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  • 1. Basic Adders +
  • 2. What is Adder?
  • 3.
    • Adder :
    • In electronics an adder is digital circuit that perform addition of numbers.
    • In modern computer adder reside in the arithmetic logic unit (ALU).
  • 4.
    • Adders :
    • Adders are important not only in the computer but also in many types of digital systems in which the numeric data are processed.
    • Types of adder:
    • Half adder
    • Full adder
  • 5.
    • Half adder :
    • The half adder accepts two binary digits on its inputs and produce two binary digits outputs, a sum bit and a carry bit.
  • 6.
    • Full adder :
    • The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry.
  • 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
    • Binary Coded Decimal Adder
    • Just adds decimal digits
  • 33. Binary Coded Decimal
    • It is possible to represent decimal numbers simply by encoding each decimal digit in binary form called binary coded decimal
    • Because there are 10 digits to represent, it is necessary to use four bits per digit.
    • From 0=0000 to 9=1001 by using 8421 code.
    • For example:
    • Convert 98 into BCD.
    • 9 8
    • 1001 1000
    • BCD representation was used in some early computers and many handheld calculators.
  • 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
    • BCD is a numerical code and can be used in arithmetic operations.
    • Addition is the most important operation in BCD.
    • Following are the steps to perform addition:
      • Step1 Add the two BCD numbers, using the rules for binary
    • addition.
      • Step2
      • If a 4-bit sum is equal to or less than 9, it is a valid BCD
    • number.
  • 36. THE BCD ADDER
    • Add the following BCD number
    • 0011 + 0100
    • 0011 3
    • + 0100 + 4
    • 0111 7
  • 37. 4-Bit Adder
    • A single full –adder is capable of adding two 1-bit numbers and input carry.
    • What happens if we want to add binary numbers with more than 1-bit?
    • 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.
  • 38. 4-Bit Adder
  • 39. Thanks!

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