How do you convert a number to base 2 in binary?

To convert a decimal number to its base 2 (binary) representation, you repeatedly divide by 2 and record the remainders. Here's a step-by-step guide based on the provided reference from cuemath.com:

Conversion Steps

1. Divide by 2 and Note the Remainder: Divide the given decimal number by 2. Note down the remainder. This remainder will be either 0 or 1, which are the digits used in binary.

2. Divide the Quotient by 2: Now, divide the quotient obtained in the previous step by 2, and note the remainder again.

3. Repeat Until Quotient is 0: Repeat the above steps until you get 0 as the quotient.

4. Read Remainders in Reverse Order: Write the remainders in reverse order (from bottom to top). This sequence of 0s and 1s represents 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 from bottom to top gives us 1101. Therefore, the binary equivalent of 13 is 1101₂.

Summary Table

Step	Description	Example (Decimal 13)
1. Divide by 2	Divide the decimal number by 2.	13 / 2 = 6 remainder 1
2. Note the Remainder	Record the remainder (0 or 1).	Remainder = 1
3. Divide the Quotient by 2	Divide the quotient from the previous division by 2.	6 / 2 = 3 remainder 0
4. Repeat Until Quotient is Zero	Continue dividing until the quotient becomes 0.	Continue until quotient is 0.
5. Read Remainders in Reverse Order	Form the binary number by reading remainders upwards.	1101 (Binary representation of 13)