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Octal Number System
The octal number system consists of eight digits from 0 to 7. Hence, the octal number system's base
is 8. In this system, each digit's position represents a power of 8. In this system, any digit is always less
than 8. The octal number system serves as a concise representation of lengthy binary numbers. The
number (841) is not valid in this number system as 8 is not a valid digit.
8
Hexadecimal Number System
The hexadecimal number system consists of 16 digits from 0 to 9 and letters from A to F. The letters A
to F represent decimal numbers from 10 to 15. This number system has a base of 16. Each digit position
in the hexadecimal number system represents a power of 16.
For example, the number (764) is a valid hexadecimal number. It is different from (764) which is
10
16
seven hundred and sixty four.
This number system provides shortcut methods to represent long binary numbers.
DECIMAL TO BINARY CONVERSION
To convert a decimal number into a binary number, follow these steps:
Divide the decimal number by 2 (the base of the binary number system).
Note down the quotient and remainder.
The decimal number system is based
Divide the quotient obtained again by 2 and note down on ten digits, which is likely influenced
the resulting quotient and remainder. by the number of human fingers.
Repeat the procedure until the quotient is less than 2.
List the last quotient and all the remainders (moving
from bottom to top). You will get your binary number.
Look at the given examples to understand the conversion better.
Example 1: Convert the decimal number 26, i.e., (26) to binary.
10
2 26
2 13 → 0
2 6 → 1
2 3 → 0
1 → 1
Start listing the last quotient and all
the remainders from here.
The binary equivalent of (26) is 11010
10
In other words, (26) = (11010) 2
10
Number System 13

