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# Logic Gates

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### Logic Gates

1. 1. 1MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Introduction to Logic Gates • Logical gates – Inverter – AND – OR – NAND – NOR – Exclusive OR (XOR) – Exclusive NOR (XNOR) • Draw Logic Circuit • Analysis of Logic Circuit
2. 2. 2MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Introduction to Logic Gates • Universal gates NAND and NOR – NAND gate – NOR gate • Execution using NAND gate • Execution using NOR gate • Positive & Negative Logic • SOP Expression Execution • POS Expression Execution • Integrated Logic Circuit Family
3. 3. 3MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates
4. 4. 4MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • Inverter gate • The use of inverter: complement
5. 5. 5MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • AND gate
6. 6. 6MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • OR gate
7. 7. 7MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • NAND gate
8. 8. 8MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • NOR gate
9. 9. 9MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • Exclusive OR (XOR) gate
10. 10. 10MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Gates • Exclusive NOR (XNOR) gate
11. 11. 11MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Draw Logic Gates • When Boolean expression is obtained, we can draw logic gates • Example: – F1 = xyz’ (use three input AND gate)
12. 12. 12MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Draw Logic Gates
13. 13. 13MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Circuit Analysis • When logic circuit is given, we can analyze the circuit to obtain logical expression • Example: – What is the Boolean expression for F4
14. 14. 14MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Logic Circuit Analysis • What is the Boolean expression for F5
15. 15. 15MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Universal Gates: NAND & NOR • Gate AND/OR/NOT is enough to build any Boolean function • Even though, other gates is also used because: – Very useful (no choice) – Save transistor’s number – Self sufficient (can build any gate from it) NAND/NOR: save, self sufficient XOR: useful (e.g. execute parity bit)
16. 16. 16MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR NAND Gate • NAND gate is self sufficient (i.e.can build any gate from it) • Can be used for building AND/OR/NOT gate • Build NOT gate using NAND gate
17. 17. 17MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR NAND Gate • Build AND gate using NAND gates • Build OR gate using NAND gates
18. 18. 18MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR NOR Gate • NOR gate is also self sufficient • Can be used for building AND/OR/NOT gate • Build NOT gate using NOR gate
19. 19. 19MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR NOR Gate • Build AND gate using NOR gates • Build OR gate using NOR gates
20. 20. 20MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Build using NAND gate • It is not impossible to build Boolean expression using NAND gates Steps – Obtain sum-of-product Boolean expression • E.g: F3 = xy’ +x’z – Use DeMorgan theorem to get expression using two level NAND gate • E.g: F3 = xy’ +x’z = (xy’+x’z)” = ((xy’)’.(x’z)’)’
21. 21. 21MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Build using NAND gate
22. 22. 22MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Build using NOR gate • It is not impossible to build Boolean expression using NOR gates Steps – Obtain product-of-sum Boolean expression • E.g: F6 = (x+y’).(x’+z) – Use DeMorgan theorem to get expression using two level NAND gate • E.g: F3 = (x+y’).(x’+z) =((x+y’).(x’+z))’’ = ((x+y’)+(x’+z)’)’
23. 23. 23MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Build using NOR gate
24. 24. 24MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Positive & Negative Logic • In logic gate, most of the time – H (High Voltage, 5V) = logic 1 – L (Low Voltage, 0V) = logic 0 • This is called positive logic • However, if it is inverted, it is negative logic – H (High Voltage, 5V) = logic 0 – L (Low Voltage, 0V) = logic 1 • Depends, some similar gate need different Boolean function
25. 25. 25MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Positive & Negative Logic • Signal which is set to logic 1 is said to be active and true • Signal which is set to logic 0 is said to be not active and false • The name of active high signal is always written in non-compliment form • The name of active low signal is always written in non-compliment form
26. 26. 26MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Positive & Negative Logic
27. 27. 27MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Construction of SOP Expression • Sum-of-product expression can be built using – Two level logic gate AND-OR – Two level logic gate AND-NOT • Logic AND-OR gate
28. 28. 28MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Construction of SOP Expression • NAND-NAND circuit (with transformation circuit) – Add two balls – Change OR with NAND with inverted input and ball on it’s compliment input
29. 29. 29MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Construction of POS Expression • Product-of-sum expression can be built using – Two level logic gate AND-OR – Two level logic gate AND-NOT • Logic AND-OR gate
30. 30. 30MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR Construction of POS Expression • NOR-NOR circuit (with transformation circuit) – Add two balls – Change AND with NOR with inverted input and ball on it’s compliment input       ”: