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Similar to BCD-Addition-and-subtraction in digital .pptx (20)
BCD-Addition-and-subtraction in digital .pptx
- 1. BCD Addition and subtraction
- 2. BCD addition Add two numbers as same as binary addition Case 1: If the result is less than or equals to 9 and carry is zero then it is valid BCD. Case 2: If result is greater than 9 and carry is zero then add 6 in four bit combination. Case 3: If result is less than or equals to 9 but carry is 1 then add 6 in four bit combination.
- 3. Summary of BCD addition Add two BCD numbers Sum <= 9, carry = 0 Answer is correct no correction required Sum > 9, carry = 0 Add 6 to sum to get correct answer Sum < = 9, carry = 1 Add 6 to sum to get correct answer
- 4. BCD addition case 1 example Ex: perform in BCD (2)10 + (6)10 Decimal BCD 2 0 0 1 0 1 st number + 6 0 1 1 0 2 nd number 0 1 1 carry 8 1 0 0 0 answer 0 Final Carry
- 5. BCD addition case 2 example Ex: perform in BCD (7)10 + (6)10 Decimal BCD 7 0 1 1 1 1 st number + 6 0 1 1 0 2 nd number 1 1 carry 8 1 1 0 1 answer (invalid BCD) 0 1 1 0 ADD 6 1 0 0 1 1 1 3 final answer 0 Final Carry 1
- 6. BCD addition case 3 example Ex: perform in BCD (9)10 + (8)10 Decimal BCD 9 1 0 0 1 1 st number + 8 1 0 0 0 2 nd number carry 17 0 0 0 1 answer (valid BCD but carry 1) 0 0 0 1 0 1 1 0 ADD 6 0 0 0 1 0 1 1 1 1 7 final answer 1 Final Carry
- 8. Solve????? 1. Perform in BCD (57)10 + (26)10 2. Perform in BCD (83)10 + (34)10 3. Perform in BCD (421)10 + (975)10
- 9. 9’s complement: 9’s complement of a BCD number can be obtained by subtracting it from 9. 10’s compliment: 10’s compliment is obtained by adding 1 to 9’s compliment
- 10. 9’s complement • The 9’s complement of BCD number is obtained by subtracting it from 9. • Ex: 9’s complement of 1 = 9 – 1 = 8 Decimal number BCD number 9’s complement 0 0000 1001 1 0001 1000 2 0010 0111 3 0011 0110 4 0100 0101 5 0101 0100 6 0110 0011 7 0111 0010 8 1000 0001 9 1001 0000
- 11. Find the 9’s complement • 9’s COMPLEMENT of 28 = 99 – 28 = 71 • 9’s COMPLEMENT of 562 = 999 – 562 = 437
- 12. 10’s complement • 10’s complement of a number is obtained by adding 1 to its 9’s complement. Decimal number BCD number 9’s complement 10’s complement 0 0000 1001 1 0000 1 0001 1000 1001 2 0010 0111 1000 3 0011 0110 0111 4 0100 0101 0110 5 0101 0100 0101 6 0110 0011 0100 7 0111 0010 0011 8 1000 0001 0010 9 1001 0000 0001
- 13. BCD subtraction • Two methods: 1. 9’s complement method 2. 10’s complement method
- 14. BCD subtraction using 9’s complement • Perform BCD subtraction using 9’s complement method (A)10 - (B)10 1. Obtain 9’s complement of no. B 2. Add no. A and 9’s complement of no. B 3. If carry is generated in step 2 then add it to sum to obtain final result. The carry is called as end around carry. 4. If carry is not produced then the result is negative hence take 9’s complement of the result.
- 15. Examples • Perform (8)10 - (3)10 9’s complement of 3 8
- 16. Ex.
- 17. Ex.
- 18. Ex.
- 21. Solve following subtraction of decimal numbers using 9’s complement method. 1. Perform (7)10 - (3)10 2. Perform (4)10 - (7)10 3. Perform (83)10 - (21)10 4. Perform (52)10 – (89)10
- 22. BCD subtraction 10’s complement method • Perform BCD subtraction using 10’s complement method (A)10 - (B)10 1. Obtain 10’s complement of no. B 2. Add no. A and 10’s complement of no. B 3. If carry is generated in step 2 then discard it. 4. If carry is not produced then the result is negative hence take 10’s complement of the result.
- 23. Example using 10’s complement
- 24. Solve following subtraction of decimal numbers using 9’s complement method. 1. Perform (7)10 - (3)10 2. Perform (4)10 - (7)10 3. Perform (83)10 - (21)10 4. Perform (52)10 – (89)10
- 25. 9’s complement and 10’s complement
- 26. Perform (9)10 – (4)10 using 1’s complement method
- 27. Perform (4)10 – (9)10 using 1’s complement method
- 28. Solve • Perform following subtraction using 1’s complement method. 1. (-5)10 - (-7)10 2. (48)10 – (61)10 3. (33)10 – (54)10 4. (99)10 – (22)10
- 29. Perform (9)10 – (4)10 using 2’s complement method
- 30. Perform (4)10 – (9)10 using 2’s complement method
- 31. Solve • Perform following subtraction using 2’s complement method. 1. (-5)10 - (-7)10 2. (48)10 – (61)10 3. (33)10 – (54)10 4. (99)10 – (22)10 5. (1010)2 – (101)2