Radix Number System
The numeric system we use daily is the decimal system, but this system is not convenient for machines since the information is handled codified in the shape of on or off bits, this way of codifying takes us to the necessity of knowing the positional calculation which will allow us to express a number is any base where we need it.
A base of a number system or radices defines the range of values that a digit may have.
1. In the binary system or base 2, there can be only two values for each digit of a number, either a “0”
or a “1”.
2. In the octal system or base 8, there can be eight choices for each digit of a number:
“0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”
3. In the decimal system or base 10, there are ten different values for each digit of a number:
“0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”, “8”, “9”
4. In the hexadecimal system, we allow 16 values for each digit of a number:
“0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”, “8”, “9”, “A”, “B”, “C”, “D” and “F”
where “A” stands for 10, “B” for 11 and so on.
In general, a positive number N can be written in positional notation as
N=(an – 1 an – 2 … a1 a0 . a–1 a–2 … a–m)
where,
. = radix point separating the integer and fractional digits.
r = radix or base of the number system being used
n = number of integer digits to the left of the radix point
m=number of fractional digits to the right of the radix point
ai = integer digits i when n – 1 ≥ i ≥ 0
aj = fractional digits j when –1 ≥ i ≥ –m
an – 1 = most significant digit
an – 2 = least significant digit
A number system with base or radix ‘r’ will have r number of different digits from 0 → (r– 1) thus, number system is represented by (N)b
where,
N= Number ; b = Base or radix
Dear Aspirants,
Your preparation for GATE, ESE, PSUs, and AE/JE is now smarter than ever — thanks to the MADE EASY YouTube channel.
This is not just a channel, but a complete strategy for success, where you get toppers strategies, PYQ–GTQ discussions, current affairs updates, and important job-related information, all delivered by the country’s best teachers and industry experts.
If you also want to stay one step ahead in the race to success, subscribe to MADE EASY on YouTube and stay connected with us on social media.
MADE EASY — where preparation happens with confidence.
MADE EASY is a well-organized institute, complete in all aspects, and provides quality guidance for both written and personality tests. MADE EASY has produced top-ranked students in ESE, GATE, and various public sector exams. The publishing team regularly writes exam-related blogs based on conversations with the faculty, helping students prepare effectively for their exams.
