Base or Radix (r) of a Number System

Base or Radix (r) of a Number System

The Base or Radix of a number system is defined as the number of different symbols (Digits or Characters) used in that number system.

The Radix of Binary number system = 2, i.e., it uses two different symbols 0 and 1 to write the number sequence.

The Radix of Octal number system = 8, i.e., it uses eight different symbols 0, 1, 2, 3, 4, 5, 6 and 7 to write the number sequence.

The Radix of Decimal number system = 10, i.e., it uses ten different symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write the number sequence.

The Radix of Hexadecimal number system = 16, i.e., it uses sixteen different symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E & F to write the number sequence.

Table: - number systems
S. No
Name of Number System
Base/Radix
First Digit
Last Digit
All Digits/ Characters
1.
Binary
2
0
1
0,1
2.
Octal
8
0
7
0,1,2,3,4,5,6,7
3.
Decimal
10
0
9
0,1,2,3,4,5,6,7,8,9
4.
Hexadecimal
16
0
F
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F


E.g.: (10)2 Binary Number; (10)8 Octal Number; (10)10 Decimal Number; (10)16 Hexadecimal Number.

REFERENCES

1.        Digital Design by M. Morris Mano, Michael D Ciletti, Pearson
2.        Digital Fundamentals by Thomas L. Floyd, R. P. Jain, Pearson
3.        Digital Circuits and Design by S Salivahanan, S Arivazhagan, Vikas Publishing House Pvt Ltd.
4.        Digital Systems by Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss, Pearson
5.        Digital Electronics Principles And Integrated Circuits by Anil K. Maini
6.        Fundamentals of Digital Circuits by Anand Kumar
7.        Digital Electronics by John Morris
8.        Digital Electronics : An Introduction To Theory And Practice By William Gothmann.

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