Binary is a base-2 numeral system that uses two symbols, 0 and 1, to represent numbers. It is the most common numeral system used by computers and other electronic devices.

To convert a decimal number to binary, we can use the following steps:

  1. Divide the decimal number by 2.
  2. Write down the remainder of the division.
  3. Continue dividing the quotient by 2 and writing down the remainders until the quotient is 0.
  4. The remainders, written in reverse order, are the binary representation of the decimal number.

For example, to convert the decimal number 190 to binary, we would follow these steps:

  1. 190 ÷ 2 = 95 with a remainder of 0.
  2. 95 ÷ 2 = 47 with a remainder of 1.
  3. 47 ÷ 2 = 23 with a remainder of 1.
  4. 23 ÷ 2 = 11 with a remainder of 1.
  5. 11 ÷ 2 = 5 with a remainder of 1.
  6. 5 ÷ 2 = 2 with a remainder of 1.
  7. 2 ÷ 2 = 1 with a remainder of 0.

The remainders, written in reverse order, are 1, 1, 1, 1, 0, 1. Therefore, the binary representation of 190 is 10111110.

Here is a table of the first 100 decimal numbers and their binary representations:

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010

I hope this helps! Let me know if you have any other questions.

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