Grop-to-Binory tonversion
The gray to binary code conversion can be achieved using following steps.
1. The most signicant bit of the binary number is the same as the most
significant bit of the gray code number. So'write it down.
2. To obtain the next bin
Locations of the Purity Bits In the Code
Now we lmow that how to calculate the number of parity bits required to provide
single error correction for given number of information bits. In our example we have
tour information bits and three parity bits. Ther
1.1 introduction
Number system is a basis for counting various items. Cln hearing the word
'number, ail of us immediately think of the familiar decimal number system with its
iii digits : U, i, 2, 3, 4, 5, ti, '5', El and 9.
Modern computers communicate a
linear Block Codes
Block tildes are net i'IJtscessair'iI,I linear, but general all black codes used in practice
are linear. A linear bis-ck cede consists at it message bits and :- check bits. These r
check bits are derived from the original 1". message bi
Rules In Boolean Algebra
1. The symbol which represent an arbitrary elements of an Boolean algiebra Is
known as variable. Any single variable or a function of several variables
can have either a 1 or 0 value. For example, in expression Y = A + BC,
' varia
Successive Ilultiplication for Fractional Pan Conversion
Conversion of fractional decimal numbers to another radix number is
accomplished using a successive multiplication method. in this method. the number to
be converted is multiplied by the radix of th
Error 'Correction
it is assumed that the codingfdecoding system has been designed to correct single
error only. in order to correct the codeword we multiplyr received codeword with
transpose of parity-check matrix to get syndrome. Then result of RHT, i.e.
Rulel: =:. 1+A=1oro+1=1
1 + = 1
Fifi-
.rr!
RIMS: L: :5 A+A=A
',._.;._.-.r.]
+ 1
Ruled: = A+I=1orI+A=1 _
+ 1
I5. The logical AND operator in the Boolean algebra with variables having
value either a U or a 1 gives following results.
[I - U = D 1 - = D
D -
Detecting and Correcting on Error
in the last section we have seen how to construct Hamming code for given
number oi information bits. Now we will see how to use it to locate and correct an
error. To do this. ead'r parity bit. along with its corresponding
Generalized Steps for Censtructien ef Cede
1. Construct G matrix as
G = [1k Ell"ll h. u n
1where ls : liientitjir matrix of order k
A : iiirttit'rar,Ir matrix
[e1.cz.en]=[e1.a2.ak] oo1.o manning
MnVFI-il W .
n -oode hits I-t- message bits
2. Determine at]
Hexadecimal Number System
The hexadecimal number system has a base of us having 16 digits : ill. 1. 2. 3, s, 5,
6, if. 3. 9. a. B. C. D. E and F. It is another number system that is particularly useful
for human communications with a computer. Although it
UNIT-V
Sl
No.
1
Module
Outcomes
Able to identify capabilities and limitations of finite
state machine
Able to know Mealy and Moore minimization
models
Able to know partition techniques and merger chart
methods
Able to know about concept of minimal cover t
Detecting and Correcting on Error
in the last section we have seen how to construct Hamming code for given
number oi information bits. Now we will see how to use it to locate and correct an
error. To do this. ead'r parity bit. along with its corresponding
7. The NOT operator in the Boolean algebra with variable having value either
a 0 or a 1 gives following results.
O=l=o
T = Cl = 1
From the previous result following rule is dened in Boolean algebra
3'!
Rule 9 :
laws of Boolean Algebra
Three of the basic
Matrix Representation of linear Block Codes
In this method, matrices are used to encode the massage. Now before going to see
generalized equations for matrix encoding we will see the illustration of matrix
encoding with the help of example.
Let us assume
10001000
+1
add
10001001
That is 10001001 2 = - 119 10
1
Properties of Two's Complement Numbers
1.
X plus the complement of X equals 0.
2.
There is one unique 0.
3.
Positive numbers have 0 as their leading bit ( MSB ); while negatives have 1 as their MSB
UNIT-II
GATE LEVEL MINIMIZATION
Karnaugh Maps
Karnaugh maps provide a systematic method to obtain simplified sum-of-products (SOPs)
Boolean expressions. This is a compact way of representing a truth table and is a technique
that is used to simplify logic
UNIT-V
Sl
No.
1
Module
Outcomes
Able to identify capabilities and limitations of finite
state machine
Able to know Mealy and Moore minimization
models
Able to know partition techniques and merger chart
methods
Able to know about concept of minimal cover t
3. Vision of EEE
To provide excellent Electrical and electronics education by building strong teaching and research environment
4. Mission of EEE
To offer high quality graduate program in Electrical and Electronics education and to prepare students for
pr
SWITCHING THEORY AND LOGIC DESIGN
COURSEFILE
Coursefile contents:
1. Cover Page
2. Syllabus copy
3. Vision of the department
4. Mission of the department
5. PEOs and POs
6. Course objectives and outcomes
7. Brief note on the importance of the course and h
Locations of the Purity Bits In the Code
Now we lmow that how to calculate the number of parity bits required to provide
single error correction for given number of information bits. In our example we have
tour information bits and three parity bits. Ther