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:
- Divide the decimal number by 2.
- Write down the remainder of the division.
- Continue dividing the quotient by 2 and writing down the remainders until the quotient is 0.
- 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:
- 190 ÷ 2 = 95 with a remainder of 0.
- 95 ÷ 2 = 47 with a remainder of 1.
- 47 ÷ 2 = 23 with a remainder of 1.
- 23 ÷ 2 = 11 with a remainder of 1.
- 11 ÷ 2 = 5 with a remainder of 1.
- 5 ÷ 2 = 2 with a remainder of 1.
- 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.