Short division by two with remainder
This method is much easier to understand when visualized on paper. It relies only on division by two.
For this example, let's convert the decimal number 15610 to binary. Write the decimal number as the dividend inside an upside-down "long division" symbol. Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.
2)156
Write the integer answer (quotient) under the long division symbol, and write the reminader (0 or 1) to the right of the dividend.
2)156 0
78
Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 1.
2)156 0
2)78 0
2)39 1
2)19 1
2)9 1
2)4 0
2)2 0
1
Starting with the bottom 1, read the sequence of 1's and 0's upwards to the top. You should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002
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