Basic Adders +
What is Adder?
<ul><li>Adder : </li></ul><ul><li> In electronics an adder is digital circuit that perform addition of numbers. </li></ul>...
<ul><li>Adders : </li></ul><ul><li>Adders are important not only in the computer but also in many types of digital systems...
<ul><li>Half adder : </li></ul><ul><li>The half adder accepts two binary digits on its inputs and produce two binary digit...
<ul><li>Full  adder : </li></ul><ul><li>The full adder accepts two inputs bits and an input carry and generates a sum outp...
Half adder to Full adder
Truth Table of Adder
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
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
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
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
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
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
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
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
Circuit of Adder A B
Circuit of Adder A B X
Circuit of Adder A B C in ∑
Circuit of Adder A B C in ∑ Y
Circuit of Adder A B C in ∑ = A.B Y
Circuit of Adder A B C in ∑ C out C out = (A  B). C in  + A.B
Verification of Truth Table A B C in ∑ C out A B C in 0 0 0 C out ∑ 0 0
Verification of Truth Table A B C in ∑ C out A B C in 0 0 1 C out ∑ 0 1
Verification of Truth Table A B C in ∑ C out A B C in 0 1 0 C out ∑ 0 1
Verification of Truth Table A B C in ∑ C out A B C in 0 1 1 C out ∑ 1 0
Verification of Truth Table A B C in ∑ C out A B C in 1 0 0 C out ∑ 0 1
Verification of Truth Table A B C in ∑ C out A B C in 1 0 1 C out ∑ 1 0
Verification of Truth Table A B C in ∑ C out A B C in 1 1 0 C out ∑ 1 0
Verification of Truth Table A B C in ∑ C out A B C in 1 1 1 C out ∑ 1 1
Applications of Adder THE BCD ADDER
BCD Adder <ul><li>Binary Coded Decimal Adder </li></ul><ul><li>Just adds decimal digits </li></ul>
Binary Coded Decimal  <ul><li>It is possible to represent decimal numbers simply by encoding each decimal digit  in binary...
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
The BCD Adder <ul><li>BCD is a numerical code and can be used in arithmetic operations. </li></ul><ul><li>Addition is the ...
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...
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 h...
4-Bit Adder
Thanks!
Upcoming SlideShare
Loading in...5
×

Adders

25,226
-1

Published on

2 Comments
10 Likes
Statistics
Notes
No Downloads
Views
Total Views
25,226
On Slideshare
0
From Embeds
0
Number of Embeds
30
Actions
Shares
0
Downloads
567
Comments
2
Likes
10
Embeds 0
No embeds

No notes for slide

Adders

  1. 1. Basic Adders +
  2. 2. What is Adder?
  3. 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. 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. 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. 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. 7. Half adder to Full adder
  8. 8. Truth Table of Adder
  9. 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. 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. 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. 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. 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. 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. 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. 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. 17. Circuit of Adder A B
  18. 18. Circuit of Adder A B X
  19. 19. Circuit of Adder A B C in ∑
  20. 20. Circuit of Adder A B C in ∑ Y
  21. 21. Circuit of Adder A B C in ∑ = A.B Y
  22. 22. Circuit of Adder A B C in ∑ C out C out = (A B). C in + A.B
  23. 23. Verification of Truth Table A B C in ∑ C out A B C in 0 0 0 C out ∑ 0 0
  24. 24. Verification of Truth Table A B C in ∑ C out A B C in 0 0 1 C out ∑ 0 1
  25. 25. Verification of Truth Table A B C in ∑ C out A B C in 0 1 0 C out ∑ 0 1
  26. 26. Verification of Truth Table A B C in ∑ C out A B C in 0 1 1 C out ∑ 1 0
  27. 27. Verification of Truth Table A B C in ∑ C out A B C in 1 0 0 C out ∑ 0 1
  28. 28. Verification of Truth Table A B C in ∑ C out A B C in 1 0 1 C out ∑ 1 0
  29. 29. Verification of Truth Table A B C in ∑ C out A B C in 1 1 0 C out ∑ 1 0
  30. 30. Verification of Truth Table A B C in ∑ C out A B C in 1 1 1 C out ∑ 1 1
  31. 31. Applications of Adder THE BCD ADDER
  32. 32. BCD Adder <ul><li>Binary Coded Decimal Adder </li></ul><ul><li>Just adds decimal digits </li></ul>
  33. 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. 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. 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. 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. 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. 38. 4-Bit Adder
  39. 39. Thanks!
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×