## Using Repeated Division by 2 to Convert Decimal to Binary

To change binary numbers to decimal numbers, each binary digit should be multiplied by the power of 2 and then add the results. One of the main methods of changing decimal numbers into binary format is repeated division by 2.

When divided by two, any decimal number leaves a reminder of 0 or 1. Consequently, repeated division by 2 results in a string of 0s and 1s which is the binary equal to the decimal number. Suppose you are asked to convert the decimal number B into binary format. When you divide B by 2, you will get a quotient B1 and reminder which has a value of either 0 or 1.

I.e. B = 2 * B1 + r1, where r1 can be either 0 or 1

Next divide the quotient B1 by 2. You will obtain quotient B2 and a new remainder r2.

ie., B1 = 2 * B2 + r2 , where r2 can be either 0 or 1

So that B = 2 (2 * B2 + r2) + r1

= 22B2 + r2 * 21 + r1* 20

Next divide the quotient B2 by 2. The resulting quotient will be B3 and a remainder r3.

i.e., B2 = 2 * B3 + r3

So that B = 2 (2 * (2 * B3 + r3) + r2) + r1

= 22(2 * B3 + r3) + r2 * 21 + r1* 20

= 23 B3 + r3 * 22 + r2 * 21 + r1* 20

Let now convert 2510 into an equivalent binary number.

23/2= 11 reminder 1

11/2=5 reminder 1

5/2= 2 reminder 1

2/2=1 reminder 0

1/2 =0 reminder 1

Now to write the binary equivalent of 2310, read the remainders from the bottom to the top. In our case 2310=101112