A topic from "Digital Logic Design"

1. Welcome
To
Our presentation
Presented by
Shahriar Reza Rusel
ID-011132065
Samrin Ahmed Riya
ID-011142021
Rayhan Ahamed
ID-011142141
Rakib Hasan Suvo
ID-011142016
Dept-CSE

3.  A digital circuit.
 Sums the amplitudes of two input signals.
Representation of Adders:
 Binary-Coded-Decimal or Excess-3
Processor Use:
 Calculate addresses, table indices and
similar operations.
What is ADDER ?

4. Types of Adder

5. Half ADDER:
 A computational device.
 Adds two binary digits .
 No carry as input.
 Produces a sum bit and
a carry bit.
Types of Adder
INPUTS OUTPUTS
A B SUM CARRY
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Half Adder Circuit

6. Full Adder:
 A computational device.
 Adds three one-bit binary numbers.
 Produces a sum of two inputs and a carry value.
Types of ADDER (Cont...)
INPUTS OUTPUTS
A B CIN COUT S
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
Full Adder Circuit

7.  Also Known as 8421 digit.
 A 4-bit binary adder.
 Adds two 4-bit digits having a BCD.
 Resulting format 4-bit output digit.
 Sum exceeding decimal value of 9, a carry’s
generated.
What is BCD ADDER?

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

9.  A 4-bit BCD code’s used to represent 0 to 9 digits.
 Adding BCD numbers using BCD addition.
 Adding 6 with the sum while exceeding 9 and generating a carry.
 By adding 6 to the sum, make an invalid digit valid.
.

10. Maximum sum is 9+9 + 1 = 19
Max digit Carry from previous digits

11. Number C S3 S2 S1 S0
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

12. Number C S3 S2 S1 S0
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

13. BCD adder sum Binary sum
Number
C S3 S2 S1 S0
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 s3 s2 s1 s0
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
+6

14.  If sum is up to 9
 Use the regular Adder.
 If the sum > 9
 Use the regular adder and add 6 to the result

15.  Sum of two BCD digits exceeding 9.
 A carry is generated.
 Converting the invalid digit into valid digit.
 Carry generated by adding 6 to the invalid BCD digit’s
passed on to the next BCD digit.

16. Binary sum
Number
K S3 S2 S1 S0
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
C = K +

17. Binary sum
Number
K S3 S2 S1 S0
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
C = K + S3*S2+

18. Binary sum
Number
K S3 S2 S1 S0
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
C = K + S3*S2+
S3*S1

20. 4-bit Adder
4-bit Adder
0 0
s3 s2 s1 s0
S3 S2 S1 S0
Cin
K
0 1 1 00 1 1 1
1 1 0 1
0
1 1 0 1
1 1
1
0 0 1 1
1
0
1

21.  Applications in Decimal Number Display.
 Systematic running of counters.
 Organized digital clocks.

22.  http://www.electronics-
tutorials.ws/combination/comb_7.html
 http://www.encyclopedia.com/doc/1O11-
binarycodeddecimal.html
 http://www2.elo.utfsm.cl/~lsb/elo211/aplicaci
ones/katz/chapter5/chapter05.doc4.html
 https://tams-www.informatik.uni-
hamburg.de/applets/hades/webdemos/20-
arithmetic/10-adders/bcd-adder.html