Number Systems

Number Systems:

We can't read easily the format with which data is stored inside a computer system. Due to that reason it requires an input-output interface. Here, my goal is to explain the basics of number systems so that the reader will be comfortable in understanding the codded forms of stored data (numbers, characters etc.). Mainly there are following two types of number systems.

Classification of the Number System:

Non- Positional Number System:

In the early days, humans used to count using fingers, stones, sticks, etc. This method of counting uses additive approaches which makes the process of counting and performing arithmetic operations difficult.  Later on the positional number system was developed to get rid of these limitations.

Counting using stones

Positional Number System:

In the positional number system, there are few digits. And the value of the digits depends on the position they occupy in the number and the base (the total number of digits available in the number system)  of the number system. There are following few number systems.

Decimal number system:

The Decimal number system is the most often used number system in our day-to-day life. There are ten digits (0,1,2,3,4,5,6,7,8,9) available in this number system. Each position represents a specific power of the base 10. let's consider one example to describe this number system.
The number 572, we call it five hundred and seventy-two. First identify the digits in each position. The digit 2 is there in the unit position, 7 is there in the tens position and 5 is there in the hundreds position. Now observe that,

572
= 500 + 70 +2
= 5✕100+7✕10+2
= ;

Decimal number is written as 572₁₀,

So like the decimal number system, it is important to identify the base and the digits of the number system. Another fact is that, the digits in every number system must be less than the value of the base.

There are many such positional number systems like Binary number system, Octal number system, Hexadecimal number systems, etc.

Binary number system:

Each number system has it's unique base. The base for the Binary number system is 2. And there are only two digits viz., 0 and 1. For example let's consider one number (101₂). Observe that,
(101₂) ≠ One hundred and one
(101₂)
=
=510 
(i.e., Five with respect to base 10)

The binary digits are called "bit" in computer terminology. A binary number having n digits are called an "n-digit" number. So in computer terminology (101₂) is a 3-digit binary number, which is equivalent to 5 in decimal numbers. Computer stores data in the form of n-bit numbers.
One can check that the binary equivalent of the decimal number 572 is 1000111100.

Click to convert!

3-bit Numbers with their corresponding decimal equivalent values:

Octal number system:

From the name, it is very evident that the base for this number system is 8. And the digits are the numbers less than 8 (i.e., 0,1,2,3,4,5,6,7).  So the decimal equivalent of the octal number 572 is

Hexadecimal Number System:

The base of the number system is 16. And the digits are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The last six characters represent the decimal numbers 10, 11, 12, 13, 14, and 15. So in this number system the largest single digit is F (which is decimal equivalent to 5).

Summary Table:

What number system do computers use?

There are many advanced computer codes available nowadays. One of the earliest memory code is the Binary Coded Decimal (BCD). The whole idea of BCD is to convert each digit of decimals into its equivalent binary numbers.

Quizzes on Number Systems:

1.  What are the 4 types of number systems?.

Answer: 

1. Decimal Number System
2. Binary Number System
3. Octal Number System
4. Hexadecimal Number System

2.  The Number System with base 10 is ------.

Answer: Decimal

3.  The Number System with base 2 is ------.

Answer: Binary

4. Give examples of each Number System.

Answer: See the above article.

So we got an idea of number systems. One must note that binary numbers are coded to represent characters in the computer memory. Besides numeric data, different alphanumeric data are being handled by a computer system. To get advanced knowledge of processing and storing data the basics of the number systems must be internalized by us.

Recommended Books:

 

The below book is an advanced level book. So, if you want an in-depth knowledge about number systems, then this one is for you. Check out the books on Amazon by clicking them.