbcd8.vhd
architecture binbcd_arch of binbcd isbegin bcd1: process(B)
variable z: STD_LOGIC_VECTOR (17 downto 0);
begin for i in 0 to 17 loop
z(i) := '0'; end loop; z(10 downto 3) := B; for i in 0 to 4 loop
if z(11 downto 8) > 4 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 bcd1; end binbcd_arch;
Operation Hundreds Tens Units Binary B 7 4 3 0
HEX F F Start 1 1 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1 1 1 Shift 2 1 1 1 1 1 1 1 1 Shift 3 1 1 1 1 1 1 1 1 Add 3 1 0 1 0 1 1 1 1 1 Shift 4 1 0 1 0 1 1 1 1 1 Add 3 1 1 0 0 0 1 1 1 1 Shift 5 1 1 0 0 0 1 1 1 1 Shift 6 1 1 0 0 0 1 1 1 1 Add 3 1 0 0 1 0 0 1 1 1 1 Shift 7 1 0 0 1 0 0 1 1 1 1 Add 3 1 0 0 1 0 1 0 1 0 1 Shift 8 1 0 0 1 0 1 0 1 0 1 BCD 2 5 5
P 9 8 7 4 3 0 z 17 16 15 12 11 8 7 4 3 0
binbcd8.vhd (cont.)
Operation Hundreds Tens Units Binary B 7 4 3 0
HEX F F Start 1 1 1 1 1 1 1 1
Shift 1 1 1 1 1 1 1 1 1 Shift 2 1 1 1 1 1 1 1 1 Shift 3 1 1 1 1 1 1 1 1 Add 3 1 0 1 0 1 1 1 1 1 Shift 4 1 0 1 0 1 1 1 1 1 Add 3 1 1 0 0 0 1 1 1 1 Shift 5 1 1 0 0 0 1 1 1 1 Shift 6 1 1 0 0 0 1 1 1 1 Add 3 1 0 0 1 0 0 1 1 1 1 Shift 7 1 0 0 1 0 0 1 1 1 1 Add 3 1 0 0 1 0 1 0 1 0 1 Shift 8 1 0 0 1 0 1 0 1 0 1 BCD 2 5 5
P 9 8 7 4 3 0 z 17 16 15 12 11 8 7 4 3 0
binbcd8.vhd
C1
C2
C3
C4C6
C5C7
B7
0
0 B6 B5 B4 B3 B2 B1 B0
P7 P6 P5 P4 P3 P2 P1 P0P9 P8
8-bit binary input
BCD output
hunds tens units
1 1 1 1 1 1 1 1
1 0 1 0
1 0 0 0
1 1 0 0 0 1
1 0 0 1 0 0 1 1
1 0 0 1 0 1 0 1 0 1
1 1
2 5 5
Hex FF
C1
C2
C3
C4C14
C5C15
B150 B14 B13 B12 B11B10 B9 B8
16-bit binary input
B7 B6 B5 B4 B3 B2 B1 B0
BCD output
hundreds tens units
C6C16
C7C17C24
C8C18C25
C9C19C26
C11C21C28C32
C12C22C29C33
C13C23C30C34
0
0
C10C20C27C31
0
thousandsten thousands
P15 P14 P13 P12 P11 P10 P9 P8 P7 P6 P5 P4 P3 P2 P1 P0P19 P17P18 P16
16-bitBinary-to-BCDConverter
binbcd16.vhd
-- Title: Binary-to-BCD Converterlibrary IEEE;use IEEE.std_logic_1164.all;use IEEE.std_logic_unsigned.all; entity binbcd16 is port ( B: in STD_LOGIC_VECTOR (15 downto 0); P: out STD_LOGIC_VECTOR (18 downto 0) );end binbcd16;
architecture binbcd16_arch of binbcd16 isbegin bcd1: process(B)
variable z: STD_LOGIC_VECTOR (34 downto 0);
C1
C2
C3
C4C14
C5C15
B150 B14 B13 B12 B11B10 B9 B8
16-bit binary input
B7 B6 B5 B4 B3 B2 B1 B0
BCD output
hundreds tens units
C6C16
C7C17C24
C8C18C25
C9C19C26
C11C21C28C32
C12C22C29C33
C13C23C30C34
0
0
C10C20C27C31
0
thousandsten thousands
P15 P14 P13 P12 P11 P10 P9 P8 P7 P6 P5 P4 P3 P2 P1 P0P19 P17P18 P16
begin for i in 0 to 34 loop
z(i) := '0'; end loop; z(18 downto 3) := B; for i in 0 to 12 loop
if z(19 downto 16) > 4 then z(19 downto 16) := z(19 downto 16) + 3;end if;if z(23 downto 20) > 4 then z(23 downto 20) := z(23 downto 20) + 3;end if;if z(27 downto 24) > 4 then z(27 downto 24) := z(27 downto 24) + 3;end if;if z(31 downto 28) > 4 then z(31 downto 28) := z(31 downto 28) + 3;end if;z(34 downto 1) := z(33 downto 0);
end loop; P <= z(34 downto 16); end process bcd1;end binbcd16_arch;
C1
C2
C3
C4C14
C5C15
B150 B14 B13 B12 B11B10 B9 B8
16-bit binary input
B7 B6 B5 B4 B3 B2 B1 B0
BCD output
hundreds tens units
C6C16
C7C17C24
C8C18C25
C9C19C26
C11C21C28C32
C12C22C29C33
C13C23C30C34
0
0
C10C20C27C31
0
thousandsten thousands
P15 P14 P13 P12 P11 P10 P9 P8 P7 P6 P5 P4 P3 P2 P1 P0P19 P17P18 P16
binbcd16.vhd (cont.)
C1
C2
C3
C4C14
C5C15
B150 B14 B13 B12 B11B10 B9 B8
16-bit binary input
B7 B6 B5 B4 B3 B2 B1 B0
BCD output
hundreds tens units
C6C16
C7C17C24
C8C18C25
C9C19C26
C11C21C28C32
C12C22C29C33
C13C23C30C34
0
0
C10C20C27C31
0
thousandsten thousands
P15 P14 P13 P12 P11 P10 P9 P8 P7 P6 P5 P4 P3 P2 P1 P0P19 P17P18 P16
binbcd16.vhd