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Digital Circuits II

Review of Digital Circuits and Systems

References: Text Book: Digital Logics: A Practical Approach with VHDL,

9th Edition, by William Kleitz, published by Pearson.

Ch 1. Number Systems and Codes

Ch 2. Digital Electronic Signals and Switched

Ch 3. Basic Logic Gates

Ch 5. Boolean Algebra and Reduction Techniques

Ch 6. Ex-OR and Ex-NOR Gates

Ch 8. Code Converters, Multiplexers, and Demultiplexer

Paul I-Hai Lin, Professor

Dept. of Computer, Electrical and Information Technology

Indiana University-Purdue University Fort Wayne

Prof. Paul Lin

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Outline

1. Digital Logic Families, voltage Levels: TTL, CMOS

(Complementary Metal Oxide Semiconductor), Emitter-

coupled logic (ECL)

2. Number systems

3. Basic logic gate (NOT, AND, OR, NAND, NOR, EX-OR,

EX-NOR), truth tables

4. Combinational logic, Boolean algebra

5. Code converters, multiplexers and de-multiplexers

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Characteristics of TTL, CMOS, and ECL

Logic Circuits Dissipated power

Fan-in (max number of inputs to a gate)

Fan-out (max number of standard loads)

Voltage transfer curve, Threshold voltage

Propagation delay time

Rise and fall times

Noise immunity

Voltage levels (logic 0/Logic 1)

Input impedance

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Examples of Binary Logic Levels

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Technology L voltage H voltage Notes

CMOS 0 V to 1/3 VDD 2/3 VDD to VDD

VDD =

Supply voltage

TTL 0 V to 0.8 V 2 V to VCC

VCC = 5 V

±10%

ECL VEE to −1.4 V −1.2 V to 0 V

VEE is

about −5.2 V;

VCC=Ground

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Number Systems

Binary: 0, 1

Octal: 0, 1, 2, 3, 4, 5, 6, 7

Decimal: 0, 1, 2, …9

Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

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Number Systems

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Decimal Binary Octal Hexa-

decimal

Decimal Binary Octal Hexa-

decimal

0 0000 0 (000) 0 8 1000 10

(001 000)

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1 0001 1 (001) 1 9 1001 11

(001 001)

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2 0010 2 (010) 2 10 1010 12

(001 010)

A

3 0011 3 (011) 3 11 1011 13

(001 011)

B

4 0100 4 (100) 4 12 1100 14

(001 100)

C

5 0101 5 (101) 5 13 1101 15

(001 101)

D

6 0110 6 (110) 6 14 1110 16

(001 110)

E

7 0111 7 (111) 7 15 1111 17

(001 111)

F

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Logic Gates and Shift Registers

NOT, AND, OR, NOR, NAND, EX-OR, EX-NOR

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AND OR

EX-OR

Shift

Left

1 0 1 0 1 1 1 1 1 1 1 1 0 1 Shift

Right0

1 0 1 0 1 1 1 1 1 1 1 1 1 0 0

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Example: The truth table for the Two-Input

AND, OR, and EXOR Gates Two inputs: A, B; One output: X

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AND

OR

EX-OR

A B X=A∙B Y=A+B Z= A B

A&B A|B A ^ B

0 0 0 0 0

0 1 0 1 1

1 0 0 1 1

1 1 1 1 0

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Example: Software implementation of two

input AND, OR, and EXOR gates using 8-bit

data word

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bit0

bit1

bit2

bit3

bit4

bit5

bit6

bit7

b0

c0

b1

c1

b2

c2

b3

c3

b4

c4

b5

c5

b6

c6

b7

c7

bit0

bit1

bit2

bit3

bit4

bit5

bit6

bit7

b0

c0

b1

c1

b2

c2

b3

c3

b4

c4

b5

c5

b6

c6

b7

c7

bit0

bit1

bit2

bit3

bit4

bit5

bit6

bit7

b0

c0

b1

c1

b2

c2

b3

c3

b4

c4

b5

c5

b6

c6

b7

c7

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Examples of TTL IC Chips

7400 (Quad 2-input NAND Gates)

7402 (Quad 2-input NOR Gates)

7404 (Hex Inverters)

7408 (Quad 2-input AND Gates)

7432 (Quad 2-input OR Gates)

7486 ((Quad 2-input EXOR Gates

74126 ((Quad Tri-state buffers)

74266 (Quad ExNOR Gates with open collector outputs)

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Combinational Logics [15][16]

A type of digital logic which is implemented by Boolean circuits,

where the output is a pure function of the present input only.

Examples

• Arithmetic & Logic Functions: adders, substractors, comparators,

PLDs (programmable logic devices)

• Code coders: binary, BCD (Binary Coded Decimal), 7-segments,

gray code to binary

• Data transmission: multiplexers, demultiplexers, encoders and

decoders

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CombinationalLogic Circuit

MultipleInputs

A

B

C

X

Y

Output

Output = f(Inputs)

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Three Main Methods of Specifying the

Function of a Combinational Logic

(a) Boolean algebra, (b) Truth table, (c ) Logic diagram

Boolean Algebra [17][18][19]

• Boolean algebra was introduced by George Boole in his book

entitled “The Mathematic Analysis of Logic (1847).

• The subarea of algebra in which the values of the variables are

the truth values and false, usually denoted 1 and 0 respectively.

• Main operations of Boolean algebra are the conjunction (AND),

disjunction (OR), and the negation (NOT).

• A formalism for describing logic relations in the same way that

ordinary algebra describe numeric relations.

• Boolean algebra has been fundamental in the development of

digital electronics, and is provided for in all modern programming

languages.

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Example: Logic Diagram, write a set of Boolean

equations for the following multiple inputs, multiple

outputs logic circuit.

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D

E

A B C

F

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Example: Implementation of a four variable Boolean function

which is expressed in the SOP (Sum of Product) form:

F_out = B’D’ + B’C’ + A’D

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F_out =

B’D’ + B’C’ + A’D

AND-1

OR

AND-3

AND-2

A

A’

B C D

Four Input Bits

B’ C’ D’

B’D’

B’C’

A’D

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Example: Implementation of a four variable Boolean function

which is expressed in the SOP (Sum of Product) form:

F_out = B’D’ + B’C’ + A’D

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The Truth Table

A B C D | F

---------------|-----

0 0 0 0 | 1

0 0 0 1 | 1

0 0 1 0 | 1

0 0 1 1 | 1

0 1 0 0 | 0

0 1 0 1 | 1

1 0 0 0 | 1

0 1 1 0 | 0

0 1 1 1 | 0

The Truth Table

A B C D | F

---------------|-----

1 0 0 1 | 1

1 0 1 0 | 1

1 0 1 1 | 1

1 1 0 0 | 0

1 1 0 1 | 0

1 1 1 0 | 0

1 1 1 1 | 0

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Code Converters

BCD (Binary Coded Decimal)

• 7442 BCD to Decimal Decorder

• 7445 BCD to Decimal Decoder/Driver (4 inputs, 10 outputs)

• 74145 BCD-toDecimal

• CD 4028 BCD to Decimal decoder (DIP-16)

• 74147 (1o-line decimal to 4-line BCD priority encoders)

Octal to Decimal Encoder

• 8-line to 3-line octal priority encoders, 74148

Gray Code

7 segment display code

• 7447 BCD to Seven Segment display (Open collector)

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Decimal Digit – BCD Code

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Decimal

Digit

0 1 2 3 4 5 6 7 8 9

BCD

Code

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001

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Binary to Gray Code

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Decimal Binary Gray Decimal Binary Gray

0 0000 0000 8 1000 1100

1 0001 0001 9 1001 1101

2 0100 0011 10 1010 1111

3 0011 0010 11 1011 1110

4 0100 0110 12 1100 1010

5 0101 0111 13 1101 1011

6 0110 0101 14 1110 1001

7 0111 0100 15 1111 1000

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Multiplexers (Data Selector) [22]

2-to-4 Selector/Multiplexer, two selection lines (74LS139, Dual 2-to-

4 line decoders/multiplexer)

3-to-8 Selector/Multiplexer, 3 address section lines (74LS138)

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IC Name Function/Output

74157 Quad 2:1 Mux, Output is the same as the

input

74158 Quad 2:1 Mux, Output is inverted

74153 Dual 4:1 Mux, Output is the same as the

input

74352 Dual 4:1 Mux, Output is inverted

74151 8:1 Mux

74150 16:1 Mux, Output is inverted

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De-Multiplexers/Decocoders

Dual 2-to-4 Line decoder, 74155

4-Line to 16-Line Decoders/Demultiplexers, 74154

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IC Name Function/Output

74139 Dual 1:4 Demux, Output is inverted, 2-to-4 line

74156 Dual 1:4 Demux, Output is open collector

74138 1:8 Demux, Output is inverted

74238 1:8 Demux

74154 1:16 Demux, Inverted output

74159/CD

4514/15

1:16 Demux, Output is open collector

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Interfaces to the Digital Circuits

Example: Interface to SPST switch and push button switch using debouncing circuit.

Prof. Paul Lin

SPST

switch

+5V

Vout7414

Schmitt

Trigger

R = 33k

Input 0

+5V

C = 5µF

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Interfaces to the Digital Circuits

Example: Interface to Micro switch.

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NC NOC

NC – Normally OpenNO – Normally CloseC - Common

+5V

10K

+5V

7404 Hex Inverter

NC NO

C

Digital Multimeter

+

-

Vi= 1.6v

Vo = 0v

Switch OFF

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Digital Multimeter

+

-

+5V

10K

+5V

7404 Hex Inverter

NC NO

C

Digital Multimeter

+

-

Vi= 5v

Vo = 0v

Switch ON

1 2 7

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Digital Multimeter

+

-

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Interfaces to the Digital Circuits

Example: Interface to On/Off switch.

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+5V

10K

+5V

7404 Hex Inverter

NC

NO

C

Digital Multimeter

+

-

Vi=0v

Vo =3.8v

Switch OFF

1 2 7

14

+5V

+5V

10K

7404 Hex Inverter

NC

NO

C

Digital Multimeter

+

-

Vi=5v

Vo = 0v

Switch ON

1 2 7

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Interfaces to the Digital Circuits

Example: Interface to Microcontroller using 7404 inverter.

Example: Interface to Control system.

Prof. Paul Lin

Switch

R = 33k

Input 0

+5V

C = 5µF

Microcontroller

Switch

R = 33k

Input 0

+5V

C = 5µF

Computer

Control System

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References1. Logic Gate, http://en.wikipedia.org/wiki/Logic_gate

2. Basic Logic Gates and Functions, http://www.ee.surrey.ac.uk/Projects/CAL/digital-

logic/gatesfunc/index.html

3. An Introduction to Digital Logic – Signals and Gates,

http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Logic/Logic1.html

4. Digital Logic, Skarkfun, https://learn.sparkfun.com/tutorials/digital-logic

5. Chapter 3 Logic Gates, Lessons in Electric Circuits – Vol. IV,

http://www.ibiblio.org/kuphaldt/electricCircuits/Digital/DIGI_3.html

6. Logic Gates Test, Circuit Lab, https://www.circuitlab.com/circuit/gwjr96/logic-gates-

test/

7. Logic Level, http://en.wikipedia.org/wiki/Logic_level

8. What are the Basic Difference Between CMOS and TTL Signals,

http://digital.ni.com/public.nsf/allkb/2D038D3AE1C35011862565A8005C5C63

9. Experiment 3: TTL and CMOS Characteristics,

http://www.lns.cornell.edu/~ib38/teaching/p360/lectures/wk09/l26/EE2301Exp3F10.pd

f

10. 5V TTL and CMOS Input and Output Voltage Levels, Intro to Mechtronics,

http://engr.sjsu.edu/~bjfurman/courses/ME106/ME106pdf/TTL-CMOS_logic-levels.pdf

11. 3.3 C CMOS Logic Levels, https://learn.sparkfun.com/tutorials/logic-levels/33-v-cmos-

logic-levels

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References12.Voltage Level Translation between 3.3V, 2.5V, 1.8V and 1.5V Logic

Standards, http://www.ti.com/lit/an/scea030a/scea030a.pdf

13.CD4504B - Hex voltage-level shifter for TTL-to-CMOS or CMOS-to-CMOS, http://www.ti.com/product/cd4504b

14.MC14504B – Hex Level Shifter for TTL to COMS or CMOS to CMOS, http://www.onsemi.com/pub_link/Collateral/MC14504B-D.PDF

15.Combinational Logic, http://en.wikipedia.org/wiki/Combinational_logic

16.Combinational Logic Circuits, Electronics Tutorial, http://www.electronics-tutorials.ws/combination/comb_1.html

17.Boolean Algebra, http://en.wikipedia.org/wiki/Boolean_algebra

18.Boolean Algebra, http://www.ee.surrey.ac.uk/Projects/Labview/boolalgebra/index.html

19.Boolean Algebra, Wolfram Mathworld, http://mathworld.wolfram.com/BooleanAlgebra.html

20.Boolean Arithmetics, http://www.allaboutcircuits.com/vol_4/chpt_7/2.html

21.Introduction to Boolean Logic, http://www.i-programmer.info/babbages-bag/235-logic-logic-everything-is-logic.html

22.Multiplexer, http://en.wikipedia.org/wiki/Multiplexer

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Summary & Conclusion

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