Numbering Systems


For communicating with the computer you need to write a program. In earlier days the programmers used to write program in a machine code (a language in the form of 0 & 1) but it was a very difficult task so assembly language was invented. The hexadecimal system was used to communicate with computer that was better & faster from binary system. 

For converting a program written in assembly language to hex file an assembler program is used. But the assembly language too is cumbersome as it deals directly with the internal architecture of a CPU therefore it is referred as a low level language. Today we have so many other high level languages such as C, C++, Java, etc (they have a compiler to convert a program to hex file). We shall learn now how the decimal, binary & hexadecimal numbers are inter-related.


Numbering System 

In this session I will familiarize you with the number systems those who are already familiar can skip this session.  

Decimal is number system to the base 10 i.e. from 0-9, 10-19 & so on.  We use this in our day to day life.

Binary is number system to base 2, the language of computing. 

For e.g. 3010 = 111102 (the number in subscript denotes the base)

Converting from decimal to binary


Converting from binary to decimal number system


Converting from binary to decimal:

e.g. 1010101= 20*1+21*0+22*1+23*0+24*1+25*0+26*1= 1+4+16+64= 85

Hexadecimal: (Hex) to base 16, all the program need to be converted to hexadecimal as they represent the machine language.

Converting Decimal to Hex

Decimal no. :1111 0101 0101


Converting hexadecimal to binary number system


For converting a hex to decimal number system convert first to binary & then to decimal system.


You can also use a scientific calculator (provided by Windows) to convert the number among different base. (Provided in accessories of Windows)


A binary number is made of bits. A group of four bit is called a nibble and a group of eight bit is called a byte.