Information Science in Action Week 3 Codes

Information Science in Action
Week 3: Codes
Spring 2024
Valentinus Roby HANANTO
College of Information Science and Engineering
Ritsumeikan University

2
Today’s class outline
l Previous lecture overview
– Number systems: decimal, binary, octal, hexadecimal
– Binary arithmetic: addition, subtraction, multiplication,
division
l BSD code
l Gray code
l Hamming code
l ASCII code

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l Digital circuits use binary signals but are required
to handle data which may be alphabetic, numeric,
or special characters.
l Hence the signals that are available in some other
form other than binary have to be converted into
suitable binary form before they can be processed
further by digital circuits.
l To achieve this, a process of coding is required
where each letter, special character, or numeral is
coded in a unique combination of 0s and 1s using
a coding scheme known as code.
Introduction

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l In digital systems a variety of codes are used to
serve different purposes, such as data entry,
arithmetic operation, error detection and
correction, etc.
l Selection of a particular code depends on the
requirement.
l Even in a single digital system a number of
different codes may be used for different
operations, and it may even be necessary to
convert data from one type of code to another.
Introduction

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l The full form of BCD is ‘Binary-Coded Decimal.’
Since this is a coding scheme relating decimal
and binary numbers, four bits are required to code
each decimal number.
l For example, (35)10 is represented as 0011 0101
using BCD code, rather than (100011)2.
l From the example it is clear that it requires a
greater number of bits to code a decimal number
using BCD code than using the straight binary
code.
l However, in spite of this disadvantage it is
convenient to use BCD code for input and output
operations in digital systems.
Binary coding: BCD

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l I/O equipment of modern computers mostly deals
with decimal digits, while computing is realized in
binary codes.
l The easiest way is to code each decimal digit
separately by a binary equivalent, e.g.
l The above coding is called as binary-coded-
decimal (BCD)
Binary coding: BCD

9
l BCD: 8-4-2-1
l 6-3-1-1
6-3-1-1

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l BCD: 8-4-2-1
l 6-3-1-1
l Excess-3: BCD plus 3 to each code
Excess-3

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l BCD: 8-4-2-1
l 6-3-1-1
l Excess-3: BCD plus 3 to each code
Excess-3

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l Gray code belongs to a class of code known
as minimum change code, in which a number
changes by only one bit as it proceeds from
one number to the next.
l Hence this code is not useful for arithmetic
operations. This code finds extensive use for
position encoders to minimize errors.
Gray code

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l Convert binary to gray code
– Gray code belongs to a class of code known as
minimum change code
– the MSB of the Gray code is the same as the
MSB of the binary number
– the second bit next to the MSB of the Gray code
equals the Ex-OR of the MSB and second bit of
the binary number; it will be 0 if there are same
binary bits or it will be 1 for different binary bits;
– the third bit for Gray code equals the exclusive-
OR of the second and third bits of the binary
number, and similarly all the next lower order bits
follow the same mechanism.
Gray code
0⊕0=0，1⊕0=1，0⊕1=1，1⊕1=0

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l Convert gray code to binary
– the MSB of the binary number is the same as the
MSB of the Gray code;
– the second bit next to the MSB of the binary
number equals the Ex-OR of the MSB of the
binary number and second bit of the Gray code; it
will be 0 if there are same binary bits or it will be 1
for different binary bits;
– the third bit for the binary number equals the
exclusive-OR of the second bit of the binary
number and third bit of the Gray code, and
similarly all the next lower order bits follow the
same mechanism.
Gray code

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l Data can be corrupted during transmission. For
reliable communication, errors must be detected and
corrected.
l Developed by R. W. Hamming where one or more
parity bits are added to a data character
methodically in order to detect and correct errors.
Hamming code

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Hamming code
l Encoding: from binary to Hamming code

l Decoding: from Hamming code to binary
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Hamming code

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l ASCII : American Standard Code for Information
Interchange
l We need to code not only digits, but also symbols,
letters, signs
l Originally, 7-bit code (128 symbols can be coded),
fragment of code:
ASCII code

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l BCD: 8-4-2-1
l 6-3-1-1
l Excess-3 : BCD plus 3 to each code
l Gray code
l Hamming code
l ASCII code
Summary

30
l Basic Boolean operators
–NOT, AND, OR
l Boolean functions
l DeMorgan's theorem
l Logic gates
Next class

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