SEE1223: Digital Electronicsfke.utm.my/.../3-Logic_Gates_and_Boolean_Algebra_1.pdf · SEE1223: Digital Electronics 2 – Logic Gates and Boolean Algebra Zulkifil Md Yusof Dept. of

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