How do you convert binary numbers with point into octal? - Answers

You convert binary numbers with a binary point into octal then same way you convert any number with a point in any other base to any other base. Multiply or divide the number by its base until it is an integer, remembering how many times you multiplied or divided. Iteratively divide the number by the new base, using the rules of arithmetic of the old base, recording the remainders, until the result is zero. Represent the number in its new base by using the remainder in reverse order. Divide or multiply the new number by the old base the same number of times you originally multiplied or divided it when you scaled it into an integer, using the rules of arithmetic of the new base. You are done. Now, it turns out that converting binary to octal is easy and can be done on sight, because dividing by 10002 is the same as right shifting by three, and you don't have to prescale to an integer. Take the number 1101011.10011012. Simply group it into groups of three bits, starting at the binary point, giving you 001 101 011.100 110 1002. Note that I padded on the left and right with zeroes. Now you can convert by sight into octal. The result is 1534.4648.