
Decimal system: This is the system which we use in daily life
Value of b=10
e.g. (456)_{10}
= 4*10^{2} + 5*10^{1} + 6* 10^{0}
The weights of the corresponding bits for decimal system are as
10^{4} 
10^{3} 
10^{2} 
10^{1} 
10^{0} 
. 
10^{1} 
10^{2} 
10000 
1000 
100 
10 
1 
. 
0.10 
0.01 
MSB 




Decimal point 


 Binary system: This is number system which is used to represent values in the digital environment. Here value of b=2
(11101.01)_{2}
=1*2^{4 }+ 1 *2^{3} + 1 * 2^{2} + 0 *2^{1} + 1 * 2^{0}+ 0 *2^{1} + 1 * 2^{2}
= (29.25)_{10} so number given is equal to 29 in decimal.
Representing large values in binary system may be very cumbersome and also it’s very difficult to a human to work with such large values in binary as it require 3 to 4 time more digits than for decimal system for same value e.g. 1010111101110111_{2}.Hence the number systems like octal and hexadecimal systems are developed just to simplify this. Corresponding equivalents of the value above in octal and hexadecimal are 127567_{8} and AF77_{16 }that are easier to read and remember for engineers and other technicians
The weights of the corresponding bits for binary system are as
2^{4} 
2^{3} 
2^{2} 
2^{1} 
2^{0} 
. 
2^{1} 
2^{2} 
16 
8 
4 
2 
1 
. 
0.50 
0.25 
MSB 




Decimal point 


However, any series of 1’s and 0’s is not binary number. Sometimes it may represent some other information like some binary codes as gray code, parity bit numbers etc
Binary number formats:

Bit: It is defined as smallest unit of data. Eg. 0, 1

Nibble: It is a combination of 4 bits Eg. 0000, 1010, 1000, 0100 etc

Byte: A byte is a combination of 8 bits Eg. 0010 1010—it has 2 nibbles

Word: it is defined as combination of 16 bits Eg. 0010 0011 0111 1111 – it has 4 nibbles or 2 bytes

Double word: It is defined as combination of 32 bits.Eg. 0010 0011 0111 1111 0010 0011 0111 1111 it has 8 nibbles or 4 bytes
