Name: Imtiaz Ahmad
Sap ID: 57905
Semester No: 01
Department: BS Software Engineering
Instructor: Mr. Riaz Ul Haq
Assignment No: 02
Question 01: What is Number System in Computer and its types.
Question 02: Write there Conversions with examples .
Number System
Number System:
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.
Types of Number System
There are various types of number systems in mathematics. The four most common number system
types are:
1. Decimal number system (Base- 10)
2. Binary number system (Base- 2)
3. Octal number system (Base-8)
4. Hexadecimal number system (Base- 16)
Now, let us discuss the different types of number systems with examples.
Decimal Number System (Base 10 Number System)
The decimal number system has a base of 10 because it uses ten digits from 0 to 9. In the decimal
number system, the positions successive to the left of the decimal point represent units, tens,
hundreds, thousands and so on. This system is expressed in decimal numbers. Every position shows a
particular power of the base (10).
Example of Decimal Number System:
The decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in
the hundreds position, and 1 in the thousands place whose value can be written as:
(1×103) + (4×102) + (5×101) + (7×100)
(1×1000) + (4×100) + (5×10) + (7×1)
1000 + 400 + 50 + 7
1457
Binary Number System (Base 2 Number System)
The base 2 number system is also known as the Binary number system wherein, only two binary
digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this
system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is
a binary number.
We can convert any system into binary and vice versa.
Example
Write (14)10 as a binary number.
Solution:
2 14
2 7 0
2 3 1
1 1
Base 2 Number System Example
∴ (14)10 = 11102
Octal Number System (Base 8 Number System)
In the octal number system, the base is 8 and it uses numbers from 0 to 7 to represent numbers.
Octal numbers are commonly used in computer applications. Converting an octal number to decimal
is the same as decimal conversion and is explained below using an example.
Example:
Convert 2158 into decimal.
Solution:
2158 = 2 × 82 + 1 × 81 + 5 × 80
= 2 × 64 + 1 × 8 + 5 × 1
= 128 + 8 + 5
= 14110
Hexadecimal Number System (Base 16 Number System)
In the hexadecimal system, numbers are written or represented with base 16. In the hexadecimal
system, the numbers are first represented just like in the decimal system, i.e. from 0 to 9. Then, the
numbers are represented using the alphabet from A to F. The below-given table shows the
representation of numbers in the hexadecimal number system.
Number System Chart
In the number system chart, the base values and the digits of different number systems can be
found. Below is the chart of the numeral system.
Number System Conversion
Numbers can be represented in any of the number system categories like binary, decimal,
hexadecimal, etc. Also, any number which is represented in any of the number system types can be
easily converted to another. how to convert numbers in decimal to binary and vice versa,
hexadecimal to binary and vice versa, and octal to binary and vice versa using various examples.
Assume the number 349. Thus, the number 349 in different number systems is as follows:
The number 349 in the binary number system is 101011101
The number 349 in the decimal number system is 349.
The number 349 in the octal number system is 535.
The number 349 in the hexadecimal number system is 15D
Number System Solved Examples
Example 1:
Convert (1056)16 to an octal number.
Solution:
Given, 105616 is a hex number.
First, we need to convert the given hexadecimal number into decimal number
(1056)16
= 1 × 163 + 0 × 162 + 5 × 161 + 6 × 160
= 4096 + 0 + 80 + 6
= (4182)10
Now we will convert this decimal number to the required octal number by repetitively dividing by 8.
Therefore, taking the value of the remainder from bottom to top, we get;
(4182)10 = (10126)8
Therefore,
(1056)16 = (10126)8
Example 2:
Convert (1001001100)2 to a decimal number.
Solution:
(1001001100)2
= 1 × 29 + 0 × 28 + 0 × 2 7 + 1 × 2 6 + 0 × 25 + 0 × 24 + 1 × 2 3 + 1 × 22 + 0 × 2 1 + 0 × 20
= 512 + 64 + 8 + 4
= (588)10
Example 3:
Convert 101012 into an octal number.
Solution:
Given,
101012 is the binary number
We can write the given binary number as,
010 101
Now as we know, in the octal number system,
010 → 2
101 → 5
Therefore, the required octal number is (25)8
Example 4:
Convert hexadecimal 2C to decimal number.
Solution:
We need to convert 2C16 into binary numbers first.
2C → 00101100
Now convert 001011002 into a decimal number.
101100 = 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20
= 32 + 8 + 4
= 44
( END )
