So to deal with a binary number system is quite easier than a decimal system. So we generally use the binary system when we deal with the digital world. Fig. Introduction: What is a Number System? This relation allows us to easily convert between them by simply … Say for the number twenty one, we can realise that it is more than 16 = 2 4 and not as big as 32 = 25. Note that since these number systems possess base 2k, all numbers within these systems can be uniquely represented by k binary bits. There is no state in between these two. Here comes the utility of a binary system. (110.11) 2 = (6.75) 10. 1.1 : The number line Just imagine you start from zero and go on walking along this number line in the positive direction. Binary Hex/Octal 20 Introduction to Computer Science, Fall, 2010 Conversion between Number Systems Binary/Hex/Octal Decimal. You probably already know what a number system is - ever hear of binary numbers or hexadecimal numbers? At least for small numbers, there is a way to find the binary digits for a given number ( i.e., given in base 10) by repeatedly dividing by 2. We are used to using the base-10 number system, which is also called decimal. –Number Systems –Binary Numbers, Bits, and Bytes –Algorithms: converting binary to decimal and vice versa –Encoding: Hexadecimal 32 Announcements and To Do List –HW04 due Wednesday 2/16 –Readings: •Reed ch 5, pp 83-87, 89-90 (today) –Quiz 2 on Friday 2/18 •Covers lectures 6,7,9,10,11 . 1.1). B. Forouzan and F. Mosharraf, Foundations of Computer Science, 2nd ed., 2008. Simply put, a number system is a way to represent numbers. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary). Such number systems include binary, octal, hex, and base-32 number systems. NUMBER SYSTEMS 1.1 Introduction In your earlier classes, you have learnt about the number line and how to represent various types of numbers on it (see Fig. Fig. Introduction to Binary Numbers • Consider a 4 bit binary number • Examples of binary arithmetic Decimal Binary Binary 0 0000 1 0001 2 0010 For example, octal numbers can be represented by three bits; hex numbers can be represented by four bits, etc. Now, in a digital world, we can think in binary nature, e.g., a light can be either off or on. 17 33 Want to learn more? For very small numbers, we can more or less do it by eye. As far as your eyes can see, there are numbers, numbers and numbers!