[email protected] Lecture 10 - Lecture10... · 2009-07-10 · Fixed-function IC 12 An integrated circuit (IC) is an electronic circuit that is constructed entirely on a single

Dr. Prapun [email protected]

Lecture 10

1

Digital CircuitsECS 371

Office Hours:

BKD 3601-7

Monday 9:00-10:30, 1:30-3:30

Tuesday 10:30-11:30

Announcement

2

HW4 posted on the course web site

Chapter 5: 4(b,c,e), 20a, 22a, 56

Write down all the steps that you have done to obtain your

answers.

Due date: July 16, 2009 (Thursday)

There will be a quiz today.

Review

3

NAND gate is a universal gate.

NOR gate is a universal gate.

NAND Gate as a Universal Gate

4

NAND gates are sometimes called universal gates because they can

be used to produce the other basic Boolean functions.

Inverter

AA

AND gate

AB

AB

A

B

A + B

OR gate

A

B

A + B

NOR gate

Example

5

Implement the following logic circuit using only NAND gates:

Solution:Negative-OR NAND

C

C

C

Example

6

Implement the following logic circuit using only NAND gates:

Solution:

It is easy to turn

AND-OR

configuration

into a NAND-

gate-only circuit

Negative-OR NAND

NOR Gate as a Universal Gate

7

NOR gates are also universal gates and can form all of the

basic gates.

Inverter

AA

OR gate

AB

A + B

A

B

AB

AND gate

A

B

AB

NAND gate

Example

8

Implement the following logic circuit using only NOR gates:

Solution:

Combinational Logic

9

We studied the theoretical principles used in

combinational logic design.

We will build on that foundation and describe many of the

devices, structures, and methods used by engineers to solve

practical digital design problems.

A complex circuit or system is conceived as a collection of

smaller subsystems, each of which has a much simpler

description.

Digital System Concept

10

A digital system

is an arrangement

of the individual

logic functions

connected to

perform a

specified

operation or

produce a defined

output.

Combinational Building Blocks

11

There are several straightforward structures that turn up

quite regularly as building blocks in larger systems.

Encoder

Decoders

Comparators

Multiplexers

Where can we find these

building blocks?

Fixed-function IC

12

An integrated circuit (IC) is an electronic circuit that is

constructed entirely on a single small chip of silicon.

Two broad categories of digital ICs.

1. Fixed-function logic

2. Programmable logic

In fixed-function logic, the logic functions are set by the

manufacturer and cannot be changed.

Fixed-function IC package

13 Cutaway view of DIP (Dual-In-line Pins) chip

Complexity Classifications

14

Fixed-function digital lCs are classified according to their complexity.

Small-scale integration (SSI)

up to ten equivalent gate circuits on a single chip

basic gates and flip-flops.

Medium-scale integration (MSI)

from 10 to 100 equivalent gates on a chip.

encoders, decoders, counters, registers, multiplexers, arithmetic circuits, small memories

Large-scale integration (LSI)

Very large-scale integration (VLSI)

Ultra large-scale integration (ULSI)

SSI

15

74x00

MSI

16

For the next couple lectures, we will study

most of these 74-series MSI.

MSI

17 DECODER

C

D

B

A

G1N

G2N

O0N

O12N

O15N

O10N

O11N

O1N

O13N

O14N

O4N

O3N

O2N

O7N

O6N

O5N

O9N

O8N

74154

inst

BCD TO DEC

D

B

C

A

O7N

O8N

O9N

O0N

O3N

O2N

O1N

O6N

O5N

O4N

7442

inst1

BCD TO 7SEG

LTN

B

C

D

RBIN

BIN

A

OB

OC

OE

OD

OF

OG

OA

RBON

7447

inst2

COMPARATOR

A3

B2

A2

AEBI

AGBI

ALBI

A0

B0

B3

A1

B1

ALBO

AGBO

AEBO

7485

inst3

3:8 DECODER

A

B

G1

C

G2AN

G2BN

Y0N

Y1N

Y2N

Y3N

Y4N

Y5N

Y6N

Y7N

74138

inst4 2:4 DECODER

A1

A2

B1

B2

G1N

G2N

Y10N

Y20N

Y13N

Y12N

Y11N

Y21N

Y22N

Y23N

74139

inst5

ENCODER

1N

2N

3N

6N

5N

4N

9N

8N

7N

CN

BN

AN

DN

74147

inst6 ENCODER

5N

0N

1N

2N

3N

4N

EIN

6N

7N

A1N

A0N

A2N

EON

GSN

74148

inst7

MULTIPLEXER

GN

C

B

A

D5

D0

D1

D4

D3

D2

D6

D7

Y

WN

74151

inst8

MULTIPLEXER

A1

B1

SEL

B2

A3

B3

A2

B4

GN

A4

Y2

Y1

Y4

Y3

74157

inst9

PARITY GEN.

B

A

F

E

D

I

C

G

H

EVEN

ODD

74280

inst10 4 BIT ADDER

CIN

A1

A2

B2

A3

A4

B4

B1

B3

SUM4

COUT

SUM1

SUM2

SUM3

74283

inst11

Simple Decoder

18

A decoder is a logic circuit that detects the presence of a specific

combination of bits at its input.

Two simple decoders that detect the presence of the binary code

0011 are shown below. The first has an active HIGH output; the

second has an active LOW output.

A1

A0

A2

A3

X

Active HIGH decoder for 0011

A1

A0

A2

A3

X

Active LOW decoder for 0011

(A0 is the LSB and A3 is the MSB)

Exercise

19

Assume the output of the decoder shown below is a logic 1.

What are the inputs to the decoder?

A0 = 0

A1 = 1

A2 = 0

A3 = 1

1

Binary-to-Decimal Decoder

20

The binary-to-decimal decoder shown here has 16 outputs –

one for each combination of binary inputs.

Bin/Dec

A0

0123456789

101112131415

4-bit binary

input

Decimaloutputs

A1

A2

A3

1

1

0

1111111111101111

1

The bubbles indicate active-

LOW outputs.

Application: Port Address Decoder

21

Decoder can be used in computers for input/output selection.

Computers communicate with peripherals by sending and/or receiving data through what is known as input/output (I/O) ports.

A decoder can be used to select the I/O port so that data can be sent or received from a specific external device.

2:4 decoder

22

2-to-4 line decoder with enable input

Exercise

23

Find the truth table of the 1-to-2 line decoder below.

Then, implement the 1-to-2 line decoder.

I Y0

Y1

74x139: Dual 2:4 Decoder

24

Two independent 2:4 decoders

The outputs and the enable (E) input are active-LOW.

When E is HIGH all outputs are forced HIGH.

E

3O

Most MSI decoders

were originally

designed with active-

LOW output.

Notice that all of the signal names inside the symbol

outline are active-HIGH, and that bubbles indicate

active-LOW inputs and outputs.

74x139

25

74x139: Logic diagram

26

This is a

usual 2:4

decoder.

Active-

LOW

Enable

Active-LOW output because NAND gates are used instead of AND gates

Example: Building a larger decoder

27

Construct a 3-to-8 decoder from two 2-to-4 decoders

Low order bits (A1, A0) select within decoders. High order bit (A2) controls which

decoder is active.

How can we add an

active-HIGH enable

input?

Notice that

this part is

equivalent to a

1:2 decoder.

Building larger decoder from smaller

ones

28

To construct (k+n)-to-2n+k decoders, can use 1. 2n of k-to-2k decoders with enable input and 2. one n-to-2n decoders.

The connections are: For each of the k-to-2k decoder with enable input, all have k input

we put in A0…Ak-1.

The enable line of the rth decoder is connected to Dr of the n-to-2n

decoders. The inputs of the n-to-2n decoder get Ak to An+k-1.

Basically, each k-to-2k decoder works on the last k bits.

We use the first n bit, via the n-to-2n decoder, to select which one (and only one) of the k-to-2k decoders will be enabled.

Example

29

Construct a 4:16 decoder

with an active-LOW enable

from three 2:4 decoders.

74x138: 3:8 Decoder

30

Active-LOW outputs

Three enable inputs.

Example

31

Construct a 4:16 decoder

with an active-LOW enable

(EN) from two 74x138

decoder.

Example

32

Construct a 5:32

decoder with two active-

low enable and one

active-high enable

from four 74x138 and

one 74x139.

74x154:

4:16 Decoder

33 DECODER

C

D

B

A

G1N

G2N

O0N

O12N

O15N

O10N

O11N

O1N

O13N

O14N

O4N

O3N

O2N

O7N

O6N

O5N

O9N

O8N

74154

inst

Include two active-LOW chip select (CS)

lines which must be at the active level to

enable the outputs. These lines can be used

to expand the decoder to larger inputs.

Alternative logic

symbol

A LOW level on each

chip select input is

required to make the

enable gate output

(EN) HIGH.

5:32 Decoder

34

Decoder as general purpose logic

35

Any combinational circuit with n inputs and m outputs can be

implemented with an n-to-2n-line decoder and m OR gate

Observe that the

3:8 decoder

generates all

possible minterms.

Example

36

Implement a full adder circuit with a decoder and OR gates

S = X,Y,Z(1,2,4,7)

C = X,Y,Z (3,5,6,7)

OutputsInputs

A B C out SCin

0

1

0

1

0

1

0

1

0

0

0

0

0

0

1

1

1

1

0

0

1

1

1

1

0

0

0

1

0

1

1

0

0

1

1

0

1

1

0

1

X Y Z SC

Other Decoders

37

In general, a decoder converts coded information,

such as binary number, into non-coded form.

Later, (if time permitted) we will talk about

other types of decoder.