Binary number 1197. Note that the first Prior Value of 0 is simply an initial decimal value. This method is an application of the Horner scheme. The fractional parts of a number are converted with similar methods. They are again based on the equivalence of shifting with doubling or halving. In a fractional binary number such as 0.11010110101, the first digit is formula_7, the second formula_8, etc. So if there is a 1 in the first place after the decimal, then the number is at least formula_7, and vice versa. Double that number is at least 1. This suggests the algorithm: Repeatedly
Binary number In fact, the only binary fractions with terminating expansions are of the form of an integer divided by a power of 2, which 1/10 is not. The final conversion is from binary to decimal fractions. The only difficulty arises with repeating fractions, but otherwise the method is to shift the fraction to an integer, convert it as above, and then divide by the appropriate power of two in the decimal base. For example: Another way of converting from binary to decimal, often quicker for a person familiar with hexadecimal, is to do so indirectly—first converting (formula_12 in binary) into (formula_12