1. Introduction to Logic Gates
Logical gates
Inverter
AND OR
NAND
NOR
Exclusive OR (XOR)
Exclusive NOR (XNOR)
Draw Logic Circuit
Analysis of Logic Circuit
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2. 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
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3. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
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4. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
Inverter gate
The use of inverter: complement
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5. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
AND gate
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6. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
OR gate
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7. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
NAND gate
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8. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
NOR gate
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9. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
Exclusive OR (XOR) gate
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10. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Logic Gates
Exclusive NOR (XNOR) gate
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11. MOHD. 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)
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12. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Draw Logic Gates
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13. 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
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14. Logic Circuit Analysis
What is the Boolean expression for F5
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15. 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)
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16. MOHD. 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
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17. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
NAND Gate
Build AND gate using NAND gates
Build OR gate using NAND gates
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18. MOHD. 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
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19. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
NOR Gate
Build AND gate using NOR gates
Build OR gate using NOR gates
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20. MOHD. 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
= (xy’+x’z)”
= ((xy’)’.(x’z)’)’
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21. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Build using NAND gate
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22. MOHD. 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)’)’
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23. MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Build using NOR gate
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24. 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
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25. 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
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26. Positive & Negative Logic
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27. 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
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28. 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
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29. 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
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30. 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 ”:
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