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MKT2802 Logic Circuits
Mechatronics Engineering Department

Spring : 2023

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Logic Circuits

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Digital Codes
Coding is the process of altering the characteristics of information to make it
more suitable for intended application
Coding schemes depend on
 Security requirements
 Complexity of the medium of transmission
 Levels of error tolerated
 Need for standardization
Information is coded to facilitate

When numbers, letters, or
words are represented by a
special group of symbols, we
say that they are being
encoded, and the group of
symbols is called a code
...


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Binary Codes : Binary coded decimal codes (BCD)

Since a decimal digit
can be as large as 9,
four bits are required
to code each digit
(the binary code for 9
is 1001)
...


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Comparison of BCD and binary
 It is important to realize that BCD is not another number system like
binary, decimal, and hexadecimal
...
It is also important to understand that a BCD number is not the
same as a straight binary number
...
To illustrate, take the number 137 and compare its straight
binary and BCD codes:

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The Gray Code
 Digital systems operate at very fast speeds and respond to changes that
occur in the digital inputs
...

 In order to reduce the likelihood of a digital circuit misinterpreting a
changing input, the Gray code has been developed as a way to represent
a sequence of numbers
...


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The Gray Code

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The Gray Code Conversion

SAME  0
DIFFERENT 1

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The Gray Code Conversion

SAME  0
DIFFERENT 1

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Excess-3 (+3) Coding
In excess-3 coding, digit codes is obtained from their binary equivalent after adding 3
...

 The major cause of any transmission errors is electrical noise, which consists of
spurious fluctuations in voltage or current that are present in all electronic systems
to varying degrees
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Parity Method for Error Detection

 A parity bit provides for the detection of a single bit error (or any odd number of
errors, which is very unlikely) but cannot check for two errors in one group
let’s assume that we wish to transmit the
BCD code 0101

Now let’s assume that an error occurs
in the third bit from the left (the 1
becomes a 0)
...
Because an
even number of 1s does not appear in the code when it is received, an error is
indicated
...
In other words, a computer should recognize codes that represent letters of
the alphabet, punctuation marks, and other special characters as well as numbers
...

The most widely used alphanumeric code is the American Standard Code for
information interchange (ASCII)
...
(0↔127)

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Arithmetic Operations on Binary Numbers

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Arithmetic Operations on Binary Numbers

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Arithmetic Operations on Binary Numbers

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Complement Representation

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Complement Representation

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Complement Representation

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Complement Arithmetic

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Complement Arithmetic

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Complement Arithmetic

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Complement Arithmetic

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1’s-Complement Form
The 1’s complement of a binary number is obtained by changing each 0 to a
1 and each 1 to a 0
...
The process is shown below
...

The process is illustrated below for (101101)2 = (45)10

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