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TRANSCRIPT
SEE1223: Digital Electronics 2 – Logic Gates and Boolean Algebra
Zulkifil Md Yusof Dept. of Microelectronics and Computer Engineering
The Faculty of Electrical Engineering Universiti Teknologi Malaysia
Logic Gates and Boolean Algebra
• Logic Gates – Inverter, OR, AND, Buffer, NOR, NAND, XOR, XNOR
• Universal Gates – NAND and NOR
• Boolean Theorem – Commutative, Associative, Distributive – Basic Rules
• DeMorgan’s Theorem • Canonical/Standard Forms of Logic
– Sum of Product (SOP) – Product of Sum (POS) – Minterm and Maxterm
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Inverter/Not Gate
• Logic Symbol and Truth Table
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XZ X
0 1
01
Logic Symbol
Truth Table
Logic Expression
X Z
Inverter/Not Gate
• Timing Diagram
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0
1
0
1
X
Z
X Z t
Time on the horizontal axis
OR Gate
• Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
0
1
1
1
AND Gate
• Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
0
0
0
1
Buffer
XZ X
0 0
11
X XZ
• Logic Symbol and Truth Table
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Buffer
• How to design buffers? Clue: NOT gates
• What is the use of buffers?
– Refresh weak signals
– Purposely put delays
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X XX
XOR
• Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
0
1
1
0
YXZ X
Y
Result is ‘1’ when exactly one input is ‘1’
XOR
• How to make XOR using basic gates (AND, OR, NOT)?
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YXYX
YXZ
X
Z
Y
XNOR • Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
1
0
0
1
YXZ X
Y
Result is ‘1’ when both inputs are the same logic
XNOR
• How to make XNOR using basic gates (AND, OR, NOT)?
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YXYX
YXZ
X
Z
Y
NOR • Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
1
0
0
0
YXZ X
Y
Result is ‘1’ only when both inputs are ‘0’
NOR
• How to make NOR gate using basic gates?
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YXZ
X Z
Y
X + Y
NAND • Logic Symbol and Truth Table
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YXZ X
0 0
10
Y
01
11
1
1
1
0
YXZ X
Y
Result is ‘0’ only when both inputs are ‘1’
NAND
• How to make NAND gate using basic gates?
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YXZ
X Z
Y
X . Y
Example
• Draw the timing diagram for the following
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X
Z
Y
X
Z
Y
X Z
Y
X Z
Y