Ece 331 digital system design
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ECE 331 – Digital System Design. Logic Circuit Design (Lecture #7). Design Concepts. Combinational Logic Circuits Outputs are functions of (present) inputs No memory Can be described using Boolean expressions Hierarchical design Used to solve large design problems

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ECE 331 – Digital System Design

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Ece 331 digital system design

ECE 331 – Digital System Design

Logic Circuit Design

(Lecture #7)


Design concepts

ECE 331 - Digital System Design

Design Concepts

Combinational Logic Circuits

Outputs are functions of (present) inputs

No memory

Can be described using Boolean expressions

Hierarchical design

Used to solve large design problems

Break problem into smaller (sub-)problems

Solve each sub-problem (i.e. realize design)

Combine individual solutions


Design concepts1

ECE 331 - Digital System Design

Design Concepts

Specification

Describes the problem to be solved.

Describes what needs to be done,

not how to do it.

Implementation

Describes how the problem is solved.


Design concepts2

ECE 331 - Digital System Design

Design Concepts

Issues

Most solutions are not unique.

More than one solution may meet the specifications.

Cannot always satisfy all of the requirements.

Must identify (and study) design tradeoffs.

Cost

Speed

Power consumption

etc.


Design process

ECE 331 - Digital System Design

Design Process

Identify requirements (i.e. circuit specifications)

Determine the inputs and outputs.

Derive the Truth Table

Determine simplified Boolean expression(s)

Implement solution

Verify solution


Ece 331 digital system design

ECE 331 - Digital System Design

Exercise:

Design a combinational logic circuit to meet the following specifications:

1. 3-bit input (A = a2a1a0)

2. 1-bit output (z)

3. Output is high (logic 1) when 2 < A <= 5.


Ece 331 digital system design

ECE 331 - Digital System Design

Example:

Design a 7-Segment Decoder


7 segment decoder

ECE 331 - Digital System Design

1. Circuit Specification

The 7-Segment Decoder must decode Binary Coded Decimal (BCD) digits so that they can be displayed on a 7-Segment Display.

7-Segment Decoder


2 determine inputs and outputs input binary coded decimal digits

ECE 331 - Digital System Design

2. Determine Inputs and Outputs

Input: Binary Coded Decimal digits

7-Segment Decoder


Binary coded decimal

ECE 331 - Digital System Design

Binary Coded Decimal

Assign a 4-bit code to each decimal digit.

A 4-bit code can represent 16 values.

There are only 10 digits in the decimal number system.

Unassigned codes are not used.

How do we interpret these unused codes?

Hint: think about K-maps.


Bcd digits

ECE 331 - Digital System Design

BCD Digits


2 determine inputs and outputs output 7 segment display

ECE 331 - Digital System Design

2. Determine Inputs and Outputs

Output: 7-Segment Display

7-Segment Decoder


7 segment display

ECE 331 - Digital System Design

7-Segment Display


7 segment display1

ECE 331 - Digital System Design

7-Segment Display


3 derive truth table

ECE 331 - Digital System Design

3. Derive Truth Table

7-Segment Decoder


7 segment decoder1

ECE 331 - Digital System Design

7-Segment Decoder


4 determine simplified boolean expression s

ECE 331 - Digital System Design

4. Determine simplified Boolean expression(s)

7-Segment Decoder


7 segment decoder2

ECE 331 - Digital System Design

7-Segment Decoder

A

y

z

w

x

00

01

11

10

00

1

0

1

1

01

0

1

1

1

11

d

d

d

d

10

1

1

d

d

A = ?


7 segment decoder3

ECE 331 - Digital System Design

7-Segment Decoder

B

y

z

w

x

00

01

11

10

00

1

1

1

1

01

1

0

1

0

11

d

d

d

d

10

1

1

d

d

B = ?


Ece 331 digital system design

ECE 331 - Digital System Design

Student Exercise:

Determine the minimized Boolean expression for each of the segments of the 7-Segment Display.

7-Segment Decoder


5 implement solution 6 verify solution

ECE 331 - Digital System Design

5. Implement Solution

6. Verify Solution

7-Segment Decoder


Ece 331 digital system design

ECE 331 - Digital System Design

Multiple-Output Logic Circuits


Ece 331 digital system design

ECE 331 - Digital System Design

Example:

Given two functions, F1 and F2, of the same input variables x1.. x4, design the minimum-cost implementation.

Multiple-Output Logic Circuits


Multiple output logic circuits

ECE 331 - Digital System Design

Multiple-Output Logic Circuits

x

x

x

x

1

2

1

2

x

x

x

x

3

4

3

4

00

01

11

10

00

01

11

10

00

1

1

00

1

1

01

1

1

1

01

1

1

11

1

1

11

1

1

1

10

1

1

10

1

1

(a) Function

f

(b) Function

f

1

2

F1 = X1'.X3 + X1.X3' + X2.X3'.X4

F1 = X1'.X3 + X1.X3' + X2.X3.X4


Multiple output logic circuits1

ECE 331 - Digital System Design

Multiple-Output Logic Circuits

x

2

x

3

x

4

f

1

x

1

x

3

x

1

x

3

f

2

x

2

x

3

x

4

f

f

(c) Combined circuit for

and

1

2


Multiple output logic circuits2

ECE 331 - Digital System Design

Example:

Given two functions, F3 and F4, of the same input variables x1.. x4, design the minimum-cost implementation for the combined circuit.

Multiple-Output Logic Circuits

Note: the minimum-cost implementation for the combined circuit may not

be the same as the minimum-cost implementations for the individual circuits.


Multiple output logic circuits3

ECE 331 - Digital System Design

Multiple-Output Logic Circuits

x

x

x

x

1

2

1

2

x

x

x

x

3

4

3

4

00

01

11

10

00

01

11

10

00

00

01

1

1

1

01

1

1

1

11

1

1

1

11

1

1

1

10

1

10

1

(a) Optimal realization of

(b) Optimal realization of

f

f

3

4

F3 = X1'.X4 + X2.X4 + X1'.X2.X3

F3 = X2'.X4 + X1.X4 + X1'.X2.X3.X4'

Logic Gates required:

2 2-input AND

1 3-input AND

1 3-input OR

Logic Gates required:

2 2-input AND

1 4-input AND

1 3-input OR

Total Gates and Inputs required:

8 Logic Gates

21 Inputs


Multiple output logic circuits4

ECE 331 - Digital System Design

Multiple-Output Logic Circuits

x

x

x

x

1

2

1

2

x

x

x

x

3

4

3

4

00

01

11

10

00

01

11

10

00

00

01

1

1

1

01

1

1

1

11

1

1

1

11

1

1

1

10

1

10

1

(c) Optimal realization of

f

and

f

together

3

4

F3 = X1'.X4 + X1.X2.X4 + X1'.X2.X3.X4'

F3 = X2'.X4 + X1.X2.X4 + X1'.X2.X3.X4'

Logic Gates required:

1 2-input AND

1 3-input AND

1 4-input AND

1 3-input OR

Logic Gates required:

1 2-input AND

1 3-input AND

1 4-input AND

1 3-input OR

shared logic gates

Total Gates and Inputs required:

6 Logic Gates

17 Inputs


Multiple output logic circuit

ECE 331 - Digital System Design

Multiple-Output Logic Circuit

x

1

x

4

x

f

1

3

x

2

x

4

x

1

x

2

x

3

x

f

4

4

x

2

x

4

f

f

(d) Combined circuit for

and

3

4


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