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ICT 101 Discrete Mathematics for IT
Binary Number System
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Table of Contents
Introduction    3
Position Notation:    4
Importance of selecting binary number system:    4
Flowchart    5
Algorithm    7
Conclusion    8
Reflection    9
Bibliography    10
Introduction
The modern binary number system has been introduced by Gottfried Leibniz in 1689. Mainly it is invented for implementing the binary code. A binary number is conveyed in the base-2 binary number system or numeral system. As there are only two Boolean values for performing either a logical “1” or a logical “0” it helps to make the system of using Binary Number appropriate for use in electronic or digital systems. Binary number system is a technique of serving the numbers that takes 2 as its base by using only the digits 0 as well as 1. Additionally power of 2 is represented by each consecutive digit. The range of these three binary number systems are shown below:
Computer uses only the binary numbers “0” and “1” to store as well as manipulate all the data, even the other numbers. Moreover computer converts videos, words, graphics as well as music in the two binary numbers. On the other hand a byte represents a group of eight bits and a Kilobyte is referred to 1,024 bytes or 8,192 bits. The method of calculating binary number or converting other number system to binary has been described below:
As an example we can consider a binary number - 10011 that represents
(1*2^4) + (0*2^3) + (0*2^2) + (1*2^1) + (1*2^0)
= 16 + 0 + 0 + 2 + 1
= 19
In binary number system 1+1=10 that means there are no existence of “2” in this number system. On the contrary the decimal number system counts using 10 digits (0 to 9). That’s why in decimal number system it may be possible to count as 1+1=2 or 7+7=14.
Position Notation:
The positional notation is used in binary number system where the base or radix is 2. An another example has been granted here to find out the formula of converting binary number to a decimal number based on the positional notation of each bit is shown below :
Let the binary number is 1101. Then the formula will be-
1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 13
Importance of selecting binary number system:
An alternative approach of decimal number system (10-base) is binary number system that is used in daily life. It plays an important role in discrete mathematics to reduce several complications that arises in solving a problem. Binary number system is also implemented to simplify the design of computers as well as related technologies (Ino et al, 2017). There are many applications of this system in modern computers that is used in binary encoding for data as well as instructions. On the other hand, Blu-ray Discs, CDs and DVDs produces video as well as sound in binary form. Telephone calls are transferred in a digital form on long distance. There are another application of binary number system in mobile phone networks using pulse-code modulation as well as on voice IP networks. Hence, it is...