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CSE-221Digital Logic Design (DLD)

Lecture-2: Logic Operations & Digital

Logic Gates

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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Analog: values vary over a broad range continuously

Digital: only discrete values

+5

V

–5

1 0 1

Time

+5 V

–5

Time

Analog vs. Digital

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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Analog vs. Digital

• Analog devices process signal that can assume any value across a continuous range and produce results that are also in continuous form.

• Digital devices process signals that take on only two discrete values such as 0 and 1 and produces output that can be represented by 0 and 1.

• Examples

Analog Devices: solid-state devices TV (except for digital TV), Audio amplifier etc.

Digital Devices: Computer, CD player, digital TV, digital cellular phone, electronic calculator, and digital camera.

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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Analog systems:

Limited precision, errors accumulate, drift

Interface circuits (i.e., sensors & actuators) often analog

Analog vs. Digital Systems

Digital systems:

More accurate and reliable

Readily available as self-contained, easy to cascade building blocks

Computers use digital circuits internally

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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AND Operator• Let’s look at the relationship between the semantic and

logical operator known as the AND operator

• Consider:If the car is fueled AND the engine works,

then the engine will startAND Operator

Truth Table

0 0 0A B Output

0 1 01 0 01 1 1

• AND means that both conditions must be true in order for the conclusion to be true

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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Digital AND• We can build an electrical device that performs the logical AND

operation on voltage equivalents of logic values• An AND gate has the electrical schematic:

For digital logic:

True = 1 is 5 voltsFalse = 0 is 0 volts

AInputs

B

Output

• Practice with the Excel spreadsheet

• Another basic operator is the OR• Consider:If I have cash OR a credit card,then I can pay the bill• OR works such that the output is true, if

either of the two inputs is true

OR Operator

0 0 0A B Output

0 1 11 0 11 1 1

OR OperatorTruth Table

6/16/2004 P.B-Dr M.A.kashem(CS&E-221,TLDD2)

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XOR (Exclusive OR) Operator• Let’s look at the relationship between the semantic and logical operator

known as the XOR operator• Consider a biological example:

If gender A XOR gender B,then reproduction is possible

• XOR works such that output is activated (equal to one) if both inputs are of a different value

• Try the Excel spreadsheet exercise

• We can build an electrical device that performs the logical XOR operation on voltage equivalents of logic values

• An XOR gate has the electrical schematic:

0 0 0A B Output

0 1 11 0 11 1 0

A

InputsOutput

B

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Multi-Input AND Gate• AND gates can be built with any number of inputs• Consider the symbol for the 4-input AND gate

• F is true only when all the inputs are true (1’s)• Using the Excel workbook “EE-WISE-Digital Lab”, open

the “Digital Locks” worksheet, and test this circuit

ABCD

F

• All digital computers are built using only three gate types: AND, OR, and NOT

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Digital Combination Lock

• Using 3 two-input AND gates, we could build a combination lock that requires a four-digit code, specifically: 1 1 1 1

• The number of inputs could be increased by using more and more AND gates

AND

AND

AND 1

1

1

1

1

1

1

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Digital Combination Lock• We could build a combination lock that only uses the AND gate, but

that would be of little use since everyone would know our combination, namely 1 1 1 1

• To build a more interesting combination lock, we will utilize the NOT (inverter) gate 0 1

• Let’s build a combination lock whose input (key code) combination is 0 1 1 0• Is there any other combination that works?

AND

AND

AND

1

11

1

1

1

1

0

0

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Each of the functions in Table 2-8 is listed with an accompanying name and a comment that explains the function in some way. The 16 functions listed can be subdivided into three categories:

1) Two functions that produce a constant 0 or 12) Four functions with unary operations: complement and transfer.3) Ten functions with binary operators that define eight different operations. AND, OR, NAND, NOR, exclusive-OR, equivalence, inhibition, and implication.

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