What is number system? Explain how to do conversion between two number systems.

A number system is a system for representing numbers using digits or other symbols. There are several different number systems that are used in mathematics and computer science, including the decimal system, the binary system, and the hexadecimal system.

To convert a number from one number system to another, you can use the following steps:

Write the number in the given number system. For example, if you are given the number 1011 in the binary system, you would write it as 1011.

Determine the base of the given number system. The base of a number system is the number of unique digits or symbols that are used in that system. For example, the base of the binary system is 2, because it only uses the digits 0 and 1.

Determine the base of the number system you want to convert the number to. For example, if you want to convert the number 1011 from the binary system to the decimal system, you would need to determine that the base of the decimal system is 10.

Write the number in the new number system using the appropriate digits or symbols. To do this, you can use the following formula:

New_Number = (Digit_1 * (Base_1)^(n-1)) + (Digit_2 * (Base_1)^(n-2)) + ... + (Digit_n * (Base_1)^(0))

where:

New_Number is the number you are trying to convert

Digit_1, Digit_2, ..., Digit_n are the digits of the number in the given number system

Base_1 is the base of the given number system

Base_2 is the base of the number system you are converting to

n is the number of digits in the number

For example, to convert the number 1011 from the binary system (base 2) to the decimal system (base 10), you would use the following calculation:

New_Number = (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 2 + 1 = 11

So the number 1011 in the binary system is equal to 11 in the decimal system.