1. DECIMAL ARITHEMATIC
OPERATIONS
PRESENTED BY :
PADMAPRIYA.G

2. INTRO
• Decimal numbers
INPUT
• Decimal numbers are placed in the registers in coded
form - Binary coded decimal (BCD )
ALU • Micro operations are performed
• Decimal numbers
output

3. DECIMAL ARITHEMATIC
MICROOPERATION SYMBOLS
 A A+B
Add contents of registers A and B, and
transfer the sum into A.
 B’
9’s complement of B.
 A A + B’ +1
content of A plus 10’s complement of B into A

4.  B B+ 1
Increment BCD number in B
 dshr A
Decimal shift right register A
 dshl A
Decimal shift left register A

5. ADDITION
BCD DIGITS
4 BIT BINARY ADDER
SUM : BINARY RANGING
FROM 0 TO 19

6. DERIVATION OF BCD ADDER
C = K + Z8 Z4 + Z8 Z2

7.  Output of binary adder : Binary form .
Conversion to BCD
Binary sum ≤ 1001 : no conversion
Binary sum ≥ 1001 : non valid BCD
add binary 6 (0110)
 3 different ways to add.

8. BLOCK DIAGRAM OF BCD ADDER
C = K + Z8 Z4 + Z8 Z2

9. Parallel decimal
addition
 BCD adders = digits in the number.
 Sum is formed in parallel.
 requires only 1 micro operations.

10. 624 + 879 =1503
1 0 1 0 1 1 0 1

11. DIGIT SERIAL, BIT PARALLEL
ADDITION
 Digits are applied to single BCD adder
serially.
Bits of each coded digit are transferred in
parallel.
For k digits – k micro operations.

12. 624 + 879 =1503

13. USING FULL ADDER

14. Example - ADDITION
6796 0110 0111 1001 0110
• 5368 + 0101 0011 0110 1000 +
• -----------------------------------------
1011 1010 1111 1110

15. 6796 0110 0111 1001 0110
5368 + 0101 0011 0110 1000 +
--------------------------------
1011 1010 1111 1110
0110 0110 0110 0110 +
-----------------------------------
10001 10000 10101 10100

16. 6796 0110 0111 1001 0110
5368 + 0101 0011 0110 1000 +
-------------------------------------------
1011 1010 1111 1110
0110 0110 0110 0110 +
-------------------------------------------
10001 10000 10101 10100
+
1 1 1 1
------------------------------------------------------
0001 0010 0001 0110 0100
------------------------------------------------------
1 2 1 6 4

17. SUBTRACTION
Using 9’s complement :
- Find 9’s complement of the –ve
number.
- Add the 2 numbers.
- IF result ≥ 10,add 6(0110).
- If the carry is generated add it with the
result, else find the 9’s complement of it.

18. Example
87 - 39
9’s complement of 39 = 99-39 = 60
87 1000 0111
60 0110 0000 +
--------------------
invalid 1110 0111

19. 87 1000 0111
60 0110 0000 +
------------------
•
1110 0111
0110
------- +
10100 0111
1+
--------------------
0100 1000
--------------------
4 8

20. 18 – 72
9’s complement of 72 = 99-72 =27
18 0001 1000
27 0010 0111
-----------------
0011 1111 invalid

21. 18 0001 1000
27 0010 0111
-----------------
0011 1111
0001 0110
------- -------
0100 (1)0101
------- --------
4 5
9’s complement of 45 = 54

22. USING 10’S COMPLEMENT
• Using 10’s complement :
- Find the 10’s complement of the number.
- Add the 2 numbers.
- If the result ≥ 10, add 6(0110).
- If the carry is not generated , then find
the 10’s complement of the result.

23. 34 – 56
10’s complement of 56 = (99-56)+1 = 44
34 0011 0100
44 0100 0100 +
---------------
0111 1000
7 8
10’s complement of 78 = 22

24. BCD SUBTRACTION
M = 0 - addition is performed.
M = 1 - subtraction is performed.