To convert a decimal (base-10) number to binary (base-2) and find the remainders, you repeatedly divide the decimal number by 2 and record the remainders. These remainders, read in reverse order, form the binary equivalent. Let's break this down:
The Process:
- Divide: Divide the decimal number by 2. Note both the quotient (the integer result of the division) and the remainder (which will always be either 0 or 1).
- Repeat: Repeat step 1 using the quotient from the previous division. Continue this process until the quotient becomes 0.
- Collect Remainders: Write down all the remainders you obtained in each division.
- Reverse: Arrange the remainders in reverse order (from the last remainder to the first). This sequence of 0s and 1s is the binary equivalent of the original decimal number.
Example:
Let's convert the decimal number 13 to binary.
| Division | Quotient | Remainder |
|---|---|---|
| 13 / 2 | 6 | 1 |
| 6 / 2 | 3 | 0 |
| 3 / 2 | 1 | 1 |
| 1 / 2 | 0 | 1 |
Reading the remainders in reverse order gives us 1101. Therefore, the binary equivalent of the decimal number 13 is 1101.
In summary: The remainders are the binary digits! The remainders from each division by 2 directly provide the binary digits, which must then be arranged in reverse order of their calculation.
