The document describes the design of a binary coded decimal (BCD) adder circuit. It explains that a BCD adder is needed to perform arithmetic addition on decimal digits coded in BCD. The BCD adder handles sums between 0-9 like a regular adder but adds 6 to the result for sums from 10-19. The document provides truth tables to illustrate the BCD addition logic and explains that the carry output is set if the sum of the most significant bits is greater than 1.

1. Conversion and Coding
(12)10

2. Conversion and Coding
(12)10
1100Conversion

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

4. BCD Adder
Design a circuit that calculates the
Arithmetic addition of two decimal digits.
9
3
2
+
1
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
0 0 0 0 0 0
1 0 0 0 0 1
2 0 0 0 1 0
3 0 0 0 1 1
4 0 0 1 0 0
5 0 0 1 0 1
6 0 0 1 1 0
7 0 0 1 1 1
8 0 1 0 0 0
9 0 1 0 0 1

7. BCD adder (sum up to 9)
Number C S8 S4 S2 S1
0 0 0 0 0 0
1 0 0 0 0 1
2 0 0 0 1 0
3 0 0 0 1 1
4 0 0 1 0 0
5 0 0 1 0 1
6 0 0 1 1 0
7 0 0 1 1 1
8 0 1 0 0 0
9 0 1 0 0 1
The sum is the same with BCD adder

8. BCD adder (sum is 10 to 19)
Number C S8 S4 S2 S1
10 1 0 0 0 0
11 1 0 0 0 1
12 1 0 0 1 0
13 1 0 0 1 1
14 1 0 1 0 0
15 1 0 1 0 1
16 1 0 1 1 0
17 1 0 1 1 1
18 1 1 0 0 0
19 1 1 0 0 1

9. BCD adder (sum is 10 to 19)
Number
C S8 S4 S2 S1
10 1 0 0 0 0
11 1 0 0 0 1
12 1 0 0 1 0
13 1 0 0 1 1
14 1 0 1 0 0
15 1 0 1 0 1
16 1 0 1 1 0
17 1 0 1 1 1
18 1 1 0 0 0
19 1 1 0 0 1
K Z8 Z4 Z2 Z1
0 1 0 1 0
0 1 0 1 1
0 1 1 0 0
0 1 1 0 1
0 1 1 1 0
0 1 1 1 1
1 0 0 0 0
1 0 0 0 1
1 0 0 1 0
1 0 0 1 1
Binary sumBCD adder sum

10. BCD adder (sum is 10 to 19)
Number
C S8 S4 S2 S1
10 1 0 0 0 0
11 1 0 0 0 1
12 1 0 0 1 0
13 1 0 0 1 1
14 1 0 1 0 0
15 1 0 1 0 1
16 1 0 1 1 0
17 1 0 1 1 1
18 1 1 0 0 0
19 1 1 0 0 1
K Z8 Z4 Z2 Z1
0 1 0 1 0
0 1 0 1 1
0 1 1 0 0
0 1 1 0 1
0 1 1 1 0
0 1 1 1 1
1 0 0 0 0
1 0 0 0 1
1 0 0 1 0
1 0 0 1 1
Binary sumBCD adder sum

11. BCD adder (sum is 10 to 19)
Number
C S8 S4 S2 S1
10 1 0 0 0 0
11 1 0 0 0 1
12 1 0 0 1 0
13 1 0 0 1 1
14 1 0 1 0 0
15 1 0 1 0 1
16 1 0 1 1 0
17 1 0 1 1 1
18 1 1 0 0 0
19 1 1 0 0 1
K Z8 Z4 Z2 Z1
0 1 0 1 0
0 1 0 1 1
0 1 1 0 0
0 1 1 0 1
0 1 1 1 0
0 1 1 1 1
1 0 0 0 0
1 0 0 0 1
1 0 0 1 0
1 0 0 1 1
Binary sumBCD adder sum
+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
Number
K Z8 Z4 Z2 Z1
10 0 1 0 1 0
11 0 1 0 1 1
12 0 1 1 0 0
13 0 1 1 0 1
14 0 1 1 1 0
15 0 1 1 1 1
16 1 0 0 0 0
17 1 0 0 0 1
18 1 0 0 1 0
19 1 0 0 1 1
Binary sum
C = K +

14. When is the result > 9
Number
K Z8 Z4 Z2 Z1
10 0 1 0 1 0
11 0 1 0 1 1
12 0 1 1 0 0
13 0 1 1 0 1
14 0 1 1 1 0
15 0 1 1 1 1
16 1 0 0 0 0
17 1 0 0 0 1
18 1 0 0 1 0
19 1 0 0 1 1
Binary sum
C = K + Z8*Z4+

15. When is the result > 9
Number
K Z8 Z4 Z2 Z1
10 0 1 0 1 0
11 0 1 0 1 1
12 0 1 1 0 0
13 0 1 1 0 1
14 0 1 1 1 0
15 0 1 1 1 1
16 1 0 0 0 0
17 1 0 0 0 1
18 1 0 0 1 0
19 1 0 0 1 1
Binary sum
C = K + Z8*Z4+
Z8*Z2

16. BCD Adder
4-bit Adder
4-bit Adder
0 0
z8 z4 z2 z1
s8 s4 s2 s1
Cin
K