PACE INSTITUTE OF TECHNOLOGY AND SCIENCES::ONGOLE
DIGITAL LOGIC DESIGN
Course File
II B.Tech I Sem CSE
Academic Year : 2014-15
Prepared by
Mr. T. RamaiahM.Tech
Assistant Professor
ram.thalluri310@gmail.com
manadld.blogspot.in
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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY KAKINADA
B.TECH COMPUTER SCIENCE ENGINEERING
II Year B.Tech. – I Sem
DIGITAL LOGIC DESIGN
Unit I : Number Systems
Binary, Octal, Decimal, Hexadecimal Number Systems. Conversion of Numbers From One
Radix To Another Radix , r’s Complement and (r-1)’s Complement Subtraction of Unsigned
Numbers, Problems, Signed Binary Numbers, Weighted and Non weighted codes.
Unit II : Logic Gates And Boolean Algebra
Basic Gates NOT, AND, OR, Boolean Theorems,Complement And Dual of Logical Expressions,
Universal Gates, Ex-Or and Ex-Nor Gates, SOP,POS, Minimizations of Logic Functions Using
Boolean Theorems, Two level Realization of Logic Functions Using Universal Gates. Verilog
programming for the minimized logic functions.
Gate- Level Minimization
Karnaugh Map Method(K-Map): Minimization of Boolean Functions maximum upto Four
Variables , POS And SOP, Simplifications With Don’t Care Conditions Using K-Map.
Unit III:
Design of Half Adder, Full Adder, Half Subtractor, Full Subtractor, Ripple Adders and
Subtractors, Ripple Adder/Subtractor Using Ones and Twos Complement Method. Design of
Decoders, Encoders, Multiplexers, Demultiplexers, Higher Order Demultiplexers and
Multiplexers, Priority Encoder, Code Converters,
Magnitude Comparator.
Unit IV: Introduction to Sequential Logic Circuits
Classification of Sequential Circuits, Basic Sequential Logic Circuits: Latch and Flip-Flop, RS-
Latch Using NAND and NOR Gates, Truth Tables. RS,JK,T and D Flip Flops , Truth and
Excitation Tables, Conversion of Flip Flops. Flip Flops With Asynchronous Inputs (Preset and
Clear).
Unit V: Registers and Counters
Design of Registers, Buffer Register, Control Buffer Registers, Bidirectional Shift Registers,
Universal ShiftRegister, Design of Ripple Counters, Synchronous Counters and Variable
Modulus Counters, Ring Counter,Johnson Counter.
Unit VI: Introduction to Programmable Logic Devices (PLD’s)
PLA, PAL, PROM. Realization of Switching Functions Using PROM, PAL and PLA. Comparison
of PLA,PAL and PROM..
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INTRODUCTION :
In the modern world of electronic, the term Digital is generally associated with a computer
because the term Digital is derived from the way computers perform operation, by counting
digits. For many years, the application of digital electronics was only in the computer
system. But now-a-days, the digital electronic is used in many other applications. Following
are some of the examples in which Digital electronics is heavily used.
Industrial process control
Military system
TV games
Communication system
Medical equipment
Radar
Navigation
Calculators
Digital watches
Clocks
E-governance
E-banking,
Internet
Household appliances (Ex: Washing machines, refrigerators, digital TVs)
Computers
The music that we listen to on our CD players or iPods, the individuals dots on a computer
screen, new digital TVs and most cell phone signals are coded into strings of binary digits.
Signal
Signal can be defined as a physical quantity, which contains some information. It is a
function of one or more than one independent variables. Signal are of two types.
Analog Signal
Digital Signal
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Analog Signal
An analog signal is defined as the signal having continuous values. Analog signal can have
infinite number of different values. In real world scenario, most of the things observed in
nature are analog. Examples of the analog signals are following.
Temperature
Pressure
Distance
Sound
Voltage
Current
Power
Graphical representation of Analog Signal (Temperature)
The circuits that process the analog signals are called as analog circuits or system. Examples
of the analog system are following.
Filter
Amplifiers
Television receiver
motor speed controller
Disadvantage of the Analog Systems
Less accuracy
More noise effect
More distortion
More effect of weather
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Digital Signal
A digital signal is defined as the signal which has only a finite number of distinct values.
Digital signal are not continuous signal. In the digital electronic calculator, the input is given
with the help of switches. This input is converted into electrical signal which having two
discrete values or levels. One of these may be called low level and another is called high
level. The signal will always be one of the two levels. This type of signal is called digital
signal. Examples of the digital signal are following.
Binary Signal
Octal Signal
Hexadecimal Signal
Graphical representation of the Digital Signal (Binary)
The circuit that process that digital signal are called digital system or digital circuit. Examples
of the digital system are following.
Registers
Flip-flop
Counters
Microprocessors
With a digital signal, we are using an analog signal to transmit numbers, which weconvert
into bits and then transmit the bits.A digital signal uses some physical property, such as
voltage, to transmit a single bitof information.
Suppose we want to transmit the number 6. In binary, that number is 110. We firstdecide
that, say, "high" means1 and "low" means 0. Thus, 6 might look like:
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The line is the signal, which rises to the maximum to indicate a 1 and falls to theminimum to
indicate a 0.
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Unit I
Binary, Octal, Decimal, Hexadecimal Number Systems. Conversion of Numbers from One
Radix to Another Radix, r’s Complement and (r-1)’s Complement Subtraction of Unsigned
Numbers, Problems, Signed Binary Numbers, Weighted and Non weighted codes.
NUMBER SYSTEMS:
In general, in any number system there is an ordered set of symbols known as digitals with
rules defined for performing arithmetic operations like addition, multiplication, etc. A
collection of these digits makes a number which in general has two parts. They are integer
and fractional, set apart by a radix point (.), that is
Where N= a number
b= radix or base of the number system
n= number of digits in integer portion
m= number of digits in fractional portion
dn-1= most significant digit (msd)
d-m= least significant digit (lsd)
The digits in a number are placed side by side and each position in the number is assigned a
weight or index of importance by some predesigned rule.
When we type some letters or words, the computer translates them in numbers as
computers can understand only numbers.
A computer can understand positional number system where there are only a few symbols
called digits and these symbols represent different values depending on the position they
occupy in the number.
A value of each digit in a number can be determined using:
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The digit
The position of the digit in the number
The base of the number system (where base is defined as the total number of digits available
in the number system).
As a computer programmer or an IT professional, you should understand the following
number systems, which are frequently used in computers.
Classification of Number systems:
The Number systems is mainly classified into four types:
1. Binary 2.Octal 3.Decimal and 4. Hexadecimal.
Characteristics of number systems:
Binary Number System
Characteristics ->
Uses two digits, 0 and 1.
Also called base2 number system.
Each position in a binary number represents a 0 power of the base (2). Example, 20.
Last position in a binary number represents a x power of the base (2). Example, 2 x where x
represents the last position - 1.
EXAMPLE:
Binary Number: 101012
Calculating Decimal Equivalent:
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Step Binary Number Decimal Number
Step 1 101012 ((1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10
Step 2 101012 (16 + 0 + 4 + 0 + 1)10
Step 3 101012 2110
Note: 101012 is normally written as 10101.
Binary Number &Corresponding decimal, octal &hexa decimal numbers:
(i) 2- bit binary number(2n):
2n = 22=4 So, we have 4 combinations
Hexadecimal
Binary number Decimal number octal
number
00 0 0 0
01 1 1 1
10 2 2 2
11 3 3 3
(ii) 3- bit binary number(2n):
2n=23=8 So, we have 8 combinations.
Hexadecimal
Binary number Decimal number octal
number
000 0 0 0
001 1 1 1
010 2 2 2
011 3 3 3
100 4 4 4
101 5 5 5
110 6 6 6
111 7 7 7
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(iii) 4- bit binary number(2n):
2n = 24=16 So, we have 16 combinations.
Hexadecimal
Binary number Decimal number octal
number
0000 0 0 0
0001 1 1 1
0010 2 2 2
0011 3 3 3
0100 4 4 4
0101 5 5 5
0110 6 6 6
0111 7 7 7
1000 8 8 10
1001 9 9 11
1010 10 A 12
1011 11 B 13
1100 12 C 14
1101 13 D 15
1110 14 E 16
1111 15 F 17
Octal Number System
Characteristics
Uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7.
Also called base 8 number system.
Each position in a octal number represents a 0 power of the base (8). Example, 8 0.
Last position in a octal number represents a x power of the base (8). Example, 8x where x
represents the last position - 1.
EXAMPLE
Octal Number: 125708
Calculating Decimal Equivalent:
Step Octal Number Decimal Number
Step 1 125708 ((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10
Step 2 125708 (4096 + 1024 + 320 + 56 + 0)10
Step 3 125708 549610
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Note: 125708 is normally written as 12570.
Decimal Number System
The number system that we use in our day-to-day life is the decimal number system.
Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number
system, the successive positions to the left of the decimal point represent units, tens,
hundreds, thousands and so on.
Each position represents a specific power of the base (10). For example, the decimal number
1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds
position, and 1 in the thousands position, and its value can be written as
(1x1000)+ (2x100)+ (3x10)+ (4xl)
(1x103)+ (2x102)+ (3x101)+ (4xl00)
1000 + 200 + 30 + 4
1234
CODES:-
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Weighted codes:
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