Convert Decimal to Binary

By using the calculation formula for converting decimal numbers to other bases, we can do the following.

Example :

67₁₀ = ……₂ ?

Suppose we are going to convert 67 base ten (decimal) to base 2 (binary).

1.     First we divide 67 by 2, we get the integer quotient is 33 with the remainder 1, or in other words 67 = 2*33 + 1

2.     Then we divide the integer quotient (33) by 2 again, 33/2 = 16, the remainder is 1.

3.     Then we repeat again, 16/2 = 8, the remainder is 0.

4.     Repeat these steps again until the integer quotient equals 0. After that, write down the remainder of the quotient starting from the bottom up.

Thus we will get that 67₁₀ = 1000011₂.