This document describes the design of a BCD adder. It discusses three cases for adding two 4-bit BCD numbers: 1) the sum is valid if less than or equal to 9 with no carry, 2) correction is needed if the sum is greater than 9 with no carry by adding 6, and 3) correction is needed if the sum is less than or equal to 9 but with a carry by adding 6. The design uses two 4-bit binary adders, with the output of the first checked by a combinational circuit to determine if correction is needed. The circuit outputs control the second adder to apply the necessary correction to produce the valid BCD sum.

1. SYED HASAN SAEED
hasansaeedcontrol@gmail.com
https://shasansaeed.yolasite.com
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Syed Hasan Saeed, Integral University,
Lucknow

2. DECIMAL ADDER
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Syed Hasan Saeed, Integral University,
Lucknow

3. BCD ADDER:
A BCD adder should perform the following
• Add two 4-bit BCD number using straight Binary Addition.
• If the sum of two numbers is equal to or less than 9, then the sum is
valid BCD number and no correction is required.
• If the sum of two numbers is greater than 9 or carry is generated
from the sum, then the sum is not valid BCD number. Then add
0110 (6) to the sum, the result will be valid BCD number. If further
a carry is generated then add 0110 to the result.
Syed Hasan Saeed, Integral University,
Lucknow
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4. Assume that two 4-bit BCD numbers are being added. In BCD
addition, there are three different cases. Let us consider one by one.
CASE 1: Sum equal to or less than 9 with carry 0
DECIMAL BCD
2 0 0 1 0
+ 3 0 0 1 1
Carry 1
SUM 5 0 0 1 0 1
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Lucknow
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Valid BCD NumberFinal Carry
If the sum of two numbers is less than or equal to 9 with final carry zero,
then the sum is valid BCD number and no correction is required.

5. Consider second case
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CASE 2: Sum greater than 9 with carry 0
DECIMAL BCD
5 0 1 0 1
+ 7 0 1 1 1
Carry 1 1
SUM 12 0 1 1 0 0
0 1 1 0
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Invalid BCD Number
Carry
Add 6 for correction
1 0 0 1 0
0 0 1 00 0 0 1
Final Carry
1 2
Final result
Valid BCD number with
carry 1
If the sum of two numbers is greater than 9 with carry zero , and the sum is
invalid BCD number, then correction is required. Add 0 1 1 0 (6) for correction.
Final result will be the valid BCD number.

6. Syed Hasan Saeed, Integral University,
Lucknow
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Syed Hasan Saeed, Integral University,
Lucknow
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CASE 3: Sum is equal to or less than 9 with carry 1
DECIMAL BCD
8 1 0 0 0
+ 8 1 0 0 0
Carry 1
SUM 16 1 0 0 0 0
0 1 1 0
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Invalid BCD Number
Add 6 for correction
0 1 1 0
0 1 1 00 0 0 1
Final Carry
1 6
Final result Valid BCD number with
carry 1
If the sum of two numbers is equal to or less than than 9 with carry 1 , and the
sum is invalid BCD number, then correction is required. Add 0 1 1 0 (6) for
correction. Final result will be the valid BCD number.
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7. DESIGN:
• In fig. 1 B3B2B1B0 and A3A2A1A0 are the BCD inputs. S3S2S1S0 and
Cout is the output of Adder 1.
• Checked the output of Adder 1, whether it is greater than or less
than 9.
• If the sum of Adder 1 is greater than 9 then the output of
combinational circuit should be 1 (i.e Cout should be high ) and
correction is required.
• Write the truth table and K-Map for combinational circuit.
• The Boolean Expression from K-Map Y= S3S2+S3S1
• The output of combinational circuit Y2 is connected to B2B1 of
Adder 2 and B3B0 are connected to the ground. Therefore B3=B0=0
• The output sum of Adder 1 is connected to Adder 2. the output of
Adder 2 is the final result of BCD addition with Carry which can be
ignored if any.
Syed Hasan Saeed, Integral University,
Lucknow
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8. INPUTS OUTPUT
S
S3 S2 S1 S0 Y1
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
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SumisvalidBCDnumber.Therefore
Y=0
SumisvalidBCD
number.Therefore
Y=1
TRUTHTABLE K-Map

9. INPUTS OUTPUT
S
S3 S2 S1 S0 Y1
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
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SumisvalidBCDnumber.Therefore
Y=0
SumisvalidBCD
number.Therefore
Y=1
TRUTHTABLE
0 0 0 0
0 0 0 0
1 1 1 1
0 0 1 1
K-Map
S3S2
S1S0
00 01 11 10
10
11
01
00

10. INPUTS OUTPUT
S
S3 S2 S1 S0 Y1
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
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SumisvalidBCDnumber.Therefore
Y=0
SumisvalidBCD
number.Therefore
Y=1
TRUTHTABLE
0 0 0 0
0 0 0 0
1 1 1 1
0 0 1 1
K-Map
S3S2
S1S0
00 01 11 10
10
11
01
00
Y1=S3S2+S3S1

11. Syed Hasan Saeed, Integral University,
Lucknow
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0
Output Carry
Cout
Cout
A1 AOA3 A2BO
B1B2B3
SOS1S2S3
SOS1S2S3
Cin
Cin
4-Bit Binary Adder 1
4-Bit Binary Adder 2
S3S1
S3S2
Final Sum Output
Combinational
Circuit
Not To Be Used
Fig.1:BLOCKDIAGRAMOFBCDADDER
Y1
Y2
M3 M2 M1 M0

12. CASE 1: Sum equal to or less than 9 with carry 0
DECIMAL BCD
2 0 0 1 0
+ 1 0 0 0 1
Carry 0
SUM 3 0 0 0 1 1
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Valid BCD NumberFinal Carry
Output of combinational circuit Y2= 0, M3 M2 M1 M0 = 0
Output of Adder 2 is same as the output of Adder 1

13. Syed Hasan Saeed, Integral University,
Lucknow
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0
Output Carry
Cout
Cout
A1 AOA3 A2BO
B1B2B3
SOS1S2S3
SOS1S2S3
Cin
Cin
4-Bit Binary Adder 1
4-Bit Binary Adder 2
S3S1
S3S2
Final Sum Output
Combinational
Circuit
Not To Be Used
Fig.1:BLOCKDIAGRAMOFBCDADDER
Y1
Y2
0 0 0 10 0 1 0
0
0
0
0
0
0 0 0 0 0 0 1 1
0 0 1 1
M3 M2 M1 M0

14. Consider second case
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CASE 2: Sum greater than 9 with carry 0
DECIMAL BCD
5 0 1 0 1
+ 7 0 1 1 1
Carry 1 1
SUM 12 0 1 1 0 0
0 1 1 0
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14
Invalid BCD Number
Carry
Add 6 for correction
1 0 0 1 0
0 0 1 00 0 0 1
Final Carry
1 2
Final result
Valid BCD number with
carry 1
Output of combinational circuit Y2= 0, M3 M2 M1 M0 = 0 1 1 0

15. Syed Hasan Saeed, Integral University,
Lucknow
15
0
Output Carry
Cout
Cout
A1 AOA3 A2BO
B1B2B3
SOS1S2S3
SOS1S2S3
Cin
Cin
4-Bit Binary Adder 1
4-Bit Binary Adder 2
S3S1
S3S2
Final Sum Output
Combinational
Circuit
Not To Be Used
Fig.1:BLOCKDIAGRAMOFBCDADDER
Y1
Y2
0 00 1 1111
1 1 0 0
1 1
1
1
0
0
1
1
0
1 1 000
00 01
2
1000
1
M3 M2 M1 M0
0 1 1 0

16. Syed Hasan Saeed, Integral University,
Lucknow
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Syed Hasan Saeed, Integral University,
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CASE 3: Sum is equal to or less than 9 with carry 1
DECIMAL BCD
8 1 0 0 0
+ 8 1 0 0 0
Carry 1
SUM 16 1 0 0 0 0
0 1 1 0
Syed Hasan Saeed, Integral University,
Lucknow
16
Invalid BCD Number
Add 6 for correction
0 1 1 0
0 1 1 00 0 0 1
Final Carry
1 6
Final result Valid BCD number with
carry 1
1
Output of combinational circuit Y2= 1, M3 M2 M1 M0 = 0 1 1 0

17. Syed Hasan Saeed, Integral University,
Lucknow
17
0
Output Carry
Cout
Cout
A1 AOA3 A2BO
B1B2B3
SOS1S2S3
SOS1S2S3
Cin
Cin
4-Bit Binary Adder 1
4-Bit Binary Adder 2
S3S1
S3S2
Final Sum Output
Combinational
Circuit
Not To Be Used
Fig.1:BLOCKDIAGRAMOFBCDADDER
Y1
Y2
1 1
1
0 0 0 000
0000
0
0
0
1
1 10 0 00 0 0
1 1 10 0
0 0 0 1
0 1 1 0 61
M3 M2 M1 M0

18. THANK YOU
Syed Hasan Saeed, Integral University,
Lucknow
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