The document defines number systems as a method of expressing numbers mathematically using a set of symbols or digits. It covers four main types: decimal (base-10), binary (base-2), octal (base-8), and hexadecimal (base-16), explaining their applications in daily life and computing. Each type serves unique purposes, with binary used in computer architecture and hexadecimal in color representation in digital applications.

1. NUMBER
SYSTEM

2. PRESENTED BY
1. ANIRBAN SAHA ANIK 18-36207-1
2. BISHOWJIT DATTA 18-37372-1
3. ZUBAER HOSSAIN ASIF 18-36248-1
4. LUTFA NOOR LABONY 18-36187-1
Submitted to : SYED MD. ANWARUL
ISLAM

3. WHAT IS NUMBER SYSTEM ?
A number system is defined as a system of writing to express numbers. It is the
mathematical notation for representing numbers of a given set by using digits
or other symbols in a consistent manner. It provides a unique representation of
every number and represents the arithmetic and algebraic structure of the
figures. It also allows us to operate arithmetic operations like addition,
subtraction and division.
The value of any digit in a number can be determined by:
• The digit
• Its position in the number
• The base of the number system
Types of Number System:
There are various types of number system in mathematics. The four most
common number system types are:
•Decimal number system (Base- 10)
•Binary number system (Base- 2)
•Octal number system (Base-8)
•Hexadecimal number system (Base- 16)

5. DECIMAL
NUMBER
SYSTEMS

6. In algebra, a decimal number can be defined as a number whose
whole number part and the fractional part is separated by a
decimal point. The dot in a decimal number is called a decimal
point. The digits following the decimal point show a value smaller
than one.
Example: The numbers we use in everyday life are decimal
numbers, because they are based on 10 digits
(0,1,2,3,4,5,6,7,8 and 9)
DECIMAL
NUMBER

7. Applications Of Decimal In Daily Life:
We use decimals every day while dealing with money, weight, length etc.
Decimal numbers are used in situations where more precision is required
than the whole numbers can provide. For example, when we calculate our
weight on the weighing machine, we do not always find the weight equal to
a whole number on the scale. To know our exact weight, we must
understand what the decimal value on the scale means. This section deals
with the concept of decimals in three important fields of our daily life.

8. Use of decimal to Represent the weight: We use decimal numbers while dealing
with weight. For example, when we are buying a watermelon, it cannot always
weigh in whole numbers, it can be less than 2 kg but more than 1 kg. In such
situations, the shopkeeper has to calculate how much to charge for a
watermelon, based on its weight. As we know,
1 kg = 1000 gm
1 gm = 1000 mg
Now suppose it is 1 kg and 750 gm. Then, he will charge as per the price of 1
kg + (750/1000) kg of the watermelon. We will learn more about the conversion
of weight into decimal from the following examples:
Example 1: Converting 250 gm to kg As we know,
1000 gm = 1 kg
So, 1 gm = 1/1000 kg
250 gm = 250 × (1/1000) kg = 250/1000 kg = 0.250 kg

9. BINARY NUMBER
SYSTEM

10. BINARY
NUMBERIn mathematics and digital electronics, a binary number is a number
expressed in the base-2 numeral system or binary numeral system, which
uses only two symbols: typically "0" (zero) and "1" (one). Each digit is
referred to as a bit.
Example: 0 1 1 0 is a binary number and the decimal value is 6.

11. BITS AND BINARY
COMPUTERS USE BINARY - THE DIGITS 0 AND 1 -
TO STORE DATA. A BINARY DIGIT, OR BIT, IS THE
SMALLEST UNIT OF DATA IN COMPUTING.
THE CIRCUITS IN A COMPUTER'S PROCESSOR ARE
MADE UP OF BILLIONS OF TRANSISTORS. A
TRANSISTOR IS A TINY SWITCH THAT IS ACTIVATED
BY THE ELECTRONIC SIGNALS IT RECEIVES. THE
DIGITS 1 AND 0 USED IN BINARY REFLECT THE ON
AND OFF STATES OF A TRANSISTOR.
COMPUTER PROGRAMS ARE SETS OF
INSTRUCTIONS. EACH INSTRUCTION IS
TRANSLATED INTO MACHINE CODE - SIMPLE
BINARY CODES THAT ACTIVATE THE CPU.

12. Binary coded decimal (BCD)
Binary codded decimal is simply another way in which denary numbers can be written as binary.
It simply details splitting up a binary number into equal portions of bits. So an 8 bit binary
number may be split in half as shown below.
00111000
0011 1000
3 8
Binary coded decimal would be 3 8
this method is widely used in clocks as with the one shown :

13. BINARY & THE INTERNET
PROTOCOLAs explained during the introduction, computers display the zeros and
ones in a way that makes the information useful to us. The Internet
Protocol works a bit like this as well, where 98% of the time we see it in
a decimal notation, but the computer understands it in binary. The
picture below gives you an example of how a computer understands an
IP Address:
The above example shows an IP address in decimal notation,
which we understand more easily, this IP Address - 192.168.0.1 is
then converted to Binary, which is what the computer understands
and you can see how big the number gets ! It's easier for us to
remember 4 different numbers than 32 zeros or ones !

14. OCTAL
NUMBER
SYSTEM

15. OCTAL NUMBER
The number system whose base is 8 is known as the octal
number system. The base 8 means the system uses eight
digits from 0 to 7.
Example : Consider the octal number 354.42 into its equivalent
decimal number. The integer part 354 converts to octal shown below
3(82)+5(81)+4(80)=236

16. Octal used to be used widely within IT basically how
hexadecimal is used today. It was used as an ideal
abbreviation of binary because the bit size (amount of
bits that could be handled at one go) of the CPUs that
were used at the time that being 26 and 36 bit. After
CPUs converted to bit sizes of 32 and 64 bit octal was no
longer utilized because, though both are still dividable by
8 they can also be divided by 16 which is far more
efficient. There are some places however where octal is
still widely utilized including within file permissions within
unix (the source code for linux, mac os and android along
with other operating systems) to avoid having to add
support for symbols for hexadecimal. It is also used
within digital displays that also have no support for
symbols.
Use of The Octal Number System in
Computer System

17. All modern computers use binary for their internal storage.
This is due to the ease the hardware can represent binary
values (on or off). However humans have issues dealing with
large strings of binary numbers. For example, the number
128 decimal is 10000000 in binary. Larger numbers get even
harder to deal with (for humans). However if binary numbers
are grouped in groups of 3, then it is easy to view the
numbers in octal. Or groups of 4 make hexadecimal
numbers. So 128 decimal is 200 octal or 80 hex. It’s all the
same number but the larger bases make it easier for humans
to use.
Octal Used for Easier Human
Understanding

18. OCTAL USED IN MINICOMPUTERSIn early days octal number system was mostly used in
minicomputers. The word “OCT” means eight. The octal number
system says that it is a number system of base 8 which means
that we require 8 different symbols in order to represent any
number in octal system. The symbols are 0, 1, 2, 3, 4, 5, 6, and
7. The smallest two digits number in this system is (10)8 which
is equivalent to decimal 8.
For example in this number system, the number is written as
(352)8. The base should be written as 8 otherwise the number is
assumed to be in decimal number system by default. So this
thing needs to be taken care of in writing the number. A little
error may result in the change in number system base. The
main advantage of using octal number system is that it can be
converted directly to binary in a very easy manner. As we know,
the computer understands only the binary number system. so
the conversion from binary to octal or from octal to binary is
quite easier so this number system is used.

19. HEXADECIMAL
NUMBER SYSTEM

20. HEXADECIMAL
NUMBER
In mathematics and computing, hexadecimal (also base 16, or hex)
is a positional system that represents numbers using a base of 16.
Unlike the common way of representing numbers with ten
symbols, it uses sixteen distinct symbols, most often the symbols
"0"–"9" to represent values zero to nine, and "A"–"F" (or
alternatively "a"–"f") to represent values ten to fifteen. The
hexadecimal numeral system, often shortened to "hex.
Example : The Decimal number of 16,295 can be represented as:-
#3FA716 ( in Hexadecimal )

21. USE OF HEXADECIMAL IN IT
APPLICATIONS
Hexadecimal is also used within digital applications
for a range of separate applications. One use of the
hexadecimal number system within computer
architecture is within RAM (Randomly access memory)
within which each memory location (section of
memory) being addressed (represented) with a
hexadecimal number. Each hexadecimal digit
represents a "nibble," which is half of a byte (4 bits),
this means that bytes can also be represented in
hexadecimal going from 0 (00) to 255 (FF) instead of
just being represented in binary which can be harder
to understand. Another location within digital
applications where the hexadecimal number system is
used is within the web safe color pallet shown:

22. HTML / CSS COLOR CODES
Hexadecimal numbers are often used to represent color
within HTML or CSS.
The 6 digits hex color code should be considered in
three parts. First two digits represents the amount of red
in the color (max FF, or 255) The next two digits
represent the amount of green in the color (max FF, or
255) The final two digits represent the amount of blue in
the color (max FF, or 255)
By changing the intensities of red, green and blue, we
can create almost any color.
Example : orange can be represented as #FFA500, which
is (255 red, 165 green, 0 blue).

23. CONCLUSION
The number system is simply a system to represent or express
numbers. There are various types of number systems and the most
commonly used ones are decimal number system, binary number
system, octal number system, and hexadecimal number system.
Number system helps to represent numbers in a small symbol set.
Computers, in general, use binary numbers 0 and 1 to keep the
calculations simple and to keep the amount of necessary circuitry
less, which results in the least amount of space, energy
consumption and cost.