Logic Gates PDF
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Uploaded by SeasonedPolynomial
Ramdeobaba University, Nagpur
Prof. P. N. Thakre
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Summary
This document provides a comprehensive overview of logic gates, including different types such as AND, OR, NOT, NAND, NOR, XOR, and XNOR gates. It also details various logic laws and theorems. The content appears to be educational material for students in computer science or related engineering fields.
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27-08-2024 Prof. P. N. Thakre EC Dept. RBU, Nagpur A logic gate is a device that acts as a building block for digital c...
27-08-2024 Prof. P. N. Thakre EC Dept. RBU, Nagpur A logic gate is a device that acts as a building block for digital circuits. Basic Logic Gates AND Gate OR Gate NOT Gate Universal Logic Gates NOR Gate NAND Gate Derived Logic Gates XOR Gate XNOR Gate 1 27-08-2024 BASIC LOGIC GATES AND OR NOT Y=A.B Z=A+B Z=𝐴̅ UNIVERSAL LOGIC GATES NAND NOR C C C 2 27-08-2024 DERIVED LOGIC GATES XOR XNOR C 1. x.0 = 0.x = 0 (Annulment Law) 2. x+1=1+x=1 (Annulment Law) 3. x+0=0+x=x (Identity Law) 4. x.1 = 1.x = x (Identity Law) 5. x+y=y+x (commutative Law) 6. x.y = y.x (commutative Law) 7. x + (y + z) = (x + y) + z = x + y + z (OR Associate Law) 8. x. (y. z) = (x. y). z = x. y. z (AND Associate Law) 9. x. (y + z) = (x. y) + (x. z) (OR distributive Law) 10. x + (y. z) = (x + y). (x + z) (AND distributive Law) 11. x+x=x (Idempotent Law) 12. x.x = x (Idempotent Law) 13. x + x’ = 1 (Complement Law) 14. x. x’ = 0 (Complement Law) 15. (x’)’ = x (Double Negation Law) 16. (x + y)’ = x’. y’ (de Morgan´s Theorem) 17. (x. y)’ = x’ + y’ (de Morgan´s Theorem) 18. x + (x. y) = x (OR Absorption Law) 19. x. (x + y) =x (AND Absorption Law) 3 27-08-2024 4 27-08-2024 5 27-08-2024 6 27-08-2024 7 27-08-2024 Simplify XOR gate using Nor gate and invert the result to obtain XNOR gate 8
