Digital Electronics(Digitaltechnik)

Number System:- 

1) Binary - used by the computer in the form of 0 and 1(Max value - 1)

2) Octal (Max Value - 7) 

3) Decimal - manually used (Max Value - 9) 

4) Hexadecimal (Max Value - 15 or F)

What is the Base or radix of a number system?

Base or radix is nothing but the value representing that number system. It specifically defines the numbers or digits or letters used in a particular number system.  The formula to determine it is 0 to r-1(The maximum number of digits that can be used in a particular number system, where r represents base or radix). For binary, the maximum number of digits that can be used is 2 so the number of digits used is 0 to r-1 which is 0 to 1 i.e 0 and 1. The base or radix for Octal is 8 and the values that can be used are from 0 to r-1(7), so in octal, the possibility of numbers is 0 to 7. In the case of 283, 8 is not in the range of the number system of the octal system that's why we don't consider this number in this system. In decimal, the base or radix is 10 and the number of digits is from 0 to 10-1(9) i.e from 0 to 9. so the 283 can be a decimal because all digits are in the decimal number system. The radix or base in Hexadecimal is 16 so the number that can be coded is from 0 to 15. And the number 10 to 15 is decoded from A to F. But why so???  This is done because if we want to send any data like I am sending the number 215 to someone so someone can interpret it in the form of a decimal number but it is not necessary I want to send the data in hexadecimal so it should be clear and there should be no confusion so to remove this confusion it better to read it like 2F in this it is clear that it is a hexadecimal number.

Question:- 283 can be decimal and hexadecimal? ya

Determine the possible unknown base of a relation

Example:- √22 = 6 Maximal value of digital in this relation is 6. So if I have the max value as 6 then the base should be n+1,  b>=7 

√22 = 6     ⅀ digit*b^power => √2*b^1+2*b^0 = 6*b^0 => √2b+2 = 6 => 2b+2 = 36 => b+1 = 18 => b = 17

Number System Conversions

Decimal to any other 

Any other to Decimal 

Octal to Binary 

Hexa to Binary 

octal to Hexa