1. Conversion and Coding
(12)10

2. Conversion and Coding
(12)10
1100
Conversion

3. Conversion and Coding (12)10 00010010 1100 Coding Conversion
(using BCD code
for each digit)
Conversion

4. BCD Adder Design a circuit that calculates the
Arithmetic addition of two decimal digits. 9 + 3 1 2
carry

5. BCD Adder Maximum sum is 9+9 + 1 = 19 Max digit
Carry from previous digits

6. BCD adder (sum up to 9)
Number C S8 S4 S2 S1 1 2 3 4 5 6 7 8 9

7. BCD adder (sum up to 9) Number C S8 S4 S2 S1 1 2 3 4 5 6 7 8 91 2 3 4 5 6 7 8 9
The sum is the same with BCD adder

8. BCD adder (sum is 10 to 19) Number C S8 S4 S2 S1 10 1 11 12 13 14 1511 12 13 14 15 16 17 18 19

9. BCD adder (sum is 10 to 19) C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18
Binary sum
Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1

10. BCD adder (sum is 10 to 19) C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18
Binary sum
Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1

11. BCD adder (sum is 10 to 19) +6 C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17
Binary sum
Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1 +6

12. Algorithm for BCD Adder
If sum is up to 9
Use the regular Adder.
If the sum > 9
Use the regular adder and add 6 to the result

13. When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18
Binary sum
Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19
C = K +

14. When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18
Binary sum
Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19
C = K + Z8*Z4+

15. When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18
Binary sum
Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19
C = K + Z8*Z4+
Z8*Z2

16. BCD Adder
4-bit Adder
Cin z8 z4 z2 z1
4-bit Adder K s8 s4 s2 s1