Chapter 4 number system

CHAPTER – 02
NUMBER SYSTEM
Unit 1
Computer Systems and Organisation
(CSO)
XI
Computer Science (083)
Board : CBSE

Unit I
Computer Systems and Organisation (CSO)
(10 Theory + 02 Practical)
DCSc & Engg, PGDCA,ADCA,MCA.MSc(IT),Mtech(IT),MPhil (Comp. Sci)
Department of Computer Science, Sainik School Amaravathinagar
Cell No: 9431453730
Praveen M Jigajinni
Prepared by
Courtesy CBSE

INTRODUCTION
"A set of values used to represent different
quantities is known as “Number System". For
example, a number system can be used to
represent the number of students in a class or
number of viewers watching a certain TV
program etc. The digital computer represents
all kinds of data and information in binary
numbers. It includes audio, graphics, video, text
and numbers. The total number of digits used in
a number system is called its base or radix. The
base is written after the number as subscript
such as 51210.

TYPES OF NUMBER SYSTEMS
1. BINARY NUMBER SYSTEM
2. OCTAL NUMBER SYSTEM
3. DECIMAL NUMBER SYSTEM
4. HEXA DECIMAL NUMBER SYSTEM

BINARY NUMBER SYSTEM
The binary number system is a
numbering system that represents numeric
values using two unique digits (0 and 1). Most
computing devices use binary numbering to
represent electronic circuit voltage state, (i.e.,
on/off switch), which considers 0 voltage
input as off and 1 input as on.

BINARY NUMBER SYSTEM ADVANTAGES

1. Binary is extremely simple to
implement. Any system that has an "on"
and "off" or "high" and "low" state can be
used to encode and/or manipulate data.
2. Binary is the lowest "base" possible (base
2) and hence any higher counting system
can be easily encoded (e.g. decimal, octal,
hexadecimal, etc.)

3. Binary would be the most effective way to
attempt to communicate with any type of
alien civilization. Just as "math" is a type of
universal language (any alien civilization
would understand a sequence of prime
numbers, for example) binary is a universal
alphabet.

4. Binary data is extremely robust in
transmission because any noise tends to be
neither fully "on" or "off" and is easy to
reject.
5. Binary would be the most effective way to
attempt to communicate with any type of alien
civilization. Just as "math" is a type of universal
language (any alien civilization would
understand a sequence of prime numbers, for
example) binary is a universal alphabet.

APPLICATIONS OF BINARY NUMBER SYSTEM

1. The most common application for the binary
number system can be found in computer
technology.
2. Digital encoding is the process of taking data
and representing it with discreet bits of
information. These discreet bits consist of
the 0s and 1s of the binary system.
For example, the images you see on your
computer screen have been encoded with a
binary line for each pixel.

If a screen is using a 16-bit code, then each
pixel has been told what color to display
based on which bits are 0s and which bits
are 1s. As a result, 2^16 represents 65,536
different colors!
3. We also find the binary number system in a
branch of mathematics known as
Boolean Algebra.

BINARY REPRESENTATION OF INTEGER

1.Sign and magnitude representation is the
conventional form of number system. It is
represented as signs ( + or - ).
2.One,s complement represents positive
numbers by their binary equivalent called
true value.
3.Two complement representation represents
their binary equivalent numbers and
negative numbers by their second
compliment form.

 Real numbers are represented in storage
medium by their exponents and mantissa.
For example numbers 32.17 can be written
as 0.3217*102, 0.3217is its mantissa and 2
is its exponent.

MORE ON BINARY NUMBER SYSTEM
Binary is the language of
computers. Everything you type, input,
output, send, retrieve, draw, paint, or
place blame on when something
doesn't work is, in the end, converted to
the computer's native language- binary.
A single binary 1 or a single binary
0 is called a bit, which is short for
"binary digit".

Four bit binary number is called nibble
1 0 1 0
Eight bits together makes most used
computer term byte A single byte can
represent the decimal values 0 to 255 (256
distinct values)
1 0 1 0 1 1 0 1

Place a couple of bytes together to
represent a single value and you have a 16-bit
word (2 bytes = 16- bits). A 16-bit word can
represent the values 0 to 65535 (65536 distinct
values).
1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1
32-bit words are 4 bytes in length. They can
represent a value from 0 to 4,294,967,295
(4,294,967,296 distinct values)

BINARY TO DECIMAL
Example binary number: 10001010
Binary representation of decimal 138.
Now, look at those numbers above the
boxes with the red 1s and 0s. Those are decimal
numbers representing powers of 2.

BINARY TO DECIMAL
These are the values that are above the
boxes. Now the actual binary number itself
consists of 1s and 0s in the blue boxes which
somehow magically represents the decimal
number 138. How do we get 138 from
10001010? In the binary number when you see
a 1, multiply that 1 times the value that is
directly over it. Where you see a 0 in the box,
just ignore it.

Black board Teaching - Various (From & to)
Binary number conversion techniques.

OCTAL NUMBER SYSTEM
Octal was widely used some 50 years
ago by Digital Equipment Corp. (DEC) and
other companies that had computers
with a 12-bit word (e.g. the PDP-8) or
other multiples of six, such as 18 and 36
(e.g. UNIVAC 1108). I used both the PDP-
8 and UNIVAC 1108 in grad school.
Characters in both machines typically
used six bits, not 8.

OCTAL NUMBER SYSTEM
According to Wikipedia, octals aren't
as common as they used to be. As others
have already mentioned, in the past,
systems used to have a 12/24/36-bit
word, which is more easily represented in
octal than hexadecimal, but currently, the
x86 and i64 architectures use a 16/32/64
bit word, which is more easily
represented in hexadecimal and
downright ugly in octal.

OCTAL NUMBER SYSTEM APPLICATIONS

1. Octal is used less these days, but C’s
standard IO functions allow specifying
characters that way.
2. Representation of IP addresses (rare,
sometimes used by spammers to obscure
addresses). Microsoft accepts octal IP
numbers for Ping and FTP.
3. Representation of UTF8 numbers (any
start byte is 3nn and any continuation
byte 2nn).

4. "Real" real-world use: the Yuki people
and in the native Mexican Pamean languages
use octal counting because they count the
spaces between their fingers
5. Historically in the 1950's, one of the
oldest debuggers, UT-3 for the TX-0
computer at MIT (an 18-bit system), could
only be operated by using commands
written in octal notation.

6. TAR files store some information in
octal representation.
7. When fields are naturally divided
into three or six bits, octal
representation comes in handy .
8. Integers, but also fractions on the
Honeywell and other legacy systems
were represented as octal.

9. A whole lot of legacy (CDC machines,
DEC PDP-8 etc), because they used multiples
of 3 bits, like 6-bit or 12-bit word sizes.
10. In 1971, octal numbers were proposed
to replace the decimal system.
11. And finally, most trivially: you use it
almost everyday when you write down the
number 0 in some programming language
that supports octals.

12. Codes squawked by Mode 3A
transponders in airplanes.
13. Key codes in the ncurses library
(ncurses (new curses) is a programming
library providing an application
programming interface(API) that allows
the programmer to write text-based
user interfaces in a terminal-
independent manner. It is a toolkit for
developing …

"GUI-like" application software that runs
under a terminal emulator. It also
optimizes screen changes, in order to
reduce the latency experienced when
using remote shells.)

HEXA DECIMAL NUMBER SYSTEM
Ah, hexadecimal. If you've ever
worked with colors in web page design,
you've proably seen something like ' or
something to that effect. Somehow, that 6
digit hexadecimal number is equal to a
lavender or light purple color. What on
earth does 'A09CF3' mean? Before we
explain that, let's look at what
hexadecimal (hex) is.

Our decimal system, as mentioned in
my Binary Tutorial, is a base-10 system,
meaning we can count to any number in
the universe using only 10 symbols or
digits, 0 thru 9. For the computer, a 10-
based system probably isn't the most
efficient system, so the computer uses
binary (in reality, it uses microscopic
switches which are either on or off, but we
represent them using the digits '1' and '0').

Unfortunately, binary isn't very efficient
for humans, so to sort of find a happy
middle ground, programmers came up
with hexadecimal. Hexadecimal is a base-
16 number format (hex=6, decimal=10).
This means that instead of having only the
digits from '0' to '9' to work with like our
familiar decimal, or '1' and '0' like binary,
we have the digits '0' to '15'.

It also means that we are using the powers
of 16, instead of the powers of 2 like in
binary
As soon as you count over 9 in hex, new
digits take over. A=10, B=11, C=12, D=13, E=14
and F=15.

0x0F In fact, the '0x' in front of a hex
number is more current than the '$'. The
'$' is sort of old school. Whether you use a
'$' or a '0x', it tells you that you're working
with a hex number, not a decimal

HEXA DECIMAL NUMBER SYSTEM APPLICATIONS

1. To define locations in memory. Hexadecimals
can characterise every byte as two hexadecimal
digits only compared to eight digits when using
binary.
2. To define colours on web pages. Each primary
colour – red, green and blue is characterised by
two hexadecimal digits. The format being used
is #RRGGBB. RR stands for red, GG stands for
green and BB stands for blue.

3. To represent Media Access Control (MAC)
addresses. MAC addresses consist of 12-digit
hexadecimal numbers. The format being used is
either MM:MM:MM:SS:SS:SS or MMMM-MMSS-
SSSS. The first 6 digits of the MAC address
represent the ID of the adapter manufacturer
while the last 6 digits represent the serial number
of the adapter.
4. To display error messages. Hexadecimals are
used to define the memory location of the
error. This is useful for programmers in finding
and fixing errors.

The American Standard Code for
Information Interchange (ASCII) is a
character-encoding scheme originally based
on the English alphabet. ASCII codes
represent text in computers,
communications equipment, and other
devices that use text. Most modern
character-encoding schemes are based on
ASCII, though they support many more
characters than ASCII does.
ASCII

ISCII
In recent past the computer activities
were limited to specific languages and with
the increase in works there was to be
develop a slandered code . In 1991, the
bureau of Indian standard develop common
code called ISCII. this is a 8-bit code capable
of coding 256 characters.

UNICODE
 Unicode provides a unique number for every
character,
 No matter what the platform
 No matter what the program.
 No matter what the language.
INDIAN LANGUAGES ON UNICODE
The standard has incorporated Indian
scripts under group name Asian scripts ,
includes Devnagari , Bengali ,Tamil ,Malayalam.

CLASS TEST
1. Write a note on ASCII 05
2. Write a note on Unicode 05
3. Convert the following 10
(i) (1111000)2 = (?) 10
(ii) (234)10 = (?)8
(iii) (564)8 = (?)16
(iv) (AA)16 = (?)10
(v) (555)8 = (?)2
Time: 40 Min Max Marks 20

Chapter 4 number system

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