Decimal Fraction to Binary
Digital systems represent all real-world analog values as finite discrete binary numbers. The conversion of fractional decimal numbers to binary requires repeated multiplication by 2. The integer part of each product forms the binary fraction bits from most significant to least significant.
Two decimal fractions are provided for conversion: 0.625 and 0.1.
Trace the conversion algorithm for both values. Determine which fraction terminates perfectly and identify the repeating bit pattern for the fraction that cannot be represented exactly in a finite binary sequence.
Constraints
- Binary fractions must be calculated to at least 5 fractional bits to detect repetition.
- The radix point strictly separates the integer component from the fractional component.
Topics
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