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By: Akash Chauhan
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Boolean Operations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
NOW WE  ARE GOING TO FOCUS ON TOPICS ,[object Object],[object Object],[object Object]
Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],+ 0 1 0 0 1 1 1 1 * 0 1 0 0 0 1 0 1
Axiom ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Axiom #5 :   Identity Element B has identity elements with respect to + and * 0 is the identity element for +, and 1 is the identity  element for * a + 0 = a and a * 1 = a Axiom #6:   Distributive * is distributive over + and + is distributive over * a * (b + c) = (a * b) + (a * c), and  a + (b * c) = (a + b) * (a + c) Axiom #7:   Complement Element For every a in B there is an element a' in B such that a + a' = 1, and a * a' = 0
PRINCIPLE OF DUALITY ,[object Object],[object Object],[object Object],[object Object],[object Object]
Basic Gates and Functions   Logic gates AND , OR , NOT , NAND , NOR , EXOR  and EXNOR
AND  gate
OR  gate
NOT  gate
  The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate .  It can also be done using NOR logic gates in the same way .
NAND  gate
NOR  gate   ,[object Object],[object Object]
EXNOR  gate
The NAND and NOR gates are called  universal functions  since with either one the AND and OR functions and NOT can be generated . ,[object Object],[object Object],[object Object],UNIVERSAL FUNCTIONS
Logic gates representation using the truth  table TRUTH  TABLE
THANK YOU

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Boolean algebra akash

  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9. Axiom #5 : Identity Element B has identity elements with respect to + and * 0 is the identity element for +, and 1 is the identity element for * a + 0 = a and a * 1 = a Axiom #6: Distributive * is distributive over + and + is distributive over * a * (b + c) = (a * b) + (a * c), and a + (b * c) = (a + b) * (a + c) Axiom #7: Complement Element For every a in B there is an element a' in B such that a + a' = 1, and a * a' = 0
  • 10.
  • 11. Basic Gates and Functions Logic gates AND , OR , NOT , NAND , NOR , EXOR and EXNOR
  • 15. The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate . It can also be done using NOR logic gates in the same way .
  • 17.
  • 19.
  • 20. Logic gates representation using the truth table TRUTH TABLE