Converting the Whole Part
Divide the base 10 number by the base you want to convert to, repeatedly, until nothing is left to divide, writing the remainder each time. Read the answer from bottom to top: the last remainder is the Most Significant Bit (MSB) and the first remainder is the Least Significant Bit (LSB).
Example: (250)10 to base 2
250 / 2 = 125 R 0 125 / 2 = 62 R 1 62 / 2 = 31 R 0 31 / 2 = 15 R 1 15 / 2 = 7 R 1 7 / 2 = 3 R 1 3 / 2 = 1 R 1 1 / 2 = 0 R 1
Reading the remainders from bottom to top: (250)10 = (11111010)2
Converting the same number to base 8 and base 16 in the same way: (250)10 = (372)8 and (250)10 = (FA)16.
Converting a Decimal Fraction to Base 2
Convert the whole part as before. For the fractional part, multiply successively by 2, keeping the whole-number part as the next binary digit, until the decimal part becomes 0.0. Read the answer from top to bottom.
Example: (15.375)10
The whole part: (15)10 = (1111)2. The fractional part (0.375)10:
0.375 x 2 = 0.75 -> 0 0.75 x 2 = 1.5 -> 1 0.5 x 2 = 1.0 -> 1 0.0 x 2 = 0.0 -> end
So (0.375)10 = (0.011)2, and therefore (15.375)10 = (1111.011)2.
