1.
Basic Adders +

2.
What is Adder?

3.
<ul><li>Adder : </li></ul><ul><li> In electronics an adder is digital circuit that perform addition of numbers. </li></ul><ul><li>In modern computer adder reside in the arithmetic logic unit (ALU). </li></ul>

4.
<ul><li>Adders : </li></ul><ul><li>Adders are important not only in the computer but also in many types of digital systems in which the numeric data are processed. </li></ul><ul><li>Types of adder: </li></ul><ul><li>Half adder </li></ul><ul><li>Full adder </li></ul>

5.
<ul><li>Half adder : </li></ul><ul><li>The half adder accepts two binary digits on its inputs and produce two binary digits outputs, a sum bit and a carry bit. </li></ul>

6.
<ul><li>Full adder : </li></ul><ul><li>The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry. </li></ul>

7.
Half adder to Full adder

8.
Truth Table of Adder

9.
Truth Table of Adder A B C in C out ∑ 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

10.
Truth Table of Adder A B C in C out ∑ 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

11.
Truth Table of Adder A B C in C out ∑ 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

12.
Truth Table of Adder A B C in C out ∑ 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

13.
Truth Table of Adder A B C in C out ∑ 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

14.
Truth Table of Adder A B C in C out ∑ 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

15.
Truth Table of Adder A B C in C out ∑ 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

16.
Truth Table of Adder A B C in C out ∑ 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

17.
Circuit of Adder A B

18.
Circuit of Adder A B X

19.
Circuit of Adder A B C in ∑

20.
Circuit of Adder A B C in ∑ Y

21.
Circuit of Adder A B C in ∑ = A.B Y

22.
Circuit of Adder A B C in ∑ C out C out = (A B). C in + A.B

23.
Verification of Truth Table A B C in ∑ C out A B C in 0 0 0 C out ∑ 0 0

24.
Verification of Truth Table A B C in ∑ C out A B C in 0 0 1 C out ∑ 0 1

25.
Verification of Truth Table A B C in ∑ C out A B C in 0 1 0 C out ∑ 0 1

26.
Verification of Truth Table A B C in ∑ C out A B C in 0 1 1 C out ∑ 1 0

27.
Verification of Truth Table A B C in ∑ C out A B C in 1 0 0 C out ∑ 0 1

28.
Verification of Truth Table A B C in ∑ C out A B C in 1 0 1 C out ∑ 1 0

29.
Verification of Truth Table A B C in ∑ C out A B C in 1 1 0 C out ∑ 1 0

30.
Verification of Truth Table A B C in ∑ C out A B C in 1 1 1 C out ∑ 1 1

31.
Applications of Adder THE BCD ADDER

32.
BCD Adder <ul><li>Binary Coded Decimal Adder </li></ul><ul><li>Just adds decimal digits </li></ul>

33.
Binary Coded Decimal <ul><li>It is possible to represent decimal numbers simply by encoding each decimal digit in binary form called binary coded decimal </li></ul><ul><li>Because there are 10 digits to represent, it is necessary to use four bits per digit. </li></ul><ul><li>From 0=0000 to 9=1001 by using 8421 code. </li></ul><ul><li>For example: </li></ul><ul><li>Convert 98 into BCD. </li></ul><ul><li>9 8 </li></ul><ul><li>1001 1000 </li></ul><ul><li>BCD representation was used in some early computers and many handheld calculators. </li></ul>

34.
Decimal Digits Decimal Number BCD Equivalent 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001

35.
The BCD Adder <ul><li>BCD is a numerical code and can be used in arithmetic operations. </li></ul><ul><li>Addition is the most important operation in BCD. </li></ul><ul><li>Following are the steps to perform addition: </li></ul><ul><ul><li>Step1 Add the two BCD numbers, using the rules for binary </li></ul></ul><ul><li> addition. </li></ul><ul><ul><li>Step2 </li></ul></ul><ul><ul><li>If a 4-bit sum is equal to or less than 9, it is a valid BCD </li></ul></ul><ul><li>number. </li></ul>

36.
THE BCD ADDER <ul><li>Add the following BCD number </li></ul><ul><li>0011 + 0100 </li></ul><ul><li>0011 3 </li></ul><ul><li>+ 0100 + 4 </li></ul><ul><li>0111 7 </li></ul>

37.
4-Bit Adder <ul><li>A single full –adder is capable of adding two 1-bit numbers and input carry. </li></ul><ul><li>What happens if we want to add binary numbers with more than 1-bit? </li></ul><ul><li>The concept of additional full-adders must be used i.e. to add 2-bit numbers two adders must be needed and to add 4-bit numbers four adders must be needed. </li></ul>

38.
4-Bit Adder

39.
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