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,
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3
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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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
Syed Hasan Saeed, Integral University,
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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,
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6
Syed Hasan Saeed, Integral University,
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6
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,
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6
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.
1
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,
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11. Syed Hasan Saeed, Integral University,
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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,
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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,
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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 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,
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16
Syed Hasan Saeed, Integral University,
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16
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,
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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,
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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
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
