Data-Processing Circuits

10CS 33 LOGIC DESIGN UNIT – 3 Data Processing Circuits

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Data-Processing Circuits

Objectives

• Design of multiplexer circuits

• Discuss multiplexer applications

• Realization of higher order multiplexers using lower orders (multiplexer trees)

Introduction

Data-processing circuits are logic circuits that process binary data. Such circuits may be multiplexers,

demultiplexers, encoder, decoder, EX-OR gates. First we consider multiplexers.

Multiplexer

Multiplex means many into one. In digital computer networks, multiplexing is a method by which

multiple digital data streams are combined into one signal over a shared medium. A digital circuit that

performs the multiplexing of digital signals is called a multiplexer (or MUX in short). Multiplexer is a

combinational logic circuit that can select one of many inputs. Multiplexer is also called a data selector.

A simple 2-to-1 multiplexer block diagram and the switch equivalent circuit are as shown:

It has two inputs but only one output. By suitable control input or select input (sel) we can steer any

input to the output.

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Unit – 3

10CS 33 LOGIC DESIGN

The general multiplexer block diagram is as shown below:

Design of 4-to-1 Multiplexer

The 4-to-1 multiplexer has four data inputs.

control inputs. The block diagram is as shown below:

The truth table describing the behavior of the 4


The general multiplexer block diagram is as shown below:

1 multiplexer has four data inputs. To steer the four data inputs to the output we need two

am is as shown below:

The truth table describing the behavior of the 4-to-1 multiplexer is as shown below:

Control Inputs Output

A B Y

0 0 D0

0 1 D1

1 0 D2

1 1 D3

3 Data Processing Circuits

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to the output we need two

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From the truth table we obtain the logic equation

Y = A’B’D0 + A’BD1 + AB’D2 + ABD

The equation cannot be further simplified

The 74150

The 74150 is a 16-to-1 TTL multiplexer

disables or enables the multiplexer. If

The block diagram is as shown below:

The 74151

The 74151 is an 8-to-1 TTL multiplexer


From the truth table we obtain the logic equation

+ ABD3

The equation cannot be further simplified. The logic circuit realization is as shown below:

Y = A’B’D0 + A’BD1 + AB’D

TTL multiplexer. It has active low output. It has a STROBE, an input signal that

. If STROBE = 0, MUX is enabled and if STROBE = 1, MUX is disabled


1 TTL multiplexer. It has complementary outputs.


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. The logic circuit realization is as shown below:

+ AB’D2 + ABD3

It has a STROBE, an input signal that

STROBE = 1, MUX is disabled.

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The 74153

The 74153 is a dual 4-to-1 TTL multiplexer

multiplexer and common select lines

The 74157

The 74157 is a quad 2-to-1 TTL multiplexer IC


low:

1 TTL multiplexer. It has non-inverting outputs. It has separate enable for each

ommon select lines.

1 TTL multiplexer IC. The block diagram is as shown below:


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eparate enable for each

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Multiplexer Applications

Multiplexer’s important application is in sharing the circuits, ports, devices and resources

can be used in design of combinational logic circuits

Nibble Multiplexer

Nibble Multiplexer is used when we want to

nibbles, A3A2A1A0 and B3B2B1B0. The 74157 IC is used to realize the nibble multiplexer as shown below:

The control signal SELECT determines which nibble is transmitted to output

When SELECT is low, the left nibble is steered to the o

Y3Y2Y1Y0 = A3A2A1A0

When SELECT is high, the right nibble is steered to the output.

Y3Y2Y1Y0 = B3B2B1B0

Multiplexer Logic

We can use multiplexer to realize a given

because a 2n-to-1 multiplexer can be used to design solution for any n

Example 1:

Realize Y = A’B + B’C’ + ABC using an 8

Solution:

First we express Y in canonical SOP form


Multiplexer’s important application is in sharing the circuits, ports, devices and resources

can be used in design of combinational logic circuits.

Nibble Multiplexer is used when we want to select one of two input nibbles. Consider the two input

The 74157 IC is used to realize the nibble multiplexer as shown below:

The control signal SELECT determines which nibble is transmitted to output. STROBE input is

When SELECT is low, the left nibble is steered to the output. We have,

nibble is steered to the output. We have,

We can use multiplexer to realize a given Boolean equation. Multiplexer is called universal logic circuit

1 multiplexer can be used to design solution for any n-variable truth table

using an 8-to-1 multiplexer

in canonical SOP form


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Multiplexer’s important application is in sharing the circuits, ports, devices and resources. Multiplexers

. Consider the two input

The 74157 IC is used to realize the nibble multiplexer as shown below:

STROBE input is made 0.

Multiplexer is called universal logic circuit

variable truth table.

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Y = A’B + B’C’ + ABC

= A’B.1 + 1.B’C’ + ABC

= A’B.(C’ + C) + (A’ + A).B’C’ + ABC

= A’BC’ + A’BC + A’B’C’ + AB’C’ + ABC

= Σ m (2, 3, 0, 4, 7)

= Σ m (0, 2, 3, 4, 7)

Consider the 8-to-1 multiplexer truth table as shown below:

A B C Y

0 0 0 D0

0 0 1 D1

0 1 0 D2

0 1 1 D3

1 0 0 D4

1 0 1 D5

1 1 0 D6

1 1 1 D7

From the truth table we have,

Y = A’B’C’D0 + A’B’CD1 + A’BC’D2 + A’BCD3 + AB’C’D4 + AB’CD5 + ABC’D6 + ABCD7

Y = moD0 + m1D1 + m2D2 + m3D3 + m4D4 + m5D5 + m6D6 + m7D7

The given equation is Y = f(A, B, C) = Σ m (0, 2, 3, 4, 7). The variables A, B, & C are used as select inputs.

Comparing multiplexer output expression with the given logic equation in canonical SOP form we find by

substituting D0 = D2 = D3 = D4 = D7 = 1 and D1 = D5 = D6 = 0 we have the realization as shown.

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The truth table for the given logic equation is shown below:

Example 2:

Realize Y = A’B + B’C’ + ABC using 4-

Solution:

We consider variables A and B as selector

input. Given logic equation Y = A’B + B’C’ + ABC in canonical form

is as shown.


The truth table for the given logic equation is shown below:

A B C Y

0 0 0 1

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

-to-1 multiplexer.

as selector inputs in 4-to-1 multiplexer and variable C in given as data

Given logic equation Y = A’B + B’C’ + ABC in canonical form is Y= Σ m (0, 2, 3, 4, 7)


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1 multiplexer and variable C in given as data

m (0, 2, 3, 4, 7). The truth table

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A B C Y

0 0 0 1

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

Similar to procedure adopted in entered variable map, output Y is written in terms of variable C.

A B C Y Y

0 0 0 1 C’

0 0 1 0

0 1 0 1 1

0 1 1 1

1 0 0 1 C’

1 0 1 0

1 1 0 0 C

1 1 1 1

Comparing with equation of 4-to-1 multiplexer we see

D0 = C’

D1 = 1

D2 = C’

D3 = C

generate the given logic function.

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The given logic equation is realized using the 4

Example 3:

Realize Y = Σ m(0, 2, 3, 4 ,5, 8, 9, 10, 11, 12, 13, 15) using 8

Solution:

The truth table for the given expression is as shown below:


The given logic equation is realized using the 4-to-1 multiplexer as shown below:

A B Y

0 0 C’

0 1 1

1 0 C’

1 1 C

m(0, 2, 3, 4 ,5, 8, 9, 10, 11, 12, 13, 15) using 8-to-1 multiplexer.

The truth table for the given expression is as shown below:


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The logic expression is realized using 8

Multiplexer Trees

A number of m-to-1 multiplexers can be arranged in tree topology to obtain a bigger n

(n > m).

Example 1:

Design a 4-to-1 multiplexer using 2

Solution:

The 2-to-1 multiplexer truth table is as

Two units of 2-to-1 multiplexers are used together to realize 4 inputs, and another unit of 2

multiplexer is used to steer the inputs to a single output. The multiplexer tree is realized as shown:


The logic expression is realized using 8-to-1 multiplexer as shown below:

1 multiplexers can be arranged in tree topology to obtain a bigger n

1 multiplexer using 2-to-1 multiplexers.

1 multiplexer truth table is as shown:

1 multiplexers are used together to realize 4 inputs, and another unit of 2


A B Y

0 0 D0

0 1 D1

1 0 D2

1 1 D3


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-to-1 multiplexer

1 multiplexers are used together to realize 4 inputs, and another unit of 2-to-1


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Example 2:

Design a 32-to-1 multiplexer using two 16

Solution:

Questions

1. What is a multiplexer? Design 4

2. Implement the given Boolean function by using

f(A, B, C, D) = ∑m(0, 1, 3, 5, 7, 11, 12, 13, 14)


1 multiplexer using two 16-to-1 multiplexers and one 2-to-1 multiplexer

1. What is a multiplexer? Design 4-to-1 multiplexer and implement using gates.

2. Implement the given Boolean function by using 8:1 multiplexer.

∑m(0, 1, 3, 5, 7, 11, 12, 13, 14)


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1 multiplexer.

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3. Realize the Boolean expression f(w, x, y, z) = ∑m(4, 6, 7, 8, 10, 12, 15) using a 4 to 1 line multiplexer

and external gates.

4. Write the truth table of a 4-bit Binary to Gray code converter and realize the same using four 74151

ICs (8-to-1 multiplexer).

5. Show how two 1-to-16 demultiplexers can be connected to get a 1-to-32 demultiplexer.

6. Design a 32-to-1 multiplexer using two 16-to-1 multiplexer and one 2-to-1 multiplexer.

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10CS 33 LOGIC DESIGN UNIT

Data Processing Circuits

Objectives

• Design of demultiplexers and demultiplexer t

• Understanding decoders

• Combinational logic design using d

• Understanding seven-segment d

Demultiplexers

Demultiplex means one into many.

input and many outputs. By applying control signals, we can steer the input signal to one of the output

lines. The block diagram of a simple

is as shown below:

Consider the block diagram of the general

33 LOGIC DESIGN UNIT – 3 Data Processing Circuits


and demultiplexer trees

Combinational logic design using decoders

segment decoders and encoders

. A demultiplexer (DEMUX) is a combinational logic circuit with one

By applying control signals, we can steer the input signal to one of the output

The block diagram of a simple 1-to-2 demultiplexer block diagram and its switch equivalent circuit

general demultiplexer as shown below:


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A demultiplexer (DEMUX) is a combinational logic circuit with one

By applying control signals, we can steer the input signal to one of the output

block diagram and its switch equivalent circuit

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Unit – 3


It has one input signal, ‘m’ control input or select signals

Design of 1-to-2 Demultiplexer

The truth table of 1-to-2 demultiplexer

The output expressions are Y0 = D.A’ and

Demultiplexer ICs

The popular demultiplexer TTL ICs are listed below. They can also be used as decoders.

IC No.

74154

74138

74155

The TTL IC 74154

The 74154 is a 1-to-16 demultiplexer / decoder

must be low to activate the IC. Data is inverted at the input and again on any output

inversion, data passes through the circuit unchanged


‘m’ control input or select signals, and ‘n’ output signals (n <= 2

2 demultiplexer is as shown below:

Data

input

Select

input Outputs

D A Y0 Y1

0 0 0 0

1 0 1 0

0 1 0 0

1 1 0 1

= D.A’ and Y1 = A.D and the logic circuit realization is as shown below:


IC No. DEMUX Type Decoder Type

74154 1-to-16 4-to-16

74138 1-to-8 3-to-8

74155 1-to-4 2-to-4

16 demultiplexer / decoder. G1 is used as data input. G2 is used as strobe input and

Data is inverted at the input and again on any output

through the circuit unchanged.


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(n <= 2m).

and the logic circuit realization is as shown below:


G2 is used as strobe input and

Data is inverted at the input and again on any output. With double

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The pin out diagram is as shown:

Demultiplexer Tree

Example 1:

Realize 1-to-32 demultiplexer using two 1

Solution:

1-to-32 demux has 5 select variables A, B,C, D, E

32 outputs. If A = 0, the top IC is chosen

BCDE, data is directed to one of the outputs


using two 1-to-16 demultiplexers

32 demux has 5 select variables A, B,C, D, E. We use two units of 1-to-16 demultiplexers to obtain

If A = 0, the top IC is chosen, and if A = 1, the bottom IC is chosen. Depending on value of

BCDE, data is directed to one of the outputs. The 1-to-32 demultiplexer is realized as sh


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16 demultiplexers to obtain

Depending on value of

32 demultiplexer is realized as shown below:

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Decoder

Demultiplexer can be used as a decoder

logic 1. The decoder inputs are given to the control or select lines

one of the output lines. 1-to-n demult

lines will be high.

The block diagram of 1-of-n decoder is as shown below:

1-of-16 Decoder IC

74154 IC can be used as 1-of-16 decoder

block diagram is as shown below:


Demultiplexer can be used as a decoder. The data input of the demultiplexer is always connected to

The decoder inputs are given to the control or select lines. The inputs are decoded by activating

n demultiplexer converted in to 1-of-n decoder. Only one of the ‘n’ output

n decoder is as shown below:

16 decoder. 1-of-16 decoder is also called 4 line-to-16 line decoder


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The data input of the demultiplexer is always connected to

The inputs are decoded by activating

Only one of the ‘n’ output

16 line decoder. The

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Decoder Applications

Decoders can be used in combination logic circuit design

Example 1 :

Show how using a 3-to-8 decoder and multi

realized simultaneously:

f1(A, B, C) = Σ m(0, 4, 6)

f2(A, B, C) = Σ m(0, 5)

f3(A, B, C) = Σ m(1, 2, 3, 7)

Solution:

f1 = Σ m(0, 4, 6) = m0 + m4 + m6

f2 = Σ m(0, 5) = m0 + m5

f3 = Σ m(1, 2, 3, 7) = m1 + m2 + m3 + m7

We use OR gates to add the minterms.

Example 2:

Realize a full adder using 3-to-8 decoder IC 74138 and NAND gates

Solution:

The pin out diagram of the 3-to-8 decoder IC 74138 is as shown:


ombination logic circuit design.

8 decoder and multi-input OR gates following Boolean expressions can be

= m0 + m4 + m6

= m1 + m2 + m3 + m7

We use OR gates to add the minterms. The Boolean expressions are realized as shown below:

8 decoder IC 74138 and NAND gates.

8 decoder IC 74138 is as shown:


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input OR gates following Boolean expressions can be

The Boolean expressions are realized as shown below:

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The truth table of full adder is written as shown below:

Inputs Outputs

A B Ci S Co

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

The output expressions in SOP form:

S = Σ m(1, 2, 4, 7)

Co = Σ m(3, 5, 6, 7)

Full adder is realized as shown:

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BCD-to Decimal Decoders

BCD is an abbreviation for binary-coded decimal

number by its nibble equivalent.

Example: Decimal number 429 in its BCD form is

4

0100

The 7445 IC

The 7445 is a BCD to Decimal Decoder / Driver IC

diagram is as shown below:


coded decimal. The BCD code expresses each digit in a decimal

Decimal number 429 in its BCD form is

2 9

0100 0010 1001

Decoder / Driver IC. It is also called 1-of-10 decoder and its pin out


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The BCD code expresses each digit in a decimal

and its pin out

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Seven-Segment Decoders

A seven-segment decoder-driver is used to drive a seven

has 7 Light-emitting Diodes labeled a

It may be the common-anode or the common

display the decimal digits 0 -9.

The 7446 IC

The 7446 is a TTL IC decoder-driver that can be used to drive a common

It requires external current-limiting resistors

The 7448 IC

The 7446 is a TTL IC decoder-driver that can be used to drive a common

indicator. It has its own current-limiting resistors on the chip

Encoder

Encoding is the process of converting familiar numbers or symbols into some code format

is a digital circuit that receives digits (decimal, octal, etc.) or alphabets or special symbols and converts

them into their respective binary codes

input is converted to a coded binary output with ‘m’ bits

Encoder performs operation reverse to that of a


driver is used to drive a seven-segment indicator. A seven-segment indicator

labeled a – g as shown:

anode or the common-cathode type. By forward-biasing different LED’s, we can

driver that can be used to drive a common-anode seven-se

limiting resistors.

driver that can be used to drive a common-cathode seven

limiting resistors on the chip.

is the process of converting familiar numbers or symbols into some code format


them into their respective binary codes. It has ‘n’ input lines, only one of which is active

input is converted to a coded binary output with ‘m’ bits. Basically it is a combinational logic circuit

erforms operation reverse to that of a decoder. The block diagram is as shown:


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segment indicator

biasing different LED’s, we can

segment indicator.

cathode seven-segment

is the process of converting familiar numbers or symbols into some code format. An encoder


nput lines, only one of which is active. The active

Basically it is a combinational logic circuit.

The block diagram is as shown:

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Octal-to-Binary Encoder

It has 8 inputs, corresponding to 8 octal digits.

output. The truth table is as shown:

Inputs – Octal Digits

I0 I1

1 0

0 1

0 0

0 0

0 0

0 0

0 0

0 0

The output expressions are:

B0 = I1 + I3 + I5 + I7

B1 = I2 + I3 + I6 + I7

B2 = I4 + I5 + I6 + I7

The octal-to-binary encoder is realized as shown:


corresponding to 8 octal digits. It converts the selected octal digit into 3

The truth table is as shown:

Octal Digits Binary

Outputs

I2 I3 I4 I5 I6 I7 B2 B1 B0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1

1 0 0 0 0 0 0 1 0

0 1 0 0 0 0 0 1 1

0 0 1 0 0 0 1 0 0

0 0 0 1 0 0 1 0 1

0 0 0 0 1 0 1 1 0

0 0 0 0 0 1 1 1 1

binary encoder is realized as shown:


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It converts the selected octal digit into 3-bit binary

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Decimal-to-BCD Encoder

It has 10 inputs, corresponding to 1

output.

The 74147 IC

The 74147 TTL IC is a decimal-to-BCD encoder

highest-order input.

Design of Priority Encoder

Example:

Design a priority encoder, the truth table of which is shown below. The order of priority for three inputs

is X1>X2>X3. However, if the encoder is not enabled by S or all the inputs are inactive the output

AB = 00.


It has 10 inputs, corresponding to 10 decimal digits. It converts the selected decimal digit into 4

BCD encoder. It is a priority encoder because it gives priority to the


2>X3. However, if the encoder is not enabled by S or all the inputs are inactive the output

Inputs Outputs

S X1 X2 X3 A B

0 X X X 0 0

1 1 X X 0 1

1 0 1 X 1 0

1 0 0 1 1 1

1 0 0 0 0 0


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It converts the selected decimal digit into 4-bit BCD

It is a priority encoder because it gives priority to the


2>X3. However, if the encoder is not enabled by S or all the inputs are inactive the output

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Simplification using K-map:

For output A:

We obtain A = SX1’X3’ + SX1’X2.

For output B:

We obtain B = SX1 + SX2’X3.

The output expressions are realized using logic gates.

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Questions

1. Define decoder. Draw logic diagram of 3:8 decoder with enable input.

2. Design a circuit that realizes the following two functions using a decoder and logic gates:

F1(A, B) = ∑m(0, 3) and F2(A, B) = ∑m(1, 2)

2. Define encoder. Design decimal-to-BCD encoder?

4. What is a priority encoder?

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Objectives

• Write the truth table for exclusive-OR (EX-OR) Gates

• Explain the purpose of Parity Checking

• Design Parity Generators and Checkers

• Show how a Magnitude Comparator works

• Design of n-bit Magnitude Comparator

• Describe a diode ROM

Exclusive-OR Gates

The exclusive-OR gate has a high output only when an odd number of inputs are high. The 2-input

Exclusive-OR (EX-OR) gate truth table is as shown:

Inputs Output

A B Y

0 0 0

0 1 1

1 0 1

1 1 0

The output expression is

Y = A’B + AB’.

The logic circuit of 2-input EX-OR gate is as shown:

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Its logic symbol is as shown:

The 7486 IC

The 7486 TTL IC is a quad 2-input Exclusive

performs the logic exclusive-OR function

Full Adder using EX-OR gates

The truth table of full adder is as shown:


input Exclusive-OR gate. It has four independent gates each of which

OR function. The pin out diagram is as shown below:

The truth table of full adder is as shown:


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It has four independent gates each of which

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Inputs

A

0

0

0

0

1

1

1

1

Full Adder Realizations:

a. Using 3-input EX-OR gate

b. Using 2-input EX-OR gates

Parity Generators and Checkers

In data communications, parity checking refers to the use of parity bits to check that data has been

transmitted accurately. The parity bit is added to every data unit that is transmitted

each data unit is set so that all bytes have either an odd number or even number of set bits

Even Parity

Even parity means an n-bit input has an even number of set bit (1’s)

Example:

Data unit 110011 has even parity. It has four set bits (1’s) i.e. even no. of 1’s


Inputs Outputs

A B Ci S Co

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Parity Generators and Checkers


parity bit is added to every data unit that is transmitted.

each data unit is set so that all bytes have either an odd number or even number of set bits

bit input has an even number of set bit (1’s).

It has four set bits (1’s) i.e. even no. of 1’s.


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. The parity bit for

each data unit is set so that all bytes have either an odd number or even number of set bits.

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Odd Parity

Odd parity means an n-bit input has an odd number of set bits (1’s)

Example:

Data unit 110001 has odd parity. It has three set bits (1’s) i.e. odd

Parity Checker

EX-OR gates are ideal for checking the parity of a binary number because they produce an output 1

when the input has an odd number of 1’s

Odd parity number

Even parity number

Parity Generation

An extra bit is added to the original binary number to produce a new binary number with even or odd

parity. The extra bit is called the parity bit

Odd-Parity Generation


bit input has an odd number of set bits (1’s).

It has three set bits (1’s) i.e. odd no. of 1’s.

OR gates are ideal for checking the parity of a binary number because they produce an output 1

when the input has an odd number of 1’s.

Input Output

Odd parity number 1

Even parity number 0

is added to the original binary number to produce a new binary number with even or odd

The extra bit is called the parity bit.


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OR gates are ideal for checking the parity of a binary number because they produce an output 1

is added to the original binary number to produce a new binary number with even or odd

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74180 Truth Table

Σ of 1’s at

A - H

Even

Odd

Even

Odd

X

X

Using a 74180 to generate odd parity

Σ of 1’s

at A -

Even

Odd

Odd parity generator


Inputs Outputs

of 1’s at

H EVEN ODD ΣEVEN ΣODD

Even 1 0 1 0

Odd 1 0 0 1

Even 0 1 0 1

Odd 0 1 1 0

1 1 0 0

0 0 1 1

odd parity

of 1’s

- H EVEN ODD ΣODD

Even 0 1

1

Odd 0


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Magnitude Comparator

Magnitude comparator compares magnitude of two n

three outputs: X > Y, X = Y, and X < Y

1-bit Magnitude Comparator

The truth table of 1-bit magnitude comparator is as shown below:

The output expressions are:

(X>Y) = XY’

(X=Y) = X’Y’ + XY = (X’Y + XY’)’

(X<Y) = X’Y

The logic circuit of 1-bit comparator is as shown:


Magnitude comparator compares magnitude of two n-bit numbers, say X & Y and activates one of the

X < Y. The logic diagram of n-bit comparator is as shown below:

bit magnitude comparator is as shown below:

Input Outputs

X Y X>Y X=Y X<Y

0 0 0 1 0

0 1 0 0 1

1 0 1 0 0

1 1 0 1 0

= (X’Y + XY’)’

bit comparator is as shown:


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say X & Y and activates one of the

bit comparator is as shown below:

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2-bit Magnitude Comparator

The truth table of 2-bit magnitude comparator is as shown below:

Inputs Outputs Inputs Outputs

X Y X>Y X=Y X<Y X Y X>Y X=Y X<Y

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

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

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

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

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

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

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

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

Comparator Design

We can obtain simplified logic equation for 4-variable expression and implement it using logic gates.

This procedure will become very complex when we try to design a comparator for 3-bits or more. The

solution steps are:

• Use a simple generic procedure

• Define

1. Bit-wise greater than terms (G):

G1 = X1Y1’ G0 = X0Y0’

2. Bit-wise less than terms (L):

L1 = X1’Y1 L0 = X0’Y0

3. Bit-wise equality terms (E):

E1 = (G1 + L1)’ E0 = (G0 + L0)’

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• From the definitions of G, L and E, we have

(X=Y) = E1E0 X= Y when both bits are equal

(X>Y) = G1 + E1G0 X>Y if MSB of X is higher than that of Y or if MSB is equal, then LSB of

X is higher

(X<Y) = L1 + E1L0 X<Y if MSB of X is lesser than that of Y or if MSB is equal, then LSB of X

is lesser

n-bit Magnitude Comparator

The output expressions are listed bel

(X=Y) = En-1En-2…. E0

(X>Y) = Gn-1 + En-1Gn-

(X<Y) = Ln-1 + En-1Ln-2

where Ei, Gi, Li represent for

respectively

The 7485 IC

It is a 4-bit magnitude comparator TTL IC. The functional diagram is as shown below:

The additional inputs (X=Y)in, (X>Y)

numbers having more than 4-bits. When 7485 is not used in cascade (X=Y)


From the definitions of G, L and E, we have 2-bit comparator output as follows:

X= Y when both bits are equal

Y if MSB of X is higher than that of Y or if MSB is equal, then LSB of

X is higher

X<Y if MSB of X is lesser than that of Y or if MSB is equal, then LSB of X

is lesser

The output expressions are listed below:

-2 + ……+ En-1En-2…E1G0

2 + ….. + En-1En-2…E1L0

represent for ith bit Xi = Yi, Xi > Yi, Xi < Yi terms

TTL IC. The functional diagram is as shown below:

, (X>Y)in, (X<Y)in are used to connect more than one 7485 to compare

When 7485 is not used in cascade (X=Y)in = 1, (X>Y) in


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bit comparator output as follows:

Y if MSB of X is higher than that of Y or if MSB is equal, then LSB of

X<Y if MSB of X is lesser than that of Y or if MSB is equal, then LSB of X

are used to connect more than one 7485 to compare

in = 0, (X<Y)in = 0.

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8-bit Comparator

The 8-bit comparator is realized using two 7485 ICs as shown below:

Read-Only Memory

A read-only memory (ROM) is used to store fixed data

be used to implement truth tables.

Diode ROM

We can build a diode circuit that stores binary numbers

Consider the binary numbers shown in the table:


bit comparator is realized using two 7485 ICs as shown below:

only memory (ROM) is used to store fixed data. ROM can be used as ‘look-up’ table

We can build a diode circuit that stores binary numbers.

Consider the binary numbers shown in the table:

Address Nibble

0 0111

1 1000

2 1011

3 1100

4 0110

5 1001

6 0011

7 0111


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up’ table. It can also

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The diode ROM matrix is as shown below:

When switch is

On-Chip Decoding

Switch that selects the addresses in diode ROM is replaced by on

3-to-8 decoder is used as shown:


The diode ROM matrix is as shown below:

When switch is

at position

Output

Y3Y2Y1Y0

0 0111

1 1000

2 1011

3 1100

4 0110

5 1001

6 0011

7 0111

Switch that selects the addresses in diode ROM is replaced by on-chip decoding. For this purpose a


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. For this purpose a

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TTL ROM ICs

Some popular TTL ROM ICs are listed below:

7488 256 bits organized as 32 x 8

74187 1024 bits organized as 256 x 4

74S370 2048 bits organized as 512 x 4

Generating Boolean Functions

Because the on-chip decoder of ROM produce all the fundamental products and the diodes OR some of

these products, diode ROM can be used to generate Boolean functions.

Questions

1. What is a parity generator?

2. Explain parity checking.

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3. What is a magnitude comparator? Write the truth table and circuit diagram of a 1-bit magnitude

comparator.

4. Write the (X>Y) output expression for a 4-bit comparator.

5. Draw a ROM diode circuit that produces the following output:

Y3 = A’BC’, Y2 = AB’C + ABC, Y1 = AB’C + A’BC + ABC, Y0 = A’BC’ + A’BC + ABC’ + ABC

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Objectives

• Review of Programmable ROM (PROM) and Erasable PROM (EPROM)

• Describe Programmable Logic Devices (PLDs): Programmable Array Logic (PAL) and

Programmable Logic Array (PLA)

Programmable ROMs

A programmable ROM (PROM) allows the user instead of the manufacturer to store the data. Mask

ROM (MROM) is a type of ROM whose contents are programmed by the IC manufacturer.

PROM

It is also called field programmable ROM (FPROM) or one-time programmable non-volatile memory

(OTP NVM).

PROM Programmer

User with the help of an instrument called a PROM programmer can program the PROM.

Programming a PROM

Consider the diode ROM. Originally, all diodes are connected at the cross points. Each of these diodes

has a fusible link ( a small fuse). The process of programming a PROM chip is called PROM ‘burning in’.

It involves burning or blowing out the fuses of selected memory cells whose value needs to be altered.

Programming like this is permanent. Data cannot be erased after it has been burned in.

The PROM programmer is first configured so that it contains the desired PROM burning instructions.

Next, the PROM chip is inserted into the ZIF socket. The PROM programmer sends a high voltage pulse

(12 to 21 V) only to the fuses belonging to memory cells whose value has to be changed from 1 to 0.

The high voltage causes the selected fuse to blow out or burn out. The burned out fuse no longer

connects a column to a row in a memory cell. The memory cell with a burned out fuse has a value 0

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Unit – 3


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Disadvantage of PROM

There is a limit on the number of input variables. Typically, PROMs have 8 inputs or less.

Drawing a PROM logic circuit

It is cumbersome to draw large PROM circuit with all the diodes. An alternative, streamlined drawing

procedure for PROMs is used. The simplified diagram of PROM is as shown:

Universal Logic Solution

PROM is an universal logic solution. The AND gates generate all the fundamental products and the user

can then OR these products as needed to generate any Boolean output.

Example:

Realize a full adder using a PROM.

Solution:

The truth table of the full adder is as shown:

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The full adder using PROM is realized as shown below:

Erasable PROMs

The erasable PROM (EPROM) uses metal

an array of floating-gate transistors individually programmed by an EPROM programmer

the memory requires selecting a given address and applying a higher voltage to the transistors

Erasing EPROM contents


Inputs Outputs

A B Ci S Co

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

The full adder using PROM is realized as shown below:

metal-oxide semiconductor field-effect transistors (MOSFETs)

gate transistors individually programmed by an EPROM programmer

the memory requires selecting a given address and applying a higher voltage to the transistors


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effect transistors (MOSFETs). It has

gate transistors individually programmed by an EPROM programmer. Storing data in

the memory requires selecting a given address and applying a higher voltage to the transistors.

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The stored data is erased by exposing the die to ultraviolet (UV) light. The UV light passes through the

quartz window in the IC package and releases all stored charges. The effect is to erase the stored

contents.

EPROM ICs

Some important EPROM IC types are listed below:

2716 16 K bits organized as 2048 x 8 (2 KB)



Importance of EPROM

The EPROM is useful in project development. The designer can modify the contents until the stored

data is perfect. When the design is finalized, the data can be burned into PROM.

Programmable Array Logic

Programmable Array Logic (PAL) is a programmable array of logic gates on a single chip. PAL is different

from a PROM. It has a programmable AND array and a fixed OR array. The structure of PAL is as shown

below:

Programming a PAL

With a PROM programmer, we can burn in the desired fundamental products, which are then ORed by

the fixed output connections.

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Example:

Realize a full adder using PAL.

Solution:

The output expressions of a full adder are:

S = Σ m(1, 2, 4, 7)

Co = Σ m(3, 5, 6, 7)

Full adder is realized using PAL as shown below:

PAL ICs

Some important PAL IC types are listed below:

10H8 10 input and 8 output AND

16H2 6 input and 2 output AND

14L4 14 input and 4 output AND


The output expressions of a full adder are:

Full adder is realized using PAL as shown below:

IC types are listed below:

10 input and 8 output AND-OR

6 input and 2 output AND-OR

14 input and 4 output AND-OR-INVERT


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PAL - Pros and Cons

PALs are not an universal logic solution

ORed at the final outputs. But PALs have enough flexibility to produce all kinds of complicated logic

functions. PALs have the advantage of 16 inputs compared to the ty

Programmable Logic Arrays

In Programmable Logic Arrays (PLAs) both the AND array and the OR array are programmable

along with ROMs and PALs, are included in the more general classification of ICs called programmabl

logic devices (PLDs).

PLDs

The block diagrams of the three PLDs are as shown below:


universal logic solution. Only some of the fundamental products can be generated and

But PALs have enough flexibility to produce all kinds of complicated logic

PALs have the advantage of 16 inputs compared to the typical limit of 8 inputs for PROMs

Programmable Logic Arrays

In Programmable Logic Arrays (PLAs) both the AND array and the OR array are programmable

along with ROMs and PALs, are included in the more general classification of ICs called programmabl

The block diagrams of the three PLDs are as shown below:


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Only some of the fundamental products can be generated and

But PALs have enough flexibility to produce all kinds of complicated logic

pical limit of 8 inputs for PROMs.

In Programmable Logic Arrays (PLAs) both the AND array and the OR array are programmable. PLAs

along with ROMs and PALs, are included in the more general classification of ICs called programmable

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The structure of Programmable Logic Array

We can use PLA for combinational logic circuit design.

Example:

Realize a 7-segment decoder using PLA

Solution:

The truth table of 7-segment decoder is as shown:


Programmable Logic Array (PLA) is as shown below:

We can use PLA for combinational logic circuit design.

decoder using PLA.

segment decoder is as shown:


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BCD Input

A B

0 0

0 0

0 0

0 0

0 1

0 1

0 1

0 1

1 0

1 0

The 7-segment decoder is realized using PLA


BCD Input Outputs

C D a b c d e f g

0 0 1 1 1 1 1 1 0

0 1 0 1 1 0 0 0 0

1 0 1 1 0 1 1 0 1

1 1 1 1 1 1 0 0 1

0 0 0 1 1 0 0 1 1

0 1 1 0 1 1 0 1 1

1 0 1 0 1 1 1 1 1

1 1 1 1 1 0 0 0 0

0 0 1 1 1 1 1 1 1

0 1 1 1 1 0 0 1 1

using PLA as shown below:


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Questions

1. Mention different types of ROMs and explain each of them.

2. Implement the following Boolean functions using an appropriate PLA:

F1(A, B, C) = ∑m(0, 4, 7); F2 (A, B, C) = ∑m(4, 6).

3. What are the different types of PLDs? Implement the 7-segment decoder using PLA.

4. Implement the following function using PLA:

X = A’B’C + AB’C’ + B’C; Y = A’B’C + AB’C’; Z = B’C

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Data-Processing Circuits