What is Binary Number System

• The binary number system is a positional number system that uses only two digits, 0 and 1. It is the fundamental number system in computer science and digital electronics because computers are based on electronic switches that can be in one of two states, representing these two digits.

• In the binary system, each digit's position represents a power of 2. The rightmost digit represents 2^0 (1), the next digit to the left represents 2^1 (2), the next digit represents 2^2 (4), and so on. The value of each digit is determined by multiplying the digit by the corresponding power of 2 and adding them together.

• A binary number's base is always 2 and the represent of a binary number 10101 is 10101₂

• For example, let's take the binary number 10101. We can break it down as follows:

     1    0    1    0    1

    -----------------------

    2^4  2^3  2^2  2^1  2^0

     16   0    4    0    1

• By adding up the values of each digit, we get: 16 + 0 + 4 + 0 + 1 = 21. Therefore, the binary number 10101 is equivalent to the decimal number 21.

• Binary numbers can represent any integer value by using the appropriate combination of 0s and 1s. For example, the binary number 1101 is equal to 13 in decimal notation (2^3 + 2^2 + 2^0 = 8 + 4 + 1 = 13).

• Binary numbers are also used to represent and manipulate other types of data in computers, such as characters, instructions, memory addresses, and more. By using a fixed number of bits, binary numbers can represent a wide range of values.

• Converting between binary and decimal numbers is straightforward. To convert a binary number to decimal, you can multiply each digit by the corresponding power of 2 and sum them up. To convert a decimal number to binary, you can repeatedly divide the decimal number by 2 and record the remainders until the quotient becomes 0.

• In computer programming, binary numbers are often written with a prefix of "0b" to indicate that they are in binary form. For example, 0b10101 represents the binary number 10101.

• Understanding the binary number system is essential for understanding computer architecture, logic circuits, data representation, and many other areas of computer science.

• Conversion: