Number Systems In Digital Electronics

Number Systems in Digital Electronics
Number Systems in Digital Electronics

Number Systems In Digital Electronics.


Introduction :

A number system defines the set of values used to represent quantity.  We use number system in our day to day life for various counting process. The study of number system is not just limited to it, the digital system also has its number system. The digital systems like computer also uses various number system. The number system in digital systems are often recognized by the “radix” or “base”. The number of values that a digit or one character can assume is called as base of the system.

Various Number Systems in Digital Electronics :

Name of number system Base
Binary 2
Octal 8
Decimal 10
Hexadecimal 16


The Decimal Number Systems in Digital Electronics :

The number system that we have been learning since school is called as decimal number system. So we are familiar with how to use decimal system and this will help us to understand other number systems. The decimal system uses the base  of 10,below diagram shows that each place represent different multiple of 10.


The Binary Number Systems in Digital Electronics :

Most modern computer systems operate using binary logic. A computer cannot operate on decimal system. The binary number system uses only two digits mainly 0&1. The binary number system works like the decimal system the only difference is it has the base 2. The binary digits are also called as bits. Thus the binary system is also called as two bits system. The leftmost bit with highest weight is called as “Most Significant Bit(MSB)”  where as rightmost bit with lowest weight is called as “Least Significant Bit(LSB)”.

4 Bit Binary Representation :

Binary Number Decimal Number
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 10
1011 11
1100 12
1101 13
1110 14
1111 15

Octal Number Systems in Digital Electronics :

The base used for octal number system is 8. Each digit in octal number system assumes 8 different values from 0to7. If larger values then 7 is required then extra column is added to left and each column in left has eight times greater value then column to its right. The figure shown below represents that each digit has different multiple of 8.

Hexadecimal Number Systems in Digital Electronics :

The base used for hexadecimal number system is 16. The number of values assumed by each digit is 16.The values include digits 0to9 and letters A,B,C,D,E,F.

Relation Between Binary Decimal And Hexadecimals in Digital Electronics :


Decimal Binary Hexadecimal
 0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F



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