logic gates.pdf

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