BINARY CONVERSION | BINARY NUMBER SYSTEM | BINARY TO DECIMAL | BINARY TO OCTAL | BINARY TO HEXADEC

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To convert a decimal number to binary, you can follow these steps:

1. Start with the decimal number you want to convert.
2. Divide the number by 2 and note down the remainder.
3. Divide the quotient from step 2 by 2 and again note down the remainder.
4. Repeat step 3 until the quotient becomes 0.
5. The binary representation of the decimal number is obtained by writing the remainders in reverse order. The remainder obtained from the last division is the least significant bit (LSB), and the remainder from the first division is the most significant bit (MSB).

For example, let's convert the decimal number 25 to binary:

1. Start with 25.
2. Divide 25 by 2. The quotient is 12, and the remainder is 1.
3. Divide 12 by 2. The quotient is 6, and the remainder is 0.
4. Divide 6 by 2. The quotient is 3, and the remainder is 0.
5. Divide 3 by 2. The quotient is 1, and the remainder is 1.
6. Divide 1 by 2. The quotient is 0, and the remainder is 1.

The remainders in reverse order are 11001. So, the binary representation of decimal 25 is 11001.

To convert a binary number to decimal, you can reverse the process. Take each binary digit, starting from the right, and multiply it by 2 raised to the power of its position (0 for the rightmost digit, 1 for the next digit, and so on). Sum up these values to get the decimal equivalent.

For example, let's convert the binary number 11001 to decimal:

1. Start with the binary number 11001.
2. Multiply the rightmost digit (1) by 2^0 = 1. Add the result to the sum (1).
3. Move to the next digit (0) and multiply it by 2^1 = 2. Add the result to the sum (1 + 0 = 1).
4. Continue this process for each digit, multiplying it by the appropriate power of 2.
- The next digit (0) contributes 0 to the sum (1 + 0 = 1).
- The next digit (0) contributes 0 to the sum (1 + 0 = 1).
- The leftmost digit (1) contributes 1 * 2^4 = 16 to the sum (1 + 16 = 17).

The sum is 17, so the decimal representation of the binary number 11001 is 17.

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