Converting from Decimal Notation to Binary Notation for Fractions

COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFORMANCE NINTH EDITION

Therefore, the conversion algorithm involves
repeated multiplication by 2. At each step, the fractional part of the number from
the previous step is multiplied by 2. The digit to the left of the decimal point in the
product will be 0 or 1 and contributes to the binary representation, starting with the
most significant digit. The fractional part of the product is used as the multiplicand
in the next step.