## 28 Apr Number Systems

At Miracle Learning Centre, we teach you interesting stuff in math tuition. In this math tuition, we are going to take a look at number systems. We are all familiar with the decimal number system which is made up of the numbers 0 to 9. Today, we are going to take a look at some other number systems. Without any further ado, let us get started with this maths tuition.

**The Binary Number System**

The number system that we are going to discuss today in this math tuition is the binary number system. The binary number system plays an extremely important role in the field of digital electronics and computer science and has various other practical applications.

In contrast to our conventional decimal number system which has ten numbers starting from 0 to 9, the binary number system has only two digits 0 and 1. The idea of such a number system might seem a bit strange to begin with. For example, if we look at the decimal number system, the first few numbers from 0 go as follows:

0,1,2,3,4,5,6,7,8,9,10,11,12,13…..,97,98,99,100,101,102…..,998,999,1000,1001……

In contrast, the first few numbers of a binary system goes as follows:

0,1,10,11,100,101,110,111,1000,1001,1010,1011,1100,…..

So what is going on here? Let us explore. If we start from 0 in the binary number system, the first two numbers 0 and 1 are identical to the decimal number system. However, while the third number is 2 in the decimal number system, it is 10 in the binary number system. Why? The answer is that the number 2 is not part of the binary number system. The only numbers which are part of the binary number systems are 0 and 1. As a result, the greatest single digit number is 1 in the binary number system whereas in the decimal number system, it is 9.

The two digit numbers in a binary system begin with 10, similar to that of the decimal number system. However, the two digit numbers end with 11 in the binary number system since 1 is the greatest single digit number in binary. In decimal, 9 is the greatest single digit number and two digit numbers go up till 99. Going by the same logic, we can figure out the subsequent numbers of the binary system.

If we draw parallels with the numbers of the binary number system and decimal number system, we can see 0 and 1 are same. However, 10 in the binary number system is equivalent to 2 (as 10 is the 3rd number in binary system and 2 is the 3rd number in the decimal system). In fact, if we look at the above lists, we can see that 11 in binary is 3 in decimal, 100 in binary is 4 in decimal, 101 is 5 in decimal and so on.

**Radix or Base**

The radix or base of a number system is the number of digits that number system is constructed of. For example, the decimal number system has 10 digits which make up all the numbers and as a result, the base or radix of the decimal number system is 10. Similarly, the binary number system has a base or radix of 2.

The mathematical representation of the radix is as follows:

(100)10

The number in the subscript, which is 10 in this case, represents the base or radix of the number. For decimal numbers, we omit it for the sake of simplicity. So, if nothing is mentioned about the base of a number, then we assume that the number is in the decimal number system. However, consider the following number:

(100)2

As we can see for the above number, the base is 2. As a result, the number is considered to be a binary number. This makes a lot of difference. If you see, for this case, the equivalent value of the number (100)2 in decimal number system is 4.

**Other number systems**

Like the binary number system, there are other number systems as well. Theoretically, there can be an infinite number of such number systems. Some of the more popular number systems apart from decimal and binary number systems are the Octal number system and the Hexadecimal number system. The Octal number system comprises eight digits, from 0 to 7. The hexadecimal number system, on the other hand, consists of 16 digits: 0 to 9 represent the first 10 digits; the letters A to F represent the last 6.

We hope you enjoyed your math tuition at Miracle Learning Centre. Look out for the next math tuition lesson from Miracle Learning Centre.

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