Decimal adder
- 1. SYED HASAN SAEED hasansaeedcontrol@gmail.com https://shasansaeed.yolasite.com 1 Syed Hasan Saeed, Integral University, Lucknow
- 2. DECIMAL ADDER 2 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 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 Syed Hasan Saeed, Integral University, Lucknow 4 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 Syed Hasan Saeed, Integral University, Lucknow 5 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, Lucknow 5 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 6 Syed Hasan Saeed, Integral University, Lucknow 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, Lucknow 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, Lucknow 7
- 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 Syed Hasan Saeed, Integral University, Lucknow 8 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 Syed Hasan Saeed, Integral University, Lucknow 9 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 Syed Hasan Saeed, Integral University, Lucknow 10 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 11 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 Syed Hasan Saeed, Integral University, Lucknow 12 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 13 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 Syed Hasan Saeed, Integral University, Lucknow 14 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, Lucknow 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 16 Syed Hasan Saeed, Integral University, Lucknow 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, 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 18